AR ONLY REAL VS SIM COMPARE
Will
2024-09-08
Setup is the same.
library(readxl)
# Path to the local file
local_file <- "C:/Users/WillLi/Downloads/ProjectPingEMA.xlsx"
# Read the data file using readxl
rawdata <- read_excel(local_file)
rawdata$pid <- match(rawdata$pid, unique(rawdata$pid))
# Create data frame with only variables that we need
rawdata <- rawdata[, c("pid", "pingTotal", "depressedmood_state", "loneliness_state_pmc", "socintsatisfaction_state_pmc", "responsiveness_state_pmc", "selfdisclosure_state_pmc", "otherdisclosure_state_pmc")]
library(dplyr)## Warning: package 'dplyr' was built under R version 4.3.3##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union# Convert columns to numeric and ensure NA values are present where needed
cols_of_interest <- c("socintsatisfaction_state_pmc", "responsiveness_state_pmc", "selfdisclosure_state_pmc", "otherdisclosure_state_pmc")
rawdata <- rawdata %>%
mutate(across(all_of(cols_of_interest), ~ as.numeric(as.character(.))))## Warning: There were 4 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `across(all_of(cols_of_interest),
## ~as.numeric(as.character(.)))`.
## Caused by warning:
## ! NAs introduced by coercion
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 3 remaining warnings.# Fill missing values using idionomics package
library(idionomics)
imputed <- imputatron_2000(data = rawdata, id_col = "pid", time_col = "pingTotal", cols_of_interest = c("depressedmood_state", "loneliness_state_pmc", "socintsatisfaction_state_pmc", "responsiveness_state_pmc", "selfdisclosure_state_pmc", "otherdisclosure_state_pmc"))## ~~ Beep Boop Beep Boop ~~
## Imputatron will try to impute your dataset
## ...
## Imputatron filtered your data
## Imputatron transformed data to wide format
## Imputatron extracted start and end indexes for each timeseries
## Imputatron dynamically created a list of variables + indexes
## ...
## ###### Imputatron completed data preprocessing ####
## Imputatron created longData3d object
## Imputatron performed copyMeans on your data
## ...
## ###### Imputatron completed data imputation ####
## Imputatron will start data extraction sequence...
## Imputatron extracted a list of dataframes from longData3d object
## Imputatron melted each dataframe back to long format
## Imputatron added names to the list of dataframes
## ...
## ###### Imputatron completed data extraction ####
## Imputatron will start tidy dataframe creation sequence...
## Imputatron created tidy dataframe with all of your variables
## ...
## Imputatron finished the imputation process.
## You can access the following elements:
## Imputed Dataframe: $imputed_df
## Long Data Object: $long_data_obj
## Long Data Object with imputed data: $imputed_data
## Your original data, but filtered: $filtered_data
## Filtered data in wide format: $wide_data
## The list with variable names and indexes to create the Long Data Object: $timeInData_list
## ...
## Imputatron turning off...
## ~~ Beep Boop Beep Boop ~~ Bye!imputed_rawdata <- imputed$imputed_df
str(imputed$imputed_df)## 'data.frame': 7140 obs. of 8 variables:
## $ pid : chr "1" "1" "1" "1" ...
## $ pingTotal : num 1 2 3 4 5 6 7 8 9 10 ...
## $ depressedmood_state : num 49.1 50.7 65.7 72.6 64.8 ...
## $ loneliness_state_pmc : num 23.3 -5.12 9.21 16.82 18.5 ...
## $ socintsatisfaction_state_pmc: num -16.46 -25.46 8.54 -64.46 6.54 ...
## $ responsiveness_state_pmc : num -14.474 -53.911 0.185 -29.907 22.9 ...
## $ selfdisclosure_state_pmc : num -12.91 -43.14 -33.15 -36.87 -9.62 ...
## $ otherdisclosure_state_pmc : num 2.355 -0.541 -7.093 -30.629 -18.596 ...# Remove self-disclosure and other-disclosure columns
imputed_rawdata <- imputed_rawdata[, -c(7,8)]
# Arrange by numerical order of pid
imputed_rawdata <- imputed_rawdata %>%
mutate(pid = as.numeric(pid)) %>%
arrange(pid, pingTotal)The main difference is I simplified the model to a VAR model only by selecting q = 0 in the VARMA model fitting. We also set the MAlag to NULL in the simulation function and so no theta matrix is extracted or simulated in the simulated data.
# Split by individuals into a list
rawdata_list <- split(imputed_rawdata, imputed_rawdata$pid)
library(MTS)## Warning: package 'MTS' was built under R version 4.3.3# Function to fit VARMA model and simulate new data
simulate_individual_AR <- function(rawdata_list) {
# Remove ID and time columns for fitting
individual_matrix <- as.matrix(rawdata_list[, -c(1, 2)])
# Fit VARMA model
fit <- VARMA(individual_matrix, p = 1, q = 0)
# Extract AR coefficients only
phi <- fit$Phi
# Extract sigma matrix (covariance matrix of the residuals)
sigma <- fit$Sigma
# Simulate new data using extracted parameters
set.seed(12345)
sim_data <- VARMAsim(n = 150, arlags = c(1), malags = NULL,
phi = phi, sigma = sigma, skip = 200)
simulated_series <- sim_data$series
# Return both the fit object and the noisy simulated series
return(list(fit = fit, simulated_series = simulated_series))
}
# Loop through each individual's data and simulate new data
simulated_data_list_AR <- lapply(rawdata_list, simulate_individual_AR)## Warning in sqrt(diag(solve(Hessian))): NaNs produced## Warning in sqrt(diag(solve(Hessian))): NaNs produced# Extract fit results and noisy simulated series into separate lists
fit_results_list_AR <- lapply(simulated_data_list_AR, function(x) x$fit)
simulated_data_list_AR <- lapply(simulated_data_list_AR, function(x) x$simulated_series)
# Combine into one large data frame for further analysis
combined_simulated_data_list_AR <- do.call(rbind, lapply(1:length(simulated_data_list_AR), function(i) {
individual_df <- as.data.frame(simulated_data_list_AR[[i]])
individual_df$ID <- i
individual_df$time <- 1:nrow(individual_df)
return(individual_df)
}))After that we do the same and run i-ARIMAX on the raw data
# i-ARIMAX on existing raw data set
imputeThese <- c("depressedmood_state", "loneliness_state_pmc", "socintsatisfaction_state_pmc", "responsiveness_state_pmc")
# Within person standardization
zDataraw <- i_standarbot_300(imputed_rawdata, imputeThese, "pid", explanation = TRUE)
# Create list of independent variables
IV <- c("loneliness_state_pmc_PSD","socintsatisfaction_state_pmc_PSD","responsiveness_state_pmc_PSD")
# Initialize an empty list to store the results
hoard.iarimax1 <- list()
# Loop through each independent variable (IV)
for (i in seq_along(IV)) {
# Create a unique model name for each IV
model_name <- paste0("IV_", i)
# Run the IARIMAXoid_Pro function and store the result in the list
hoard.iarimax1[[model_name]] <- IARIMAXoid_Pro(
zDataraw,
x_series = IV[[i]], # Current independent variable
y_series = "depressedmood_state_PSD", # The single dependent variable
id_var = "pid",
hlm_compare = TRUE,
timevar = "pingTotal",
metaanalysis = TRUE
)
}## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zooAnd the same for simulated data.
# i-ARIMAX on simulated data set
# Rename columns to same as raw data set
combined_simulated_data_list_AR <- combined_simulated_data_list_AR %>%
rename(
depressedmood_state = V1,
loneliness_state_pmc = V2,
socintsatisfaction_state_pmc = V3,
responsiveness_state_pmc = V4
)
# Within-person standardization
zDatasim_AR <- i_standarbot_300(combined_simulated_data_list_AR, imputeThese, "ID", explanation = TRUE)
# Initialize an empty list to store the results
hoard.iarimax1sim_AR <- list()
# Loop through each independent variable (IV)
for (i in seq_along(IV)) {
# Create a unique model name for each IV
model_name <- paste0("IV_", i)
# Run the IARIMAXoid_Pro function and store the result in the list
hoard.iarimax1sim_AR[[model_name]] <- IARIMAXoid_Pro(
zDatasim_AR,
x_series = IV[[i]], # Current independent variable
y_series = "depressedmood_state_PSD", # The single dependent variable
id_var = "ID",
hlm_compare = TRUE,
timevar = "time",
metaanalysis = TRUE
)
}Now we can again compare denity and ecdf plots for each variable.
We can see with the simplified model that the ecdf plots show much less extreme values in the simulated data and that it more closely mimics the real data in terms of values.
# Extracting raw i-ARIMAX scores
IARIMAXrawxreg <- hoard.iarimax1$IV_1$results_df$xreg
IARIMAXrawxreg <- data.frame(IARIMAXrawxreg)
IARIMAXrawxreg <- IARIMAXrawxreg %>%
mutate(pid = row_number())
# Extracting sim i-ARIMAX scores
IARIMAXsimxreg_AR <- hoard.iarimax1sim_AR$IV_1$results_df$xreg
IARIMAXsimxreg_AR <- data.frame(IARIMAXsimxreg_AR)
IARIMAXsimxreg_AR <- IARIMAXsimxreg_AR %>%
mutate(pid = row_number())
# Combine together
lonelinessplotdata <- left_join(IARIMAXsimxreg_AR, IARIMAXrawxreg, by = "pid")
# Prepare data set
library(tidyr)
lonelinessplotdata <- lonelinessplotdata %>%
pivot_longer(cols = c("IARIMAXsimxreg_AR", "IARIMAXrawxreg"), names_to = "Method", values_to = "estimate")
library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.3.3library(viridis)## Warning: package 'viridis' was built under R version 4.3.3## Loading required package: viridisLitelonelinessplotdata %>%
ggplot(aes(x = estimate, fill = Method)) +
geom_density(alpha = 0.5) +
ylab("Density") +
xlab("Effect Size of the Link Between loneliness and depressedmood") +
scale_fill_viridis(discrete=TRUE) +
theme_bw()
# Plot data (ecdf)
ggplot(lonelinessplotdata, aes(estimate, colour = Method)) +
stat_ecdf(geom = "step", pad = FALSE, linewidth = 1) +
ylab("Empirical Cumulative Distribution Function") +
xlab("Effect Size of the Link Between loneliness and depressedmood") +
scale_y_continuous(breaks = seq(0.00, 1.00, by = 0.10)) +
scale_x_continuous(breaks = seq(-1.0, 1.0, by = 0.20)) +
scale_color_viridis(discrete=TRUE) +
theme_bw()
Next for social interaction satisfaction.
Similarly in social interaction satisfaction plots, value are less extreme in simulated data
# Extracting raw i-ARIMAX scores
IARIMAXrawxreg <- hoard.iarimax1$IV_2$results_df$xreg
IARIMAXrawxreg <- data.frame(IARIMAXrawxreg)
IARIMAXrawxreg <- IARIMAXrawxreg %>%
mutate(pid = row_number())
# Extracting sim i-ARIMAX scores
IARIMAXsimxreg_AR <- hoard.iarimax1sim_AR$IV_2$results_df$xreg
IARIMAXsimxreg_AR <- data.frame(IARIMAXsimxreg_AR)
IARIMAXsimxreg_AR <- IARIMAXsimxreg_AR %>%
mutate(pid = row_number())
# Combine together
lonelinessplotdata <- left_join(IARIMAXsimxreg_AR, IARIMAXrawxreg, by = "pid")
# Prepare data set
lonelinessplotdata <- lonelinessplotdata %>%
pivot_longer(cols = c("IARIMAXsimxreg_AR", "IARIMAXrawxreg"), names_to = "Method", values_to = "estimate")
# Plot density
lonelinessplotdata %>%
ggplot(aes(x = estimate, fill = Method)) +
geom_density(alpha = 0.5) +
ylab("Density") +
xlab("Effect Size of the Link Between social interaction satisfaction and depressedmood") +
scale_fill_viridis(discrete=TRUE) +
theme_bw()
# Plot data (ecdf)
ggplot(lonelinessplotdata, aes(estimate, colour = Method)) +
stat_ecdf(geom = "step", pad = FALSE, linewidth = 1) +
ylab("Empirical Cumulative Distribution Function") +
xlab("Effect Size of the Link Between social interaction satisfaction and depressedmood") +
scale_y_continuous(breaks = seq(0.00, 1.00, by = 0.10)) +
scale_x_continuous(breaks = seq(-1.0, 1.0, by = 0.20)) +
scale_color_viridis(discrete=TRUE) +
theme_bw()
Lastly, responsiveness.
# Extracting raw i-ARIMAX scores
IARIMAXrawxreg <- hoard.iarimax1$IV_3$results_df$xreg
IARIMAXrawxreg <- data.frame(IARIMAXrawxreg)
IARIMAXrawxreg <- IARIMAXrawxreg %>%
mutate(pid = row_number())
# Extracting sim i-ARIMAX scores
IARIMAXsimxreg_AR <- hoard.iarimax1sim_AR$IV_3$results_df$xreg
IARIMAXsimxreg_AR <- data.frame(IARIMAXsimxreg_AR)
IARIMAXsimxreg_AR <- IARIMAXsimxreg_AR %>%
mutate(pid = row_number())
# Combine together
lonelinessplotdata <- left_join(IARIMAXsimxreg_AR, IARIMAXrawxreg, by = "pid")
# Prepare data set
lonelinessplotdata <- lonelinessplotdata %>%
pivot_longer(cols = c("IARIMAXsimxreg_AR", "IARIMAXrawxreg"), names_to = "Method", values_to = "estimate")
# Plot density
lonelinessplotdata %>%
ggplot(aes(x = estimate, fill = Method)) +
geom_density(alpha = 0.5) +
ylab("Density") +
xlab("Effect Size of the Link Between responsiveness and depressedmood") +
scale_fill_viridis(discrete=TRUE) +
theme_bw()
# Plot data (ecdf)
ggplot(lonelinessplotdata, aes(estimate, colour = Method)) +
stat_ecdf(geom = "step", pad = FALSE, linewidth = 1) +
ylab("Empirical Cumulative Distribution Function") +
xlab("Effect Size of the Link Between responsiveness and depressedmood") +
scale_y_continuous(breaks = seq(0.00, 1.00, by = 0.10)) +
scale_x_continuous(breaks = seq(-1.0, 1.0, by = 0.20)) +
scale_color_viridis(discrete=TRUE) +
theme_bw()
Meta results are also still similar. Estimates are nearly identical and in this case with the simpler model ((as seen in the plots (p = 1 q = 0)the heterogeniety is much closer to the real data and lower than in the more complex simulation model (p =1 q = 1). IV_1 = loneliness IV_2 = social interaction satisfaction IV_3 = responsivenes
# Initialize an empty list to store the results
meta_analysis_results_list_AR <- list()
# Example: extracting estimates and I² from hoard.iarimax for real and simulated data
for (i in 1:length(hoard.iarimax1)) {
# Extract variable names (optional if you need them)
variable_name <- names(hoard.iarimax1)[i]
# Extract estimates and I² from the real data
real_estimate <- hoard.iarimax1[[i]]$meta_analysis$b # Adjust based on your structure
real_I2 <- hoard.iarimax1[[i]]$meta_analysis$I2 # Adjust based on your structure
# Extract estimates and I² from the simulated data
sim_estimate <- hoard.iarimax1sim_AR[[i]]$meta_analysis$b # Adjust based on your structure
sim_I2 <- hoard.iarimax1sim_AR[[i]]$meta_analysis$I2 # Adjust based on your structure
# Store the results in a list
meta_analysis_results_list_AR[[i]] <- data.frame(
Variable = variable_name,
Estimate_Real = real_estimate,
Estimate_Simulated = sim_estimate,
I2_Real = ifelse(is.na(real_I2), "NA", paste0(round(real_I2, 2), "%")),
I2_Simulated = ifelse(is.na(sim_I2), "NA", paste0(round(sim_I2, 2), "%"))
)
}
# Combine the list into a single data frame
meta_analysis_results_AR <- do.call(rbind, meta_analysis_results_list_AR)
# Display the table
print(meta_analysis_results_AR)## Variable Estimate_Real Estimate_Simulated I2_Real I2_Simulated
## intrcpt IV_1 0.4895009 0.5134851 76.23% 88.62%
## intrcpt1 IV_2 -0.2969163 -0.2990741 77.92% 87.27%
## intrcpt2 IV_3 -0.2850702 -0.2698052 69.97% 82.72%Auto correlations
# Extract autocorrelation values (without plotting) for each variable in the real dataset
acf_real <- lapply(7:ncol(zDataraw), function(i) acf(zDataraw[, i], plot = FALSE))
# Extract autocorrelation values (without plotting) for each variable in the simulated dataset
acf_simulated <- lapply(7:ncol(zDatasim_AR), function(i) acf(zDatasim_AR[, i], plot = FALSE))
# Get the variable names (assuming zDataraw and zDatasim have the same variable names)
variable_names <- colnames(zDataraw)[7:ncol(zDataraw)] # Extract variable names starting from column 7
# Extract the autocorrelation values at lag 1
lag1_real <- sapply(acf_real, function(x) x$acf[2]) # ACF at lag 1 for real data
lag1_simulated <- sapply(acf_simulated, function(x) x$acf[2]) # ACF at lag 1 for simulated data
# Create a data frame to compare the lag 1 autocorrelations
comparison_lag1 <- data.frame(Variable = variable_names, Real = lag1_real, Simulated = lag1_simulated)
print(comparison_lag1)## Variable Real Simulated
## 1 depressedmood_state_PSD 0.3267736 0.3285859
## 2 loneliness_state_pmc_PSD 0.2312691 0.2363248
## 3 socintsatisfaction_state_pmc_PSD 0.3992218 0.3939355
## 4 responsiveness_state_pmc_PSD 0.4014451 0.3070177Then I compared the raw correlations between variables to correlations calculated using the Sigma matrix for each individual.
# Initialize an empty list to store the comparison results
cor_comparison_results_AR <- list()
# Loop through each individual's data in the rawdata_list and fit results list
for (i in 1:length(fit_results_list_AR)) {
# Step 1: Extract the Sigma matrix and convert it to the correlation matrix
cor_matrix_sigma <- cov2cor(fit_results_list_AR[[i]]$Sigma)
# Step 2: Extract the raw data for the individual, removing ID and time columns
ind_data <- simulated_data_list_AR[[i]] # Assuming columns 1 and 2 are ID and time
# Step 3: Calculate the raw correlation matrix for this individual
raw_cor_matrix <- cor(ind_data, use = "complete.obs")
# Step 4: Store the comparison results in a list
cor_comparison_results_AR[[i]] <- list(cor_matrix_sigma = cor_matrix_sigma,
raw_cor_matrix = raw_cor_matrix)
# Optionally, print the comparison results for each individual
cat("\nIndividual:", i, "\n")
cat("Correlation Matrix of Residuals (Sigma):\n")
print(cor_matrix_sigma)
cat("Raw Correlation Matrix:\n")
print(raw_cor_matrix)
}##
## Individual: 1
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4542015 -0.2201806 -0.2425065
## [2,] 0.4542015 1.0000000 -0.2601368 -0.3163386
## [3,] -0.2201806 -0.2601368 1.0000000 0.7925593
## [4,] -0.2425065 -0.3163386 0.7925593 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5515206 -0.2594899 -0.2296628
## [2,] 0.5515206 1.0000000 -0.3611189 -0.4170083
## [3,] -0.2594899 -0.3611189 1.0000000 0.8196413
## [4,] -0.2296628 -0.4170083 0.8196413 1.0000000
##
## Individual: 2
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.167761514 0.055310008 0.05840742
## [2,] 0.16776151 1.000000000 0.007683822 -0.02067849
## [3,] 0.05531001 0.007683822 1.000000000 0.41895468
## [4,] 0.05840742 -0.020678487 0.418954684 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.03126047 0.26090444 0.2374898
## [2,] 0.03126047 1.00000000 -0.06388765 -0.1317415
## [3,] 0.26090444 -0.06388765 1.00000000 0.4400261
## [4,] 0.23748981 -0.13174154 0.44002613 1.0000000
##
## Individual: 3
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6749043 -0.4547583 -0.4790951
## [2,] 0.6749043 1.0000000 -0.4508667 -0.4895312
## [3,] -0.4547583 -0.4508667 1.0000000 0.5909333
## [4,] -0.4790951 -0.4895312 0.5909333 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6847251 -0.3392664 -0.4637144
## [2,] 0.6847251 1.0000000 -0.3797709 -0.5165504
## [3,] -0.3392664 -0.3797709 1.0000000 0.5902199
## [4,] -0.4637144 -0.5165504 0.5902199 1.0000000
##
## Individual: 4
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.55369302 -0.06022389 -0.1224420
## [2,] 0.55369302 1.00000000 0.08564288 -0.0744738
## [3,] -0.06022389 0.08564288 1.00000000 0.5483066
## [4,] -0.12244201 -0.07447380 0.54830661 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.61742658 0.08348495 0.02879085
## [2,] 0.61742658 1.00000000 0.06714473 -0.10282570
## [3,] 0.08348495 0.06714473 1.00000000 0.75436183
## [4,] 0.02879085 -0.10282570 0.75436183 1.00000000
##
## Individual: 5
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.7251859 -0.4454017 -0.06151316
## [2,] 0.72518593 1.0000000 -0.4502349 -0.16404628
## [3,] -0.44540171 -0.4502349 1.0000000 0.39547360
## [4,] -0.06151316 -0.1640463 0.3954736 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7511608 -0.5724970 -0.2330001
## [2,] 0.7511608 1.0000000 -0.6125476 -0.4630967
## [3,] -0.5724970 -0.6125476 1.0000000 0.6249397
## [4,] -0.2330001 -0.4630967 0.6249397 1.0000000
##
## Individual: 6
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5042151 -0.4423675 -0.4464697
## [2,] 0.5042151 1.0000000 -0.4437669 -0.5179645
## [3,] -0.4423675 -0.4437669 1.0000000 0.6860202
## [4,] -0.4464697 -0.5179645 0.6860202 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4852648 -0.4442071 -0.4803106
## [2,] 0.4852648 1.0000000 -0.4224290 -0.5779777
## [3,] -0.4442071 -0.4224290 1.0000000 0.7446129
## [4,] -0.4803106 -0.5779777 0.7446129 1.0000000
##
## Individual: 7
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.145605150 0.162441601 -0.24274867
## [2,] 0.1456052 1.000000000 0.007036061 0.10114839
## [3,] 0.1624416 0.007036061 1.000000000 0.09331548
## [4,] -0.2427487 0.101148391 0.093315484 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.156233507 0.17986725 -0.139211408
## [2,] 0.1562335 1.000000000 0.03995718 0.008577723
## [3,] 0.1798673 0.039957183 1.00000000 0.241696540
## [4,] -0.1392114 0.008577723 0.24169654 1.000000000
##
## Individual: 8
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5519500 -0.2852967 -0.3725687
## [2,] 0.5519500 1.0000000 -0.5187991 -0.3489316
## [3,] -0.2852967 -0.5187991 1.0000000 0.6209338
## [4,] -0.3725687 -0.3489316 0.6209338 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5058341 -0.2582725 -0.4150889
## [2,] 0.5058341 1.0000000 -0.4965730 -0.4736473
## [3,] -0.2582725 -0.4965730 1.0000000 0.6883755
## [4,] -0.4150889 -0.4736473 0.6883755 1.0000000
##
## Individual: 9
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4296413 -0.2244459 -0.1114505
## [2,] 0.4296413 1.0000000 -0.3865410 -0.4158671
## [3,] -0.2244459 -0.3865410 1.0000000 0.5004880
## [4,] -0.1114505 -0.4158671 0.5004880 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4154187 -0.1908193 -0.2197672
## [2,] 0.4154187 1.0000000 -0.3494796 -0.5175862
## [3,] -0.1908193 -0.3494796 1.0000000 0.5898482
## [4,] -0.2197672 -0.5175862 0.5898482 1.0000000
##
## Individual: 10
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5384969 -0.2589689 -0.2559355
## [2,] 0.5384969 1.0000000 -0.2587827 -0.2655971
## [3,] -0.2589689 -0.2587827 1.0000000 0.4588751
## [4,] -0.2559355 -0.2655971 0.4588751 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5417654 -0.2764731 -0.2875950
## [2,] 0.5417654 1.0000000 -0.2948927 -0.4349405
## [3,] -0.2764731 -0.2948927 1.0000000 0.5241816
## [4,] -0.2875950 -0.4349405 0.5241816 1.0000000
##
## Individual: 11
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.57946369 -0.24281571 -0.16778124
## [2,] 0.5794637 1.00000000 -0.05392269 -0.05532929
## [3,] -0.2428157 -0.05392269 1.00000000 0.37470107
## [4,] -0.1677812 -0.05532929 0.37470107 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.53446041 -0.17863120 -0.0859086
## [2,] 0.5344604 1.00000000 -0.03488935 -0.1073871
## [3,] -0.1786312 -0.03488935 1.00000000 0.4025822
## [4,] -0.0859086 -0.10738707 0.40258222 1.0000000
##
## Individual: 12
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.5122223 -0.3755087 -0.08697223
## [2,] 0.51222229 1.0000000 -0.5226251 -0.45428538
## [3,] -0.37550875 -0.5226251 1.0000000 0.52060620
## [4,] -0.08697223 -0.4542854 0.5206062 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5759727 -0.3594123 -0.1263357
## [2,] 0.5759727 1.0000000 -0.5368233 -0.5191771
## [3,] -0.3594123 -0.5368233 1.0000000 0.5934977
## [4,] -0.1263357 -0.5191771 0.5934977 1.0000000
##
## Individual: 13
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.37438915 -0.2283609 -0.19024409
## [2,] 0.3743891 1.00000000 -0.3410741 -0.09900546
## [3,] -0.2283609 -0.34107406 1.0000000 0.41288477
## [4,] -0.1902441 -0.09900546 0.4128848 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4135340 -0.3443464 -0.2895297
## [2,] 0.4135340 1.0000000 -0.4334008 -0.2497986
## [3,] -0.3443464 -0.4334008 1.0000000 0.5336591
## [4,] -0.2895297 -0.2497986 0.5336591 1.0000000
##
## Individual: 14
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.57239124 -0.05558771 -0.19694508
## [2,] 0.57239124 1.00000000 -0.10083503 -0.02758128
## [3,] -0.05558771 -0.10083503 1.00000000 0.66083209
## [4,] -0.19694508 -0.02758128 0.66083209 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.61397725 0.02237017 -0.19492043
## [2,] 0.61397725 1.00000000 -0.03621647 -0.08716646
## [3,] 0.02237017 -0.03621647 1.00000000 0.59451724
## [4,] -0.19492043 -0.08716646 0.59451724 1.00000000
##
## Individual: 15
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5808425 -0.2667089 -0.4358017
## [2,] 0.5808425 1.0000000 -0.3595547 -0.4136911
## [3,] -0.2667089 -0.3595547 1.0000000 0.4881189
## [4,] -0.4358017 -0.4136911 0.4881189 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6151800 -0.2965756 -0.5165725
## [2,] 0.6151800 1.0000000 -0.3771804 -0.5036247
## [3,] -0.2965756 -0.3771804 1.0000000 0.5494519
## [4,] -0.5165725 -0.5036247 0.5494519 1.0000000
##
## Individual: 16
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.1687500 -0.7494843 -0.6310080
## [2,] 0.1687500 1.0000000 -0.1614858 -0.1426221
## [3,] -0.7494843 -0.1614858 1.0000000 0.6980502
## [4,] -0.6310080 -0.1426221 0.6980502 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.2181431 -0.7397040 -0.6133188
## [2,] 0.2181431 1.0000000 -0.2526937 -0.2527325
## [3,] -0.7397040 -0.2526937 1.0000000 0.7108221
## [4,] -0.6133188 -0.2527325 0.7108221 1.0000000
##
## Individual: 17
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.3851699 -0.2575626 -0.3638133
## [2,] 0.3851699 1.0000000 -0.2147436 -0.3489721
## [3,] -0.2575626 -0.2147436 1.0000000 0.5442449
## [4,] -0.3638133 -0.3489721 0.5442449 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4965976 -0.3310118 -0.3969703
## [2,] 0.4965976 1.0000000 -0.2487584 -0.4007460
## [3,] -0.3310118 -0.2487584 1.0000000 0.6307352
## [4,] -0.3969703 -0.4007460 0.6307352 1.0000000
##
## Individual: 18
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4400394 -0.2642336 -0.3538847
## [2,] 0.4400394 1.0000000 -0.1775639 -0.1953408
## [3,] -0.2642336 -0.1775639 1.0000000 0.6798190
## [4,] -0.3538847 -0.1953408 0.6798190 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.47810071 0.11405738 -0.03684353
## [2,] 0.47810071 1.00000000 -0.07565412 -0.16903616
## [3,] 0.11405738 -0.07565412 1.00000000 0.61053326
## [4,] -0.03684353 -0.16903616 0.61053326 1.00000000
##
## Individual: 19
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.63966426 -0.22022250 -0.31984920
## [2,] 0.6396643 1.00000000 -0.08373544 -0.38206317
## [3,] -0.2202225 -0.08373544 1.00000000 -0.02561028
## [4,] -0.3198492 -0.38206317 -0.02561028 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6583723 -0.2601208 -0.2096002
## [2,] 0.6583723 1.0000000 -0.1469614 -0.3774729
## [3,] -0.2601208 -0.1469614 1.0000000 0.1449177
## [4,] -0.2096002 -0.3774729 0.1449177 1.0000000
##
## Individual: 20
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5832989 -0.4808644 -0.4348540
## [2,] 0.5832989 1.0000000 -0.5567118 -0.5769125
## [3,] -0.4808644 -0.5567118 1.0000000 0.5929006
## [4,] -0.4348540 -0.5769125 0.5929006 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5562022 -0.4721460 -0.4107239
## [2,] 0.5562022 1.0000000 -0.5288639 -0.6131164
## [3,] -0.4721460 -0.5288639 1.0000000 0.6376073
## [4,] -0.4107239 -0.6131164 0.6376073 1.0000000
##
## Individual: 21
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3540403 -0.1909992 -0.04046235
## [2,] 0.35404027 1.0000000 -0.4538612 -0.20638462
## [3,] -0.19099921 -0.4538612 1.0000000 0.62784758
## [4,] -0.04046235 -0.2063846 0.6278476 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3861473 -0.1555299 -0.09281548
## [2,] 0.38614725 1.0000000 -0.5202701 -0.26620219
## [3,] -0.15552993 -0.5202701 1.0000000 0.48111359
## [4,] -0.09281548 -0.2662022 0.4811136 1.00000000
##
## Individual: 22
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4603233 -0.1676410 -0.2571415
## [2,] 0.4603233 1.0000000 -0.2985369 -0.3177687
## [3,] -0.1676410 -0.2985369 1.0000000 0.4142259
## [4,] -0.2571415 -0.3177687 0.4142259 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4479851 -0.1743829 -0.1996104
## [2,] 0.4479851 1.0000000 -0.2998286 -0.2730395
## [3,] -0.1743829 -0.2998286 1.0000000 0.4239317
## [4,] -0.1996104 -0.2730395 0.4239317 1.0000000
##
## Individual: 23
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.3759137 -0.3529476 -0.1441040
## [2,] 0.3759137 1.0000000 -0.1358589 -0.3167179
## [3,] -0.3529476 -0.1358589 1.0000000 0.0289425
## [4,] -0.1441040 -0.3167179 0.0289425 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3307111 -0.2311499 -0.02634747
## [2,] 0.33071113 1.0000000 -0.1526123 -0.37900376
## [3,] -0.23114993 -0.1526123 1.0000000 0.21524990
## [4,] -0.02634747 -0.3790038 0.2152499 1.00000000
##
## Individual: 24
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5800386 -0.4259330 -0.4128307
## [2,] 0.5800386 1.0000000 -0.4237617 -0.5033023
## [3,] -0.4259330 -0.4237617 1.0000000 0.5099358
## [4,] -0.4128307 -0.5033023 0.5099358 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6046042 -0.3322599 -0.3670815
## [2,] 0.6046042 1.0000000 -0.4550245 -0.5836328
## [3,] -0.3322599 -0.4550245 1.0000000 0.6210835
## [4,] -0.3670815 -0.5836328 0.6210835 1.0000000
##
## Individual: 25
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.33995455 -0.39015341 -0.3816885
## [2,] 0.3399546 1.00000000 -0.07065553 -0.2910318
## [3,] -0.3901534 -0.07065553 1.00000000 0.4220953
## [4,] -0.3816885 -0.29103181 0.42209531 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.3821393 -0.4582712 -0.3046908
## [2,] 0.3821393 1.0000000 -0.1131045 -0.3352741
## [3,] -0.4582712 -0.1131045 1.0000000 0.3782896
## [4,] -0.3046908 -0.3352741 0.3782896 1.0000000
##
## Individual: 26
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.34551051 -0.05560346 -0.07522653
## [2,] 0.34551051 1.00000000 -0.15837682 -0.06713008
## [3,] -0.05560346 -0.15837682 1.00000000 -0.33235392
## [4,] -0.07522653 -0.06713008 -0.33235392 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.35012436 0.15414816 0.07140031
## [2,] 0.35012436 1.00000000 0.03823457 -0.07612841
## [3,] 0.15414816 0.03823457 1.00000000 0.27253278
## [4,] 0.07140031 -0.07612841 0.27253278 1.00000000
##
## Individual: 27
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.21753610 -0.10167716 0.01874798
## [2,] 0.21753610 1.00000000 0.02744833 -0.13449576
## [3,] -0.10167716 0.02744833 1.00000000 0.50608043
## [4,] 0.01874798 -0.13449576 0.50608043 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.17777906 0.11083696 -0.00190857
## [2,] 0.17777906 1.00000000 0.03560156 -0.11070560
## [3,] 0.11083696 0.03560156 1.00000000 0.46887727
## [4,] -0.00190857 -0.11070560 0.46887727 1.00000000
##
## Individual: 28
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.45066341 -0.06176746 -0.04113071
## [2,] 0.45066341 1.00000000 -0.09642101 -0.25963734
## [3,] -0.06176746 -0.09642101 1.00000000 0.21395152
## [4,] -0.04113071 -0.25963734 0.21395152 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.5117461 -0.09218507 -0.2169974
## [2,] 0.51174606 1.0000000 -0.22710291 -0.4544009
## [3,] -0.09218507 -0.2271029 1.00000000 0.4474249
## [4,] -0.21699745 -0.4544009 0.44742488 1.0000000
##
## Individual: 29
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 -0.1148376 0.09088815 0.03317243
## [2,] -0.11483759 1.0000000 -0.19859813 -0.35952891
## [3,] 0.09088815 -0.1985981 1.00000000 0.61391142
## [4,] 0.03317243 -0.3595289 0.61391142 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 -0.2514616 0.1704903 0.1957678
## [2,] -0.2514616 1.0000000 -0.3004460 -0.5360919
## [3,] 0.1704903 -0.3004460 1.0000000 0.6580236
## [4,] 0.1957678 -0.5360919 0.6580236 1.0000000
##
## Individual: 30
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5744373 -0.2412999 -0.2177724
## [2,] 0.5744373 1.0000000 -0.5235210 -0.5308281
## [3,] -0.2412999 -0.5235210 1.0000000 0.6431300
## [4,] -0.2177724 -0.5308281 0.6431300 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5409565 -0.1734109 -0.1638868
## [2,] 0.5409565 1.0000000 -0.6014396 -0.6286867
## [3,] -0.1734109 -0.6014396 1.0000000 0.7453878
## [4,] -0.1638868 -0.6286867 0.7453878 1.0000000
##
## Individual: 31
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3254329 -0.07878651 -0.07185529
## [2,] 0.32543285 1.0000000 -0.18842601 -0.22679604
## [3,] -0.07878651 -0.1884260 1.00000000 0.59622202
## [4,] -0.07185529 -0.2267960 0.59622202 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3468152 -0.1209809 -0.03637547
## [2,] 0.34681525 1.0000000 -0.2960008 -0.29572082
## [3,] -0.12098088 -0.2960008 1.0000000 0.60316515
## [4,] -0.03637547 -0.2957208 0.6031652 1.00000000
##
## Individual: 32
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.07078178 -0.1542174 -0.1382007
## [2,] 0.07078178 1.00000000 0.1210744 0.1302345
## [3,] -0.15421738 0.12107436 1.0000000 0.7243531
## [4,] -0.13820072 0.13023448 0.7243531 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.06309388 -0.3371247 -0.4368405
## [2,] 0.06309388 1.00000000 -0.1015381 -0.0687985
## [3,] -0.33712469 -0.10153807 1.0000000 0.9459852
## [4,] -0.43684053 -0.06879850 0.9459852 1.0000000
##
## Individual: 33
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.3016875 -0.3202661 -0.1049255
## [2,] 0.3016875 1.0000000 -0.4014065 -0.4821703
## [3,] -0.3202661 -0.4014065 1.0000000 0.6462684
## [4,] -0.1049255 -0.4821703 0.6462684 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3215227 -0.2482208 -0.04676711
## [2,] 0.32152271 1.0000000 -0.4899639 -0.57757434
## [3,] -0.24822076 -0.4899639 1.0000000 0.71904190
## [4,] -0.04676711 -0.5775743 0.7190419 1.00000000
##
## Individual: 34
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.2545108 -0.3217415 -0.1939391
## [2,] 0.2545108 1.0000000 -0.1920622 -0.1332423
## [3,] -0.3217415 -0.1920622 1.0000000 0.6137775
## [4,] -0.1939391 -0.1332423 0.6137775 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.2962233 -0.3607669 -0.3286212
## [2,] 0.2962233 1.0000000 -0.1626738 -0.1998971
## [3,] -0.3607669 -0.1626738 1.0000000 0.7500802
## [4,] -0.3286212 -0.1998971 0.7500802 1.0000000
##
## Individual: 35
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5841496 -0.3145130 -0.4571727
## [2,] 0.5841496 1.0000000 -0.3530674 -0.4544399
## [3,] -0.3145130 -0.3530674 1.0000000 0.7150732
## [4,] -0.4571727 -0.4544399 0.7150732 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5695428 -0.2425863 -0.4208173
## [2,] 0.5695428 1.0000000 -0.3498670 -0.5124510
## [3,] -0.2425863 -0.3498670 1.0000000 0.7191734
## [4,] -0.4208173 -0.5124510 0.7191734 1.0000000
##
## Individual: 36
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7578388 -0.7465710 -0.6565970
## [2,] 0.7578388 1.0000000 -0.7690528 -0.7426781
## [3,] -0.7465710 -0.7690528 1.0000000 0.8183815
## [4,] -0.6565970 -0.7426781 0.8183815 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7434364 -0.7427262 -0.6637134
## [2,] 0.7434364 1.0000000 -0.7814712 -0.7586052
## [3,] -0.7427262 -0.7814712 1.0000000 0.8371935
## [4,] -0.6637134 -0.7586052 0.8371935 1.0000000
##
## Individual: 37
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.46602881 -0.1371171 -0.02565337
## [2,] 0.46602881 1.00000000 -0.2343725 -0.02579176
## [3,] -0.13711709 -0.23437248 1.0000000 0.20848765
## [4,] -0.02565337 -0.02579176 0.2084876 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.4887843 -0.06570112 -0.06872938
## [2,] 0.48878432 1.0000000 -0.21033824 -0.11333209
## [3,] -0.06570112 -0.2103382 1.00000000 0.27408920
## [4,] -0.06872938 -0.1133321 0.27408920 1.00000000
##
## Individual: 38
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7692592 -0.3653701 -0.3479178
## [2,] 0.7692592 1.0000000 -0.4367737 -0.4036284
## [3,] -0.3653701 -0.4367737 1.0000000 0.5573811
## [4,] -0.3479178 -0.4036284 0.5573811 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7600166 -0.3568372 -0.3636459
## [2,] 0.7600166 1.0000000 -0.4498042 -0.5096686
## [3,] -0.3568372 -0.4498042 1.0000000 0.6191223
## [4,] -0.3636459 -0.5096686 0.6191223 1.0000000
##
## Individual: 39
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.3897067 -0.1895959 -0.1885973
## [2,] 0.3897067 1.0000000 -0.3768564 -0.4082363
## [3,] -0.1895959 -0.3768564 1.0000000 0.5266788
## [4,] -0.1885973 -0.4082363 0.5266788 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4860579 -0.2257286 -0.1858965
## [2,] 0.4860579 1.0000000 -0.5192932 -0.5054808
## [3,] -0.2257286 -0.5192932 1.0000000 0.5923815
## [4,] -0.1858965 -0.5054808 0.5923815 1.0000000
##
## Individual: 40
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6165416 -0.2945385 -0.3194478
## [2,] 0.6165416 1.0000000 -0.2288765 -0.2251468
## [3,] -0.2945385 -0.2288765 1.0000000 0.6755152
## [4,] -0.3194478 -0.2251468 0.6755152 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6311045 -0.3563576 -0.3424550
## [2,] 0.6311045 1.0000000 -0.3774402 -0.4364719
## [3,] -0.3563576 -0.3774402 1.0000000 0.7695298
## [4,] -0.3424550 -0.4364719 0.7695298 1.0000000
##
## Individual: 41
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6069335 -0.4753179 -0.2649782
## [2,] 0.6069335 1.0000000 -0.5562819 -0.3551380
## [3,] -0.4753179 -0.5562819 1.0000000 0.6354548
## [4,] -0.2649782 -0.3551380 0.6354548 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5933618 -0.4208910 -0.1888887
## [2,] 0.5933618 1.0000000 -0.5439673 -0.4186396
## [3,] -0.4208910 -0.5439673 1.0000000 0.6610803
## [4,] -0.1888887 -0.4186396 0.6610803 1.0000000
##
## Individual: 42
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.1966116 -0.1585083 -0.3519936
## [2,] 0.1966116 1.0000000 -0.3076657 -0.2439968
## [3,] -0.1585083 -0.3076657 1.0000000 0.4096347
## [4,] -0.3519936 -0.2439968 0.4096347 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.1780527 -0.1805854 -0.2424487
## [2,] 0.1780527 1.0000000 -0.2248461 -0.3153361
## [3,] -0.1805854 -0.2248461 1.0000000 0.4674331
## [4,] -0.2424487 -0.3153361 0.4674331 1.0000000
##
## Individual: 43
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5817218 -0.3865198 -0.4219085
## [2,] 0.5817218 1.0000000 -0.5489536 -0.5470553
## [3,] -0.3865198 -0.5489536 1.0000000 0.6789060
## [4,] -0.4219085 -0.5470553 0.6789060 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5345750 -0.3370269 -0.3828327
## [2,] 0.5345750 1.0000000 -0.5347264 -0.6157730
## [3,] -0.3370269 -0.5347264 1.0000000 0.7160568
## [4,] -0.3828327 -0.6157730 0.7160568 1.0000000
##
## Individual: 44
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.47559689 -0.19349009 -0.2431881
## [2,] 0.4755969 1.00000000 0.01704851 -0.1615854
## [3,] -0.1934901 0.01704851 1.00000000 0.4014451
## [4,] -0.2431881 -0.16158540 0.40144507 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.5511473 -0.2842773 -0.08769441
## [2,] 0.55114733 1.0000000 -0.1725702 -0.10329608
## [3,] -0.28427732 -0.1725702 1.0000000 0.28513548
## [4,] -0.08769441 -0.1032961 0.2851355 1.00000000
##
## Individual: 45
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5287142 -0.3255689 -0.4289237
## [2,] 0.5287142 1.0000000 -0.2444784 -0.5879719
## [3,] -0.3255689 -0.2444784 1.0000000 0.3198581
## [4,] -0.4289237 -0.5879719 0.3198581 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4713310 -0.1681560 -0.2827583
## [2,] 0.4713310 1.0000000 -0.2102782 -0.6283142
## [3,] -0.1681560 -0.2102782 1.0000000 0.3791012
## [4,] -0.2827583 -0.6283142 0.3791012 1.0000000
##
## Individual: 46
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5358842 -0.3063362 -0.3000442
## [2,] 0.5358842 1.0000000 -0.4239760 -0.2263873
## [3,] -0.3063362 -0.4239760 1.0000000 0.5389985
## [4,] -0.3000442 -0.2263873 0.5389985 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5088135 -0.1748870 -0.1953065
## [2,] 0.5088135 1.0000000 -0.3812311 -0.2792102
## [3,] -0.1748870 -0.3812311 1.0000000 0.5788760
## [4,] -0.1953065 -0.2792102 0.5788760 1.0000000
##
## Individual: 47
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6015753 -0.2710183 -0.4143592
## [2,] 0.6015753 1.0000000 -0.2888143 -0.4912734
## [3,] -0.2710183 -0.2888143 1.0000000 0.4127409
## [4,] -0.4143592 -0.4912734 0.4127409 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5958992 -0.1963878 -0.3508977
## [2,] 0.5958992 1.0000000 -0.2919415 -0.5435579
## [3,] -0.1963878 -0.2919415 1.0000000 0.5257679
## [4,] -0.3508977 -0.5435579 0.5257679 1.0000000
##
## Individual: 48
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6165505 -0.5769427 -0.6316359
## [2,] 0.6165505 1.0000000 -0.5987963 -0.5826064
## [3,] -0.5769427 -0.5987963 1.0000000 0.8504206
## [4,] -0.6316359 -0.5826064 0.8504206 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6229091 -0.5832055 -0.6359843
## [2,] 0.6229091 1.0000000 -0.6535405 -0.6347723
## [3,] -0.5832055 -0.6535405 1.0000000 0.8671297
## [4,] -0.6359843 -0.6347723 0.8671297 1.0000000
##
## Individual: 49
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7258011 -0.4907548 -0.3504076
## [2,] 0.7258011 1.0000000 -0.3854274 -0.2859715
## [3,] -0.4907548 -0.3854274 1.0000000 0.6487743
## [4,] -0.3504076 -0.2859715 0.6487743 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7489998 -0.5462981 -0.4893828
## [2,] 0.7489998 1.0000000 -0.4145602 -0.3138607
## [3,] -0.5462981 -0.4145602 1.0000000 0.6457136
## [4,] -0.4893828 -0.3138607 0.6457136 1.0000000
##
## Individual: 50
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6428541 -0.4189432 -0.3029884
## [2,] 0.6428541 1.0000000 -0.3153441 -0.3987736
## [3,] -0.4189432 -0.3153441 1.0000000 0.6533963
## [4,] -0.3029884 -0.3987736 0.6533963 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6120374 -0.3633737 -0.2502379
## [2,] 0.6120374 1.0000000 -0.2869905 -0.4273073
## [3,] -0.3633737 -0.2869905 1.0000000 0.6605688
## [4,] -0.2502379 -0.4273073 0.6605688 1.0000000
##
## Individual: 51
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5197284 -0.1846528 -0.2549781
## [2,] 0.5197284 1.0000000 -0.3947467 -0.4065560
## [3,] -0.1846528 -0.3947467 1.0000000 0.8888209
## [4,] -0.2549781 -0.4065560 0.8888209 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5785691 -0.1680390 -0.2493985
## [2,] 0.5785691 1.0000000 -0.3759985 -0.4377101
## [3,] -0.1680390 -0.3759985 1.0000000 0.9086288
## [4,] -0.2493985 -0.4377101 0.9086288 1.0000000
##
## Individual: 52
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5422260 -0.3304126 -0.2922017
## [2,] 0.5422260 1.0000000 -0.3028305 -0.3372904
## [3,] -0.3304126 -0.3028305 1.0000000 0.6131190
## [4,] -0.2922017 -0.3372904 0.6131190 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5491689 -0.2803109 -0.3415259
## [2,] 0.5491689 1.0000000 -0.3194630 -0.4659704
## [3,] -0.2803109 -0.3194630 1.0000000 0.6603643
## [4,] -0.3415259 -0.4659704 0.6603643 1.0000000
##
## Individual: 53
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3780825 -0.1090722 0.03400068
## [2,] 0.37808253 1.0000000 -0.1527060 -0.20676824
## [3,] -0.10907219 -0.1527060 1.0000000 0.66318764
## [4,] 0.03400068 -0.2067682 0.6631876 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.4481200 -0.2687422 -0.01970452
## [2,] 0.44812003 1.0000000 -0.4524072 -0.35480694
## [3,] -0.26874216 -0.4524072 1.0000000 0.71296826
## [4,] -0.01970452 -0.3548069 0.7129683 1.00000000
##
## Individual: 54
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.04037282 -0.2543977 -0.1938563
## [2,] 0.04037282 1.00000000 -0.1265591 -0.2402480
## [3,] -0.25439772 -0.12655911 1.0000000 0.4907398
## [4,] -0.19385631 -0.24024796 0.4907398 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.02341572 -0.20123801 0.05418826
## [2,] 0.02341572 1.00000000 -0.07508696 -0.20964895
## [3,] -0.20123801 -0.07508696 1.00000000 0.30424316
## [4,] 0.05418826 -0.20964895 0.30424316 1.00000000
##
## Individual: 55
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.2915890 -0.1356694 -0.2056746
## [2,] 0.2915890 1.0000000 -0.2074185 -0.3625862
## [3,] -0.1356694 -0.2074185 1.0000000 0.3249606
## [4,] -0.2056746 -0.3625862 0.3249606 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.3107780 -0.1452697 -0.1889067
## [2,] 0.3107780 1.0000000 -0.2889315 -0.4991266
## [3,] -0.1452697 -0.2889315 1.0000000 0.4258312
## [4,] -0.1889067 -0.4991266 0.4258312 1.0000000
##
## Individual: 56
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.41296382 -0.04118929 -0.1697714
## [2,] 0.41296382 1.00000000 -0.08498512 -0.1021591
## [3,] -0.04118929 -0.08498512 1.00000000 0.5581663
## [4,] -0.16977140 -0.10215914 0.55816627 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.4093080 -0.02627844 -0.2106177
## [2,] 0.40930805 1.0000000 -0.05929800 -0.1474872
## [3,] -0.02627844 -0.0592980 1.00000000 0.5648986
## [4,] -0.21061773 -0.1474872 0.56489856 1.0000000
##
## Individual: 57
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.000000000 0.4763467 0.04920341 -0.005359215
## [2,] 0.476346694 1.0000000 -0.31911615 -0.318881303
## [3,] 0.049203411 -0.3191161 1.00000000 0.500548460
## [4,] -0.005359215 -0.3188813 0.50054846 1.000000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4366153 0.1949928 0.1188726
## [2,] 0.4366153 1.0000000 -0.2250266 -0.2958484
## [3,] 0.1949928 -0.2250266 1.0000000 0.6441026
## [4,] 0.1188726 -0.2958484 0.6441026 1.0000000
##
## Individual: 58
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.2167300 -0.05447107 -0.04745838
## [2,] 0.21672998 1.0000000 -0.14109644 -0.19351234
## [3,] -0.05447107 -0.1410964 1.00000000 0.65205447
## [4,] -0.04745838 -0.1935123 0.65205447 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.2614096 -0.08269278 -0.04789103
## [2,] 0.26140956 1.0000000 -0.29251949 -0.37361825
## [3,] -0.08269278 -0.2925195 1.00000000 0.69087584
## [4,] -0.04789103 -0.3736182 0.69087584 1.00000000
##
## Individual: 59
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5178657 -0.1685293 -0.2560113
## [2,] 0.5178657 1.0000000 -0.3480361 -0.3734802
## [3,] -0.1685293 -0.3480361 1.0000000 0.6093285
## [4,] -0.2560113 -0.3734802 0.6093285 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4706798 -0.1099825 -0.1776230
## [2,] 0.4706798 1.0000000 -0.4179704 -0.4542334
## [3,] -0.1099825 -0.4179704 1.0000000 0.7084833
## [4,] -0.1776230 -0.4542334 0.7084833 1.0000000
##
## Individual: 60
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7663061 -0.5131264 -0.4142917
## [2,] 0.7663061 1.0000000 -0.5245143 -0.4002862
## [3,] -0.5131264 -0.5245143 1.0000000 0.5195040
## [4,] -0.4142917 -0.4002862 0.5195040 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.9129187 -0.7137078 -0.6215187
## [2,] 0.9129187 1.0000000 -0.7341717 -0.6466524
## [3,] -0.7137078 -0.7341717 1.0000000 0.7048427
## [4,] -0.6215187 -0.6466524 0.7048427 1.0000000
##
## Individual: 61
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.3763809 -0.2458907 -0.1071356
## [2,] 0.3763809 1.0000000 -0.3816578 -0.2203353
## [3,] -0.2458907 -0.3816578 1.0000000 0.4612273
## [4,] -0.1071356 -0.2203353 0.4612273 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3449163 -0.2211462 -0.06722177
## [2,] 0.34491633 1.0000000 -0.3892776 -0.36677554
## [3,] -0.22114624 -0.3892776 1.0000000 0.47735840
## [4,] -0.06722177 -0.3667755 0.4773584 1.00000000
##
## Individual: 62
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7034916 -0.5345642 -0.4425820
## [2,] 0.7034916 1.0000000 -0.5938749 -0.5531779
## [3,] -0.5345642 -0.5938749 1.0000000 0.7087906
## [4,] -0.4425820 -0.5531779 0.7087906 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6811421 -0.5148277 -0.3947150
## [2,] 0.6811421 1.0000000 -0.6009574 -0.5841137
## [3,] -0.5148277 -0.6009574 1.0000000 0.7655313
## [4,] -0.3947150 -0.5841137 0.7655313 1.0000000
##
## Individual: 63
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6427512 -0.7204302 -0.5659898
## [2,] 0.6427512 1.0000000 -0.6818467 -0.5171961
## [3,] -0.7204302 -0.6818467 1.0000000 0.7065814
## [4,] -0.5659898 -0.5171961 0.7065814 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6890935 -0.7370389 -0.6324298
## [2,] 0.6890935 1.0000000 -0.7437102 -0.6622188
## [3,] -0.7370389 -0.7437102 1.0000000 0.8056194
## [4,] -0.6324298 -0.6622188 0.8056194 1.0000000
##
## Individual: 64
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6797686 -0.4728346 -0.4913848
## [2,] 0.6797686 1.0000000 -0.4506086 -0.4177028
## [3,] -0.4728346 -0.4506086 1.0000000 0.7667222
## [4,] -0.4913848 -0.4177028 0.7667222 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7286541 -0.4483427 -0.5244521
## [2,] 0.7286541 1.0000000 -0.4473144 -0.5092755
## [3,] -0.4483427 -0.4473144 1.0000000 0.7785017
## [4,] -0.5244521 -0.5092755 0.7785017 1.0000000
##
## Individual: 65
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.5590734 0.06335759 -0.3287049
## [2,] 0.55907342 1.0000000 -0.24951069 -0.3599010
## [3,] 0.06335759 -0.2495107 1.00000000 0.3579358
## [4,] -0.32870489 -0.3599010 0.35793582 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.000000000 0.5650383 -0.009575459 -0.3527248
## [2,] 0.565038274 1.0000000 -0.319590599 -0.4698737
## [3,] -0.009575459 -0.3195906 1.000000000 0.4816816
## [4,] -0.352724807 -0.4698737 0.481681627 1.0000000
##
## Individual: 66
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5592402 -0.5549183 -0.5392114
## [2,] 0.5592402 1.0000000 -0.5404071 -0.3994372
## [3,] -0.5549183 -0.5404071 1.0000000 0.6783724
## [4,] -0.5392114 -0.3994372 0.6783724 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5476826 -0.5504382 -0.5424107
## [2,] 0.5476826 1.0000000 -0.5038813 -0.4170923
## [3,] -0.5504382 -0.5038813 1.0000000 0.6950562
## [4,] -0.5424107 -0.4170923 0.6950562 1.0000000
##
## Individual: 67
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6630646 -0.3007958 -0.3356936
## [2,] 0.6630646 1.0000000 -0.2827123 -0.4050043
## [3,] -0.3007958 -0.2827123 1.0000000 0.5710381
## [4,] -0.3356936 -0.4050043 0.5710381 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6457356 -0.3230893 -0.3788896
## [2,] 0.6457356 1.0000000 -0.4806636 -0.5741672
## [3,] -0.3230893 -0.4806636 1.0000000 0.7853299
## [4,] -0.3788896 -0.5741672 0.7853299 1.0000000
##
## Individual: 68
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6354152 -0.4674142 -0.4647969
## [2,] 0.6354152 1.0000000 -0.5634073 -0.6366848
## [3,] -0.4674142 -0.5634073 1.0000000 0.7075744
## [4,] -0.4647969 -0.6366848 0.7075744 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7174842 -0.5496513 -0.4782080
## [2,] 0.7174842 1.0000000 -0.6565988 -0.6488888
## [3,] -0.5496513 -0.6565988 1.0000000 0.7409259
## [4,] -0.4782080 -0.6488888 0.7409259 1.0000000
##
## Individual: 69
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4635206 -0.1363715 -0.4181039
## [2,] 0.4635206 1.0000000 -0.3189901 -0.3965055
## [3,] -0.1363715 -0.3189901 1.0000000 0.5593225
## [4,] -0.4181039 -0.3965055 0.5593225 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5158057 -0.1570979 -0.4627869
## [2,] 0.5158057 1.0000000 -0.3150550 -0.4674439
## [3,] -0.1570979 -0.3150550 1.0000000 0.6555706
## [4,] -0.4627869 -0.4674439 0.6555706 1.0000000
##
## Individual: 70
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6087154 -0.3541726 -0.3348613
## [2,] 0.6087154 1.0000000 -0.3392260 -0.3260367
## [3,] -0.3541726 -0.3392260 1.0000000 0.5860167
## [4,] -0.3348613 -0.3260367 0.5860167 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6126164 -0.3238683 -0.2626814
## [2,] 0.6126164 1.0000000 -0.3209143 -0.3025788
## [3,] -0.3238683 -0.3209143 1.0000000 0.5679541
## [4,] -0.2626814 -0.3025788 0.5679541 1.0000000
##
## Individual: 71
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.2031208 -0.1853473 -0.3342844
## [2,] 0.2031208 1.0000000 -0.3835036 -0.3119079
## [3,] -0.1853473 -0.3835036 1.0000000 0.7178485
## [4,] -0.3342844 -0.3119079 0.7178485 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.3185342 -0.1307256 -0.1846791
## [2,] 0.3185342 1.0000000 -0.3715771 -0.3410357
## [3,] -0.1307256 -0.3715771 1.0000000 0.7726915
## [4,] -0.1846791 -0.3410357 0.7726915 1.0000000
##
## Individual: 72
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5510257 -0.4115863 -0.2971695
## [2,] 0.5510257 1.0000000 -0.2405344 -0.3152527
## [3,] -0.4115863 -0.2405344 1.0000000 0.4599803
## [4,] -0.2971695 -0.3152527 0.4599803 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5706126 -0.5322493 -0.3757845
## [2,] 0.5706126 1.0000000 -0.4393472 -0.4487435
## [3,] -0.5322493 -0.4393472 1.0000000 0.6055268
## [4,] -0.3757845 -0.4487435 0.6055268 1.0000000
##
## Individual: 73
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.56413624 -0.2914418 -0.06121920
## [2,] 0.5641362 1.00000000 -0.1654577 0.04493943
## [3,] -0.2914418 -0.16545770 1.0000000 0.76100022
## [4,] -0.0612192 0.04493943 0.7610002 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5480640 -0.3695152 -0.1165959
## [2,] 0.5480640 1.0000000 -0.3008635 -0.1404555
## [3,] -0.3695152 -0.3008635 1.0000000 0.8108709
## [4,] -0.1165959 -0.1404555 0.8108709 1.0000000
##
## Individual: 74
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7841381 -0.6012253 -0.5547966
## [2,] 0.7841381 1.0000000 -0.6771452 -0.6082754
## [3,] -0.6012253 -0.6771452 1.0000000 0.8038063
## [4,] -0.5547966 -0.6082754 0.8038063 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.8069983 -0.6276593 -0.5603165
## [2,] 0.8069983 1.0000000 -0.7129092 -0.6574622
## [3,] -0.6276593 -0.7129092 1.0000000 0.8371621
## [4,] -0.5603165 -0.6574622 0.8371621 1.0000000
##
## Individual: 75
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.4716333 -0.07461454 0.05127398
## [2,] 0.47163328 1.0000000 -0.24826560 -0.20486678
## [3,] -0.07461454 -0.2482656 1.00000000 0.19199263
## [4,] 0.05127398 -0.2048668 0.19199263 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3864550 0.07192514 0.1080630
## [2,] 0.38645504 1.0000000 -0.26635614 -0.2915927
## [3,] 0.07192514 -0.2663561 1.00000000 0.2911144
## [4,] 0.10806301 -0.2915927 0.29111438 1.0000000
##
## Individual: 76
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.62109541 -0.14320643 -0.2596426
## [2,] 0.6210954 1.00000000 -0.05812367 -0.1394662
## [3,] -0.1432064 -0.05812367 1.00000000 0.5284856
## [4,] -0.2596426 -0.13946620 0.52848563 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.55979097 -0.19747406 -0.2945840
## [2,] 0.5597910 1.00000000 -0.01695456 -0.1614441
## [3,] -0.1974741 -0.01695456 1.00000000 0.6196031
## [4,] -0.2945840 -0.16144414 0.61960309 1.0000000
##
## Individual: 77
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6165167 -0.2098689 -0.1557125
## [2,] 0.6165167 1.0000000 -0.2077642 -0.2267130
## [3,] -0.2098689 -0.2077642 1.0000000 0.6170991
## [4,] -0.1557125 -0.2267130 0.6170991 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5669851 -0.1157555 -0.3072386
## [2,] 0.5669851 1.0000000 -0.3287760 -0.3839937
## [3,] -0.1157555 -0.3287760 1.0000000 0.6895272
## [4,] -0.3072386 -0.3839937 0.6895272 1.0000000
##
## Individual: 78
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7067979 -0.1006762 -0.2769727
## [2,] 0.7067979 1.0000000 -0.2335115 -0.4167073
## [3,] -0.1006762 -0.2335115 1.0000000 0.3594594
## [4,] -0.2769727 -0.4167073 0.3594594 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.6684610 -0.06165411 -0.2195952
## [2,] 0.66846099 1.0000000 -0.29079660 -0.4974330
## [3,] -0.06165411 -0.2907966 1.00000000 0.4769141
## [4,] -0.21959519 -0.4974330 0.47691406 1.0000000
##
## Individual: 79
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5882562 -0.2824187 -0.4516112
## [2,] 0.5882562 1.0000000 -0.4808510 -0.6116951
## [3,] -0.2824187 -0.4808510 1.0000000 0.5474794
## [4,] -0.4516112 -0.6116951 0.5474794 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6088855 -0.2211366 -0.4362068
## [2,] 0.6088855 1.0000000 -0.4536465 -0.6672788
## [3,] -0.2211366 -0.4536465 1.0000000 0.5760818
## [4,] -0.4362068 -0.6672788 0.5760818 1.0000000
##
## Individual: 80
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3175591 -0.04872933 -0.02657709
## [2,] 0.31755908 1.0000000 -0.29459446 -0.15557395
## [3,] -0.04872933 -0.2945945 1.00000000 0.52911395
## [4,] -0.02657709 -0.1555739 0.52911395 1.00000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.000000000 0.3950171 0.008621776 0.001882103
## [2,] 0.395017104 1.0000000 -0.256461289 -0.225411079
## [3,] 0.008621776 -0.2564613 1.000000000 0.570893089
## [4,] 0.001882103 -0.2254111 0.570893089 1.000000000
##
## Individual: 81
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000000 0.3670921 -0.06187508 0.0005997275
## [2,] 0.3670921017 1.0000000 -0.19634770 -0.3313521734
## [3,] -0.0618750842 -0.1963477 1.00000000 0.5051421039
## [4,] 0.0005997275 -0.3313522 0.50514210 1.0000000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.4536254 -0.1600244 -0.04644587
## [2,] 0.45362535 1.0000000 -0.3013200 -0.39631687
## [3,] -0.16002444 -0.3013200 1.0000000 0.52425923
## [4,] -0.04644587 -0.3963169 0.5242592 1.00000000
##
## Individual: 82
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.3151621 -0.1187627 -0.1637734
## [2,] 0.3151621 1.0000000 -0.2969750 -0.0996699
## [3,] -0.1187627 -0.2969750 1.0000000 0.6084519
## [4,] -0.1637734 -0.0996699 0.6084519 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4156472 -0.1021962 -0.1661188
## [2,] 0.4156472 1.0000000 -0.3733649 -0.2826174
## [3,] -0.1021962 -0.3733649 1.0000000 0.7183161
## [4,] -0.1661188 -0.2826174 0.7183161 1.0000000
##
## Individual: 83
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7143583 -0.4501356 -0.3839908
## [2,] 0.7143583 1.0000000 -0.4208313 -0.4506395
## [3,] -0.4501356 -0.4208313 1.0000000 0.6525243
## [4,] -0.3839908 -0.4506395 0.6525243 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7419669 -0.4771314 -0.3467106
## [2,] 0.7419669 1.0000000 -0.4884850 -0.4760468
## [3,] -0.4771314 -0.4884850 1.0000000 0.7298032
## [4,] -0.3467106 -0.4760468 0.7298032 1.0000000
##
## Individual: 84
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7309865 -0.6557692 -0.3191415
## [2,] 0.7309865 1.0000000 -0.6553253 -0.4209517
## [3,] -0.6557692 -0.6553253 1.0000000 0.5449821
## [4,] -0.3191415 -0.4209517 0.5449821 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7616688 -0.6929099 -0.3128917
## [2,] 0.7616688 1.0000000 -0.6584106 -0.3536678
## [3,] -0.6929099 -0.6584106 1.0000000 0.5999465
## [4,] -0.3128917 -0.3536678 0.5999465 1.0000000
##
## Individual: 85
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7317367 -0.4962284 -0.2507460
## [2,] 0.7317367 1.0000000 -0.4936874 -0.4097092
## [3,] -0.4962284 -0.4936874 1.0000000 0.3178713
## [4,] -0.2507460 -0.4097092 0.3178713 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7243866 -0.5563537 -0.3350333
## [2,] 0.7243866 1.0000000 -0.5193104 -0.4983144
## [3,] -0.5563537 -0.5193104 1.0000000 0.4021122
## [4,] -0.3350333 -0.4983144 0.4021122 1.0000000
##
## Individual: 86
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4529088 -0.1638513 -0.4378257
## [2,] 0.4529088 1.0000000 -0.5170453 -0.5477721
## [3,] -0.1638513 -0.5170453 1.0000000 0.4851191
## [4,] -0.4378257 -0.5477721 0.4851191 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5381142 -0.3207913 -0.5226410
## [2,] 0.5381142 1.0000000 -0.5557767 -0.6526555
## [3,] -0.3207913 -0.5557767 1.0000000 0.6004745
## [4,] -0.5226410 -0.6526555 0.6004745 1.0000000
##
## Individual: 87
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6258833 -0.2909462 -0.2344138
## [2,] 0.6258833 1.0000000 -0.2527787 -0.3159721
## [3,] -0.2909462 -0.2527787 1.0000000 0.6023754
## [4,] -0.2344138 -0.3159721 0.6023754 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6526752 -0.3676429 -0.3536478
## [2,] 0.6526752 1.0000000 -0.3559401 -0.3750083
## [3,] -0.3676429 -0.3559401 1.0000000 0.6651145
## [4,] -0.3536478 -0.3750083 0.6651145 1.0000000
##
## Individual: 88
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5974193 -0.5732545 -0.2998999
## [2,] 0.5974193 1.0000000 -0.3866248 -0.1948945
## [3,] -0.5732545 -0.3866248 1.0000000 0.4609588
## [4,] -0.2998999 -0.1948945 0.4609588 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6323834 -0.5644910 -0.2437515
## [2,] 0.6323834 1.0000000 -0.4173173 -0.2839854
## [3,] -0.5644910 -0.4173173 1.0000000 0.4394701
## [4,] -0.2437515 -0.2839854 0.4394701 1.0000000
##
## Individual: 89
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6280190 -0.5584952 -0.4406350
## [2,] 0.6280190 1.0000000 -0.6281326 -0.4612510
## [3,] -0.5584952 -0.6281326 1.0000000 0.6802531
## [4,] -0.4406350 -0.4612510 0.6802531 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4792064 -0.5683924 -0.4436345
## [2,] 0.4792064 1.0000000 -0.5484831 -0.4691659
## [3,] -0.5683924 -0.5484831 1.0000000 0.7143393
## [4,] -0.4436345 -0.4691659 0.7143393 1.0000000
##
## Individual: 90
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7027939 -0.3307637 -0.3328687
## [2,] 0.7027939 1.0000000 -0.5323781 -0.4540194
## [3,] -0.3307637 -0.5323781 1.0000000 0.4236939
## [4,] -0.3328687 -0.4540194 0.4236939 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6535832 -0.2817914 -0.2836243
## [2,] 0.6535832 1.0000000 -0.5019130 -0.5126630
## [3,] -0.2817914 -0.5019130 1.0000000 0.4738923
## [4,] -0.2836243 -0.5126630 0.4738923 1.0000000
##
## Individual: 91
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5498644 -0.3788845 -0.3176427
## [2,] 0.5498644 1.0000000 -0.4181076 -0.3356464
## [3,] -0.3788845 -0.4181076 1.0000000 0.6331808
## [4,] -0.3176427 -0.3356464 0.6331808 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6441775 -0.4704147 -0.3843843
## [2,] 0.6441775 1.0000000 -0.5701576 -0.4678875
## [3,] -0.4704147 -0.5701576 1.0000000 0.7008422
## [4,] -0.3843843 -0.4678875 0.7008422 1.0000000
##
## Individual: 92
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6490665 -0.4694557 -0.4373160
## [2,] 0.6490665 1.0000000 -0.6480971 -0.4458397
## [3,] -0.4694557 -0.6480971 1.0000000 0.6315273
## [4,] -0.4373160 -0.4458397 0.6315273 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6178628 -0.4787188 -0.4302014
## [2,] 0.6178628 1.0000000 -0.5752785 -0.5061527
## [3,] -0.4787188 -0.5752785 1.0000000 0.6476154
## [4,] -0.4302014 -0.5061527 0.6476154 1.0000000
##
## Individual: 93
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7326736 -0.6358889 -0.5682383
## [2,] 0.7326736 1.0000000 -0.6053152 -0.5318732
## [3,] -0.6358889 -0.6053152 1.0000000 0.7120874
## [4,] -0.5682383 -0.5318732 0.7120874 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7821388 -0.6320009 -0.5921104
## [2,] 0.7821388 1.0000000 -0.6089797 -0.6018756
## [3,] -0.6320009 -0.6089797 1.0000000 0.7592004
## [4,] -0.5921104 -0.6018756 0.7592004 1.0000000
##
## Individual: 94
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7318186 -0.6300598 -0.5778036
## [2,] 0.7318186 1.0000000 -0.6706258 -0.6128138
## [3,] -0.6300598 -0.6706258 1.0000000 0.7381649
## [4,] -0.5778036 -0.6128138 0.7381649 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.7403090 -0.6062614 -0.5553007
## [2,] 0.7403090 1.0000000 -0.6785356 -0.6603467
## [3,] -0.6062614 -0.6785356 1.0000000 0.7827063
## [4,] -0.5553007 -0.6603467 0.7827063 1.0000000
##
## Individual: 95
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3755016 -0.07769654 -0.1363100
## [2,] 0.37550164 1.0000000 -0.26196131 -0.3657931
## [3,] -0.07769654 -0.2619613 1.00000000 0.4567352
## [4,] -0.13631004 -0.3657931 0.45673516 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.000000000 0.3051884 0.02989178 -0.009896853
## [2,] 0.305188367 1.0000000 -0.30828088 -0.471550706
## [3,] 0.029891776 -0.3082809 1.00000000 0.544941845
## [4,] -0.009896853 -0.4715507 0.54494185 1.000000000
##
## Individual: 96
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.3305569 -0.08208253 -0.0896514
## [2,] 0.33055686 1.0000000 -0.13593032 -0.1289027
## [3,] -0.08208253 -0.1359303 1.00000000 0.6314248
## [4,] -0.08965140 -0.1289027 0.63142484 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.2431693 -0.1781152 -0.09396619
## [2,] 0.24316926 1.0000000 -0.4182897 -0.46459316
## [3,] -0.17811523 -0.4182897 1.0000000 0.89104226
## [4,] -0.09396619 -0.4645932 0.8910423 1.00000000
##
## Individual: 97
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4775775 -0.2716248 -0.3569052
## [2,] 0.4775775 1.0000000 -0.2832774 -0.2501369
## [3,] -0.2716248 -0.2832774 1.0000000 0.6470966
## [4,] -0.3569052 -0.2501369 0.6470966 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5210047 -0.3461727 -0.4022330
## [2,] 0.5210047 1.0000000 -0.3281727 -0.3752542
## [3,] -0.3461727 -0.3281727 1.0000000 0.6241580
## [4,] -0.4022330 -0.3752542 0.6241580 1.0000000
##
## Individual: 98
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5258635 -0.4536778 -0.4954802
## [2,] 0.5258635 1.0000000 -0.5811565 -0.4706565
## [3,] -0.4536778 -0.5811565 1.0000000 0.6206279
## [4,] -0.4954802 -0.4706565 0.6206279 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4860514 -0.3113661 -0.4454465
## [2,] 0.4860514 1.0000000 -0.5268597 -0.4488614
## [3,] -0.3113661 -0.5268597 1.0000000 0.6994456
## [4,] -0.4454465 -0.4488614 0.6994456 1.0000000
##
## Individual: 99
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.3061509 -0.3299826 -0.3148238
## [2,] 0.3061509 1.0000000 -0.5941113 -0.4534719
## [3,] -0.3299826 -0.5941113 1.0000000 0.5584202
## [4,] -0.3148238 -0.4534719 0.5584202 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.4890982 -0.4645283 -0.4471101
## [2,] 0.4890982 1.0000000 -0.7287161 -0.6687937
## [3,] -0.4645283 -0.7287161 1.0000000 0.7193731
## [4,] -0.4471101 -0.6687937 0.7193731 1.0000000
##
## Individual: 100
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5138123 -0.6742216 -0.4514555
## [2,] 0.5138123 1.0000000 -0.4358547 -0.3790432
## [3,] -0.6742216 -0.4358547 1.0000000 0.6590601
## [4,] -0.4514555 -0.3790432 0.6590601 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5093468 -0.6370383 -0.3732036
## [2,] 0.5093468 1.0000000 -0.4015590 -0.4181242
## [3,] -0.6370383 -0.4015590 1.0000000 0.6359237
## [4,] -0.3732036 -0.4181242 0.6359237 1.0000000
##
## Individual: 101
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6212050 -0.4838543 -0.4157086
## [2,] 0.6212050 1.0000000 -0.5500212 -0.5989041
## [3,] -0.4838543 -0.5500212 1.0000000 0.5911316
## [4,] -0.4157086 -0.5989041 0.5911316 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.5074873 -0.3660598 -0.2972972
## [2,] 0.5074873 1.0000000 -0.4644667 -0.6022576
## [3,] -0.3660598 -0.4644667 1.0000000 0.6250756
## [4,] -0.2972972 -0.6022576 0.6250756 1.0000000
##
## Individual: 102
## Correlation Matrix of Residuals (Sigma):
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.8414987 -0.4917391 -0.4393282
## [2,] 0.8414987 1.0000000 -0.5170959 -0.4705787
## [3,] -0.4917391 -0.5170959 1.0000000 0.8413443
## [4,] -0.4393282 -0.4705787 0.8413443 1.0000000
## Raw Correlation Matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.8296785 -0.4381357 -0.4135461
## [2,] 0.8296785 1.0000000 -0.5239493 -0.5099875
## [3,] -0.4381357 -0.5239493 1.0000000 0.8582140
## [4,] -0.4135461 -0.5099875 0.8582140 1.0000000Again, calculated Frobenius norm to see how similar matrices are for each individual.
# Function to calculate Frobenius norm of the difference between two matrices
frobenius_norm_AR <- function(mat1, mat2) {
if (is.null(mat1) || is.null(mat2) || !all(dim(mat1) == dim(mat2))) {
return(NA) # Handle cases where the matrices are incompatible or NULL
}
return(sqrt(sum((mat1 - mat2)^2)))
}
# Initialize an empty list to store the comparison results and Frobenius norms
comparison_results_AR <- list()
frobenius_norm_list_AR <- list()
# Loop through each individual's data in the rawdata_list and fit results list
for (i in 1:length(fit_results_list_AR)) {
# Step 1: Extract the Sigma matrix and convert it to the correlation matrix
cor_matrix_sigma <- cov2cor(fit_results_list_AR[[i]]$Sigma)
# Step 2: Extract the raw data for the individual, removing ID and time columns
ind_data <- simulated_data_list_AR[[i]]
# Step 3: Calculate the raw correlation matrix for this individual
raw_cor_matrix <- cor(ind_data, use = "complete.obs")
# Step 4: Store the comparison results in a list
comparison_results_AR[[i]] <- list(cor_matrix_sigma = cor_matrix_sigma,
raw_cor_matrix = raw_cor_matrix)
# Step 5: Calculate the Frobenius norm between cor_matrix_sigma and raw_cor_matrix
frobenius_value <- frobenius_norm_AR(cor_matrix_sigma, raw_cor_matrix)
# Store the Frobenius norm result
frobenius_norm_list_AR[[i]] <- frobenius_value
}
# Convert Frobenius norms to a data frame for better visualization
frobenius_comparison_AR <- data.frame(
Individual = 1:length(fit_results_list_AR),
Frobenius_Norm = unlist(frobenius_norm_list_AR)
)
# Display the Frobenius norm results
print(frobenius_comparison_AR)## Individual Frobenius_Norm
## 1 1 0.25395423
## 2 2 0.47090040
## 3 3 0.19726404
## 4 4 0.42706052
## 5 5 0.65523574
## 6 6 0.13414682
## 7 7 0.29259749
## 8 8 0.22477254
## 9 9 0.25601211
## 10 10 0.26670374
## 11 11 0.18274416
## 12 12 0.17662608
## 13 13 0.37601019
## 14 14 0.19967242
## 15 15 0.20374237
## 16 16 0.21658507
## 17 17 0.24587970
## 18 18 0.72242078
## 19 19 0.30722986
## 20 20 0.10466534
## 21 21 0.26286472
## 22 22 0.10586869
## 23 23 0.37313586
## 24 24 0.25002102
## 25 25 0.18987600
## 26 26 0.96968178
## 27 27 0.31364339
## 28 28 0.53871302
## 29 29 0.43573668
## 30 30 0.26358235
## 31 31 0.19933666
## 32 32 0.72248340
## 33 33 0.24982664
## 34 34 0.30095571
## 35 35 0.14213278
## 36 36 0.04548921
## 37 37 0.20009055
## 38 38 0.17681568
## 39 39 0.29885795
## 40 40 0.40032793
## 41 41 0.16599315
## 42 42 0.23715375
## 43 43 0.15813927
## 44 44 0.42663642
## 45 45 0.33389484
## 46 46 0.26528963
## 47 47 0.22426701
## 48 48 0.11041701
## 49 49 0.22169003
## 50 50 0.13030581
## 51 51 0.10472642
## 52 52 0.21935620
## 53 53 0.54313611
## 54 54 0.45388610
## 55 55 0.26908768
## 56 56 0.09658061
## 57 57 0.36948029
## 58 58 0.34544781
## 59 59 0.25707016
## 60 60 0.69810332
## 61 61 0.22342080
## 62 62 0.12171255
## 63 63 0.28811439
## 64 64 0.15886003
## 65 65 0.27658626
## 66 66 0.06462307
## 67 67 0.48246242
## 68 68 0.21736622
## 69 69 0.19733892
## 70 70 0.12128771
## 71 71 0.29217788
## 72 72 0.44643842
## 73 73 0.35948152
## 74 74 0.11011657
## 75 75 0.31504913
## 76 76 0.19185636
## 77 77 0.39723494
## 78 78 0.24445208
## 79 79 0.13465573
## 80 80 0.19066033
## 81 81 0.26434694
## 82 82 0.35143292
## 83 83 0.16778200
## 84 84 0.14083758
## 85 85 0.22968398
## 86 86 0.36025349
## 87 87 0.27885718
## 88 88 0.16608988
## 89 89 0.24421586
## 90 90 0.16811944
## 91 91 0.36582010
## 92 92 0.14359062
## 93 93 0.14258474
## 94 94 0.10440986
## 95 95 0.32744491
## 96 96 0.74390007
## 97 97 0.23534656
## 98 98 0.26067749
## 99 99 0.56472938
## 100 100 0.14672908
## 101 101 0.31404308
## 102 102 0.10547378Then we fitted a VARMA model to the simulated data to see how well it fits compared to the initial VARMA model fit from the real data (that was used to simulate the simualted data)
# Initialize an empty list to store the fit results
fit_result_list_ARSIM <- list()
# Loop through each individual's data and fit the VARMA model
for (i in 1:length(simulated_data_list_AR)) {
# Fit VARMA model for simulated data
fit_simulated <- VARMA(simulated_data_list_AR[[i]], p = 1, q = 0)
# Store the fit result in the list
fit_result_list_ARSIM[[i]] <- fit_simulated
}## Number of parameters: 20
## initial estimates: -1.3273 -2.1288 -0.9575 -0.4141 0.4205 0.1447 0.1287 -0.1789 0.0591 0.5041 -0.0374 0.0572 0.126 -0.4771 0.0237 0.007 0.3219 -0.5691 -0.1672 0.1751
## Par. lower-bounds: -3.3905 -4.1148 -4.0301 -3.6921 0.2548 -0.0415 -0.0552 -0.3525 -0.1004 0.3249 -0.2145 -0.1098 -0.1207 -0.7543 -0.2503 -0.2515 0.0587 -0.8648 -0.4594 -0.1007
## Par. upper-bounds: 0.7359 -0.1428 2.1151 2.8638 0.5861 0.3308 0.3127 -0.0053 0.2185 0.6833 0.1397 0.2243 0.3727 -0.1999 0.2976 0.2655 0.585 -0.2733 0.1251 0.4509
## Final Estimates: -1.259179 -2.039009 -0.9127163 -0.5093712 0.412423 0.1502789 0.1282712 -0.1743754 0.0484156 0.5114741 -0.03804642 0.063196 0.1206941 -0.4733865 0.02336775 0.009915932 0.3331678 -0.5769135 -0.1664685 0.1687591
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.259179 1.028752 -1.224 0.2210
## [2,] -2.039009 0.992913 -2.054 0.0400 *
## [3,] -0.912716 1.528375 -0.597 0.5504
## [4,] -0.509371 1.633396 -0.312 0.7552
## [5,] 0.412423 0.082358 5.008 5.51e-07 ***
## [6,] 0.150279 0.092853 1.618 0.1056
## [7,] 0.128271 0.091958 1.395 0.1630
## [8,] -0.174375 0.086636 -2.013 0.0441 *
## [9,] 0.048416 0.079489 0.609 0.5425
## [10,] 0.511474 0.089618 5.707 1.15e-08 ***
## [11,] -0.038046 0.088760 -0.429 0.6682
## [12,] 0.063196 0.083623 0.756 0.4498
## [13,] 0.120694 0.122354 0.986 0.3239
## [14,] -0.473386 0.137950 -3.432 0.0006 ***
## [15,] 0.023368 0.136664 0.171 0.8642
## [16,] 0.009916 0.128764 0.077 0.9386
## [17,] 0.333168 0.130764 2.548 0.0108 *
## [18,] -0.576914 0.147431 -3.913 9.11e-05 ***
## [19,] -0.166469 0.146046 -1.140 0.2544
## [20,] 0.168759 0.137598 1.226 0.2200
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.259179 -2.039009 -0.9127163 -0.5093712
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.4124 0.150 0.1283 -0.17438
## [2,] 0.0484 0.511 -0.0380 0.06320
## [3,] 0.1207 -0.473 0.0234 0.00992
## [4,] 0.3332 -0.577 -0.1665 0.16876
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 140.12065 62.59447 -39.85593 -47.90875
## [2,] 62.59447 130.52651 -51.36412 -78.33511
## [3,] -39.85593 -51.36412 309.25510 268.37758
## [4,] -47.90875 -78.33511 268.37758 353.23274
## ----
## aic= 20.20795
## bic= 20.60937
## Number of parameters: 20
## initial estimates: -0.6919 -1.1291 -1.0459 -0.3564 0.1968 -0.2873 0.1705 0.0467 -0.1827 0.0278 -0.0678 0.0818 0.0351 -0.1333 0.5754 -0.4681 0.0539 0.0355 0.0654 0.3757
## Par. lower-bounds: -1.885 -2.0936 -3.1547 -1.3185 0.0458 -0.4823 0.0813 -0.1568 -0.3048 -0.1298 -0.1398 -0.0828 -0.2317 -0.4779 0.4178 -0.828 -0.0679 -0.1217 -0.0065 0.2115
## Par. upper-bounds: 0.5012 -0.1646 1.0628 0.6058 0.3477 -0.0924 0.2596 0.2503 -0.0607 0.1854 0.0043 0.2464 0.3019 0.2113 0.7329 -0.1083 0.1756 0.1928 0.1373 0.5398
## Final Estimates: -0.6525879 -1.073902 -0.9172099 -0.3963084 0.1928601 -0.2860524 0.1703649 0.05811778 -0.1882365 0.02960312 -0.06791256 0.09778071 0.02225725 -0.1290331 0.5750496 -0.4308682 0.05785835 0.03422883 0.0654844 0.3641107
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.65259 0.59285 -1.101 0.271000
## [2,] -1.07390 0.48083 -2.233 0.025521 *
## [3,] -0.91721 1.05202 -0.872 0.383289
## [4,] -0.39631 0.47855 -0.828 0.407593
## [5,] 0.19286 0.07514 2.567 0.010267 *
## [6,] -0.28605 0.09729 -2.940 0.003278 **
## [7,] 0.17036 0.04450 3.829 0.000129 ***
## [8,] 0.05812 0.10030 0.579 0.562288
## [9,] -0.18824 0.06094 -3.089 0.002010 **
## [10,] 0.02960 0.07891 0.375 0.707533
## [11,] -0.06791 0.03609 -1.882 0.059854 .
## [12,] 0.09778 0.08135 1.202 0.229355
## [13,] 0.02226 0.13335 0.167 0.867439
## [14,] -0.12903 0.17264 -0.747 0.454810
## [15,] 0.57505 0.07896 7.283 3.26e-13 ***
## [16,] -0.43087 0.17798 -2.421 0.015484 *
## [17,] 0.05786 0.06065 0.954 0.340130
## [18,] 0.03423 0.07853 0.436 0.662942
## [19,] 0.06548 0.03592 1.823 0.068271 .
## [20,] 0.36411 0.08096 4.497 6.88e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.6525879 -1.073902 -0.9172099 -0.3963084
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.1929 -0.2861 0.1704 0.0581
## [2,] -0.1882 0.0296 -0.0679 0.0978
## [3,] 0.0223 -0.1290 0.5750 -0.4309
## [4,] 0.0579 0.0342 0.0655 0.3641
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 50.307639 7.135559 8.559479 4.353255
## [2,] 7.135559 33.092918 3.706069 -2.983438
## [3,] 8.559479 3.706069 158.415086 32.033881
## [4,] 4.353255 -2.983438 32.033881 32.780002
## ----
## aic= 15.95199
## bic= 16.35341
## Number of parameters: 20
## initial estimates: -1.5961 -2.0841 -0.3824 -0.0254 0.5368 -0.2369 -0.1344 0.1838 0.194 -0.0536 -0.0977 0.1865 0.2364 -0.1081 0.2353 0.0086 -0.1846 0.3694 0.213 0.0175
## Par. lower-bounds: -3.9686 -3.9821 -2.879 -2.1079 0.3311 -0.5244 -0.3212 -0.0567 0.0294 -0.2835 -0.2472 -0.0059 0.0199 -0.4105 0.0387 -0.2445 -0.3651 0.1171 0.049 -0.1936
## Par. upper-bounds: 0.7764 -0.1861 2.1142 2.0572 0.7425 0.0505 0.0524 0.4243 0.3585 0.1764 0.0517 0.3789 0.4529 0.1944 0.4319 0.2617 -0.004 0.6218 0.377 0.2286
## Final Estimates: -1.509852 -1.985065 -0.3104024 -0.1313747 0.5302488 -0.2301168 -0.1327243 0.192176 0.1864299 -0.04575414 -0.09577867 0.1961268 0.2309253 -0.1023397 0.2366577 0.01557029 -0.1764993 0.3610473 0.2109476 0.007242531
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.509852 1.180871 -1.279 0.2010
## [2,] -1.985065 0.947113 -2.096 0.0361 *
## [3,] -0.310402 1.241489 -0.250 0.8026
## [4,] -0.131375 1.039030 -0.126 0.8994
## [5,] 0.530249 0.102488 5.174 2.29e-07 ***
## [6,] -0.230117 0.143359 -1.605 0.1085
## [7,] -0.132724 0.093303 -1.423 0.1549
## [8,] 0.192176 0.119738 1.605 0.1085
## [9,] 0.186430 0.082202 2.268 0.0233 *
## [10,] -0.045754 0.114979 -0.398 0.6907
## [11,] -0.095779 0.074834 -1.280 0.2006
## [12,] 0.196127 0.096030 2.042 0.0411 *
## [13,] 0.230925 0.107752 2.143 0.0321 *
## [14,] -0.102340 0.150716 -0.679 0.4971
## [15,] 0.236658 0.098094 2.413 0.0158 *
## [16,] 0.015570 0.125887 0.124 0.9016
## [17,] -0.176499 0.090172 -1.957 0.0503 .
## [18,] 0.361047 0.126122 2.863 0.0042 **
## [19,] 0.210948 0.082080 2.570 0.0102 *
## [20,] 0.007243 0.105286 0.069 0.9452
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.509852 -1.985065 -0.3104024 -0.1313747
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.530 -0.2301 -0.1327 0.19218
## [2,] 0.186 -0.0458 -0.0958 0.19613
## [3,] 0.231 -0.1023 0.2367 0.01557
## [4,] -0.176 0.3610 0.2109 0.00724
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 193.03280 104.50542 -87.23968 -76.53569
## [2,] 104.50542 124.17601 -68.72406 -71.27495
## [3,] -87.23968 -68.72406 213.36680 109.17584
## [4,] -76.53569 -71.27495 109.17584 149.42681
## ----
## aic= 19.2506
## bic= 19.65202
## Number of parameters: 20
## initial estimates: -1.5389 -3.4827 -1.3903 -0.3037 0.4433 0.1777 -0.0223 0.0561 0.0391 0.3981 0.0487 -0.0918 0.3379 -0.1559 0.1972 0.5077 0.2166 -0.0979 0.1246 0.4987
## Par. lower-bounds: -3.5561 -6.352 -4.1197 -2.2595 0.2757 0.0411 -0.1684 -0.1392 -0.1994 0.2039 -0.1591 -0.3697 0.111 -0.3407 -5e-04 0.2434 0.054 -0.2304 -0.017 0.3094
## Par. upper-bounds: 0.4783 -0.6134 1.3391 1.6522 0.611 0.3143 0.1238 0.2514 0.2776 0.5924 0.2565 0.186 0.5647 0.0289 0.3949 0.772 0.3791 0.0345 0.2663 0.6881
## Final Estimates: -1.446099 -3.294436 -1.253509 -0.385307 0.4389453 0.1795205 -0.01971568 0.06699609 0.030209 0.4018076 0.05393867 -0.06968678 0.3314184 -0.1531734 0.2009871 0.5237772 0.2204101 -0.09952418 0.1223251 0.4891457
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.44610 1.00411 -1.440 0.14982
## [2,] -3.29444 1.43311 -2.299 0.02152 *
## [3,] -1.25351 1.35943 -0.922 0.35648
## [4,] -0.38531 0.97299 -0.396 0.69210
## [5,] 0.43895 0.08371 5.244 1.57e-07 ***
## [6,] 0.17952 0.06826 2.630 0.00854 **
## [7,] -0.01972 0.07298 -0.270 0.78705
## [8,] 0.06700 0.09701 0.691 0.48982
## [9,] 0.03021 0.11947 0.253 0.80038
## [10,] 0.40181 0.09742 4.125 3.71e-05 ***
## [11,] 0.05394 0.10417 0.518 0.60461
## [12,] -0.06969 0.13847 -0.503 0.61478
## [13,] 0.33142 0.11333 2.924 0.00345 **
## [14,] -0.15317 0.09241 -1.658 0.09741 .
## [15,] 0.20099 0.09882 2.034 0.04197 *
## [16,] 0.52378 0.13136 3.987 6.68e-05 ***
## [17,] 0.22041 0.08112 2.717 0.00658 **
## [18,] -0.09952 0.06614 -1.505 0.13239
## [19,] 0.12233 0.07073 1.729 0.08374 .
## [20,] 0.48915 0.09402 5.203 1.96e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.446099 -3.294436 -1.253509 -0.385307
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.4389 0.1795 -0.0197 0.0670
## [2,] 0.0302 0.4018 0.0539 -0.0697
## [3,] 0.3314 -0.1532 0.2010 0.5238
## [4,] 0.2204 -0.0995 0.1223 0.4891
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 132.11043 106.09562 -2.78414 -12.46285
## [2,] 106.09562 269.11086 28.66962 -23.60760
## [3,] -2.78414 28.66962 242.15254 98.39572
## [4,] -12.46285 -23.60760 98.39572 124.05114
## ----
## aic= 20.20567
## bic= 20.60708
## Number of parameters: 20
## initial estimates: -1.8022 -3.2039 -0.043 -0.1146 0.1823 0.0756 -0.2186 -0.1482 -0.2494 0.4864 -0.1547 -0.6486 0.1067 -0.1956 0.6009 0.2242 0.1715 -0.1164 0.1003 0.3159
## Par. lower-bounds: -3.9868 -6.1464 -1.451 -0.9178 -0.0576 -0.0952 -0.4488 -0.6283 -0.5724 0.2563 -0.4648 -1.2953 -0.0479 -0.3057 0.4525 -0.0852 0.0833 -0.1792 0.0157 0.1394
## Par. upper-bounds: 0.3824 -0.2614 1.3651 0.6885 0.4221 0.2465 0.0116 0.3318 0.0737 0.7165 0.1554 -0.002 0.2613 -0.0854 0.7493 0.5337 0.2597 -0.0536 0.185 0.4924
## Final Estimates: -1.743156 -3.093005 -0.01456663 -0.1407665 0.1734622 0.07968845 -0.2189745 -0.1238558 -0.2653268 0.4938009 -0.1554764 -0.6040967 0.1039882 -0.1943107 0.6009056 0.2328351 0.1748642 -0.1179382 0.1005403 0.3063169
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.74316 1.09057 -1.598 0.109956
## [2,] -3.09301 1.47254 -2.100 0.035688 *
## [3,] -0.01457 0.70394 -0.021 0.983490
## [4,] -0.14077 0.40088 -0.351 0.725477
## [5,] 0.17346 0.11957 1.451 0.146846
## [6,] 0.07969 0.08530 0.934 0.350183
## [7,] -0.21897 0.11507 -1.903 0.057046 .
## [8,] -0.12386 0.23861 -0.519 0.603707
## [9,] -0.26533 0.16146 -1.643 0.100314
## [10,] 0.49380 0.11518 4.287 1.81e-05 ***
## [11,] -0.15548 0.15539 -1.001 0.317031
## [12,] -0.60410 0.32221 -1.875 0.060813 .
## [13,] 0.10399 0.07691 1.352 0.176338
## [14,] -0.19431 0.05487 -3.541 0.000398 ***
## [15,] 0.60091 0.07402 8.118 4.44e-16 ***
## [16,] 0.23284 0.15348 1.517 0.129269
## [17,] 0.17486 0.04398 3.976 7.01e-05 ***
## [18,] -0.11794 0.03138 -3.759 0.000171 ***
## [19,] 0.10054 0.04233 2.375 0.017533 *
## [20,] 0.30632 0.08777 3.490 0.000483 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.743156 -3.093005 -0.01456663 -0.1407665
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.173 0.0797 -0.219 -0.124
## [2,] -0.265 0.4938 -0.155 -0.604
## [3,] 0.104 -0.1943 0.601 0.233
## [4,] 0.175 -0.1179 0.101 0.306
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 163.421571 160.02330 -43.81062 -3.590775
## [2,] 160.023303 297.99122 -59.79340 -18.155730
## [3,] -43.810622 -59.79340 67.61241 17.019826
## [4,] -3.590775 -18.15573 17.01983 22.110033
## ----
## aic= 17.11621
## bic= 17.51762
## Number of parameters: 20
## initial estimates: -1.5388 -2.6394 -0.4819 0.1029 0.3522 -0.1882 0.1026 -0.2467 -0.0723 0.2083 0.054 -0.2897 -0.1197 0.2336 0.4688 0.0859 -0.1679 0.0725 0.1215 0.2315
## Par. lower-bounds: -4.4462 -5.2066 -3.4958 -2.5987 0.1691 -0.4078 -0.1001 -0.5122 -0.2341 0.0145 -0.125 -0.5241 -0.3095 0.006 0.2586 -0.1893 -0.338 -0.1315 -0.0669 -0.0152
## Par. upper-bounds: 1.3687 -0.0722 2.532 2.8046 0.5354 0.0313 0.3053 0.0188 0.0894 0.4021 0.233 -0.0553 0.0701 0.4612 0.6789 0.3612 0.0023 0.2765 0.3098 0.4782
## Final Estimates: -1.46199 -2.525373 -0.4119746 -0.005825337 0.3480354 -0.1879696 0.1053277 -0.2422171 -0.07859785 0.2086876 0.05810044 -0.2829567 -0.1235306 0.2338338 0.4713027 0.09007746 -0.1618965 0.07217792 0.1175636 0.2250857
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.461990 1.456417 -1.004 0.315462
## [2,] -2.525373 1.298003 -1.946 0.051705 .
## [3,] -0.411975 1.529323 -0.269 0.787634
## [4,] -0.005825 1.404060 -0.004 0.996690
## [5,] 0.348035 0.091220 3.815 0.000136 ***
## [6,] -0.187970 0.109592 -1.715 0.086313 .
## [7,] 0.105328 0.101117 1.042 0.297579
## [8,] -0.242217 0.132370 -1.830 0.067272 .
## [9,] -0.078598 0.080796 -0.973 0.330656
## [10,] 0.208688 0.097096 2.149 0.031611 *
## [11,] 0.058100 0.089563 0.649 0.516526
## [12,] -0.282957 0.117240 -2.413 0.015801 *
## [13,] -0.123531 0.094530 -1.307 0.191286
## [14,] 0.233834 0.113660 2.057 0.039657 *
## [15,] 0.471303 0.104785 4.498 6.87e-06 ***
## [16,] 0.090077 0.137179 0.657 0.511411
## [17,] -0.161896 0.084959 -1.906 0.056704 .
## [18,] 0.072178 0.102268 0.706 0.480331
## [19,] 0.117564 0.094192 1.248 0.211983
## [20,] 0.225086 0.123289 1.826 0.067898 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.46199 -2.525373 -0.4119746 -0.005825337
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3480 -0.1880 0.1053 -0.2422
## [2,] -0.0786 0.2087 0.0581 -0.2830
## [3,] -0.1235 0.2338 0.4713 0.0901
## [4,] -0.1619 0.0722 0.1176 0.2251
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 292.2570 130.0061 -126.1081 -112.5897
## [2,] 130.0061 229.2550 -114.3061 -133.8953
## [3,] -126.1081 -114.3061 313.8182 198.5104
## [4,] -112.5897 -133.8953 198.5104 253.4681
## ----
## aic= 21.24548
## bic= 21.6469
## Number of parameters: 20
## initial estimates: -0.5572 -1.1539 -0.5742 -0.3433 0.2273 -0.1653 -0.0811 0.0527 0.0204 0.1676 -0.0586 0.0025 0.3115 0.0011 0.3042 0.0551 0.2121 -0.0258 0.0901 0.486
## Par. lower-bounds: -1.5209 -2.1265 -1.7791 -1.8158 0.0617 -0.327 -0.2055 -0.0444 -0.1468 0.0045 -0.1842 -0.0955 0.1044 -0.201 0.1486 -0.0663 -0.041 -0.2728 -0.1 0.3377
## Par. upper-bounds: 0.4065 -0.1814 0.6307 1.1291 0.393 -0.0037 0.0433 0.1498 0.1875 0.3307 0.0669 0.1004 0.5186 0.2032 0.4598 0.1764 0.4652 0.2211 0.2802 0.6343
## Final Estimates: -0.5123054 -1.103735 -0.4975257 -0.4272603 0.2217007 -0.1663219 -0.07762438 0.05992737 0.01408329 0.1664603 -0.0547715 0.01054866 0.3018643 -0.0006365566 0.3101284 0.06738933 0.2226102 -0.02395376 0.08363474 0.4724596
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.5123054 0.4800044 -1.067 0.28584
## [2,] -1.1037353 0.4848664 -2.276 0.02282 *
## [3,] -0.4975257 0.6004074 -0.829 0.40730
## [4,] -0.4272603 0.7347872 -0.581 0.56092
## [5,] 0.2217007 0.0826695 2.682 0.00732 **
## [6,] -0.1663219 0.0806746 -2.062 0.03924 *
## [7,] -0.0776244 0.0621459 -1.249 0.21164
## [8,] 0.0599274 0.0480451 1.247 0.21228
## [9,] 0.0140833 0.0835072 0.169 0.86607
## [10,] 0.1664603 0.0816276 2.039 0.04142 *
## [11,] -0.0547715 0.0627666 -0.873 0.38287
## [12,] 0.0105487 0.0485271 0.217 0.82791
## [13,] 0.3018643 0.1035490 2.915 0.00355 **
## [14,] -0.0006366 0.0947123 -0.007 0.99464
## [15,] 0.3101284 0.0779456 3.979 6.93e-05 ***
## [16,] 0.0673893 0.0602581 1.118 0.26342
## [17,] 0.2226102 0.1265365 1.759 0.07853 .
## [18,] -0.0239538 0.1234673 -0.194 0.84617
## [19,] 0.0836347 0.0951261 0.879 0.37929
## [20,] 0.4724596 0.0735424 6.424 1.32e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.5123054 -1.103735 -0.4975257 -0.4272603
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2217 -0.166322 -0.0776 0.0599
## [2,] 0.0141 0.166460 -0.0548 0.0105
## [3,] 0.3019 -0.000637 0.3101 0.0674
## [4,] 0.2226 -0.023954 0.0836 0.4725
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 32.427905 5.8928194 7.509780 -10.1002585
## [2,] 5.892819 33.0790085 2.554306 0.8988845
## [3,] 7.509780 2.5543059 51.012407 8.9290280
## [4,] -10.100259 0.8988845 8.929028 75.9788456
## ----
## aic= 15.35761
## bic= 15.75902
## Number of parameters: 20
## initial estimates: -1.1072 -2.133 -0.4108 -0.3145 0.3205 -0.1566 -0.0287 -0.1778 -0.275 0.2782 -0.1421 -0.1808 0.0596 0.2199 0.6019 -0.1945 -0.0242 0.1708 0.3407 0.1971
## Par. lower-bounds: -2.8938 -4.2355 -2.9323 -2.61 0.1404 -0.3155 -0.1784 -0.3432 -0.4869 0.0913 -0.3183 -0.3754 -0.1946 -0.0042 0.3905 -0.4279 -0.2556 -0.0333 0.1483 -0.0153
## Par. upper-bounds: 0.6795 -0.0306 2.1107 1.981 0.5006 0.0022 0.1211 -0.0125 -0.063 0.4652 0.0341 0.0138 0.3137 0.4441 0.8132 0.0388 0.2072 0.3749 0.5331 0.4096
## Final Estimates: -1.035078 -2.056357 -0.335307 -0.4031573 0.3124183 -0.1561657 -0.02925255 -0.1708361 -0.2835684 0.2787357 -0.1427011 -0.1733807 0.05111986 0.2204356 0.6012474 -0.187226 -0.01426963 0.1702635 0.3414295 0.188529
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.03508 0.89038 -1.163 0.245026
## [2,] -2.05636 1.04713 -1.964 0.049552 *
## [3,] -0.33531 1.25465 -0.267 0.789275
## [4,] -0.40316 1.14363 -0.353 0.724444
## [5,] 0.31242 0.08969 3.483 0.000495 ***
## [6,] -0.15617 0.07942 -1.966 0.049274 *
## [7,] -0.02925 0.07487 -0.391 0.696018
## [8,] -0.17084 0.08238 -2.074 0.038091 *
## [9,] -0.28357 0.10548 -2.688 0.007178 **
## [10,] 0.27874 0.09341 2.984 0.002844 **
## [11,] -0.14270 0.08805 -1.621 0.105105
## [12,] -0.17338 0.09688 -1.790 0.073507 .
## [13,] 0.05112 0.12639 0.404 0.685863
## [14,] 0.22044 0.11192 1.970 0.048885 *
## [15,] 0.60125 0.10551 5.699 1.21e-08 ***
## [16,] -0.18723 0.11608 -1.613 0.106771
## [17,] -0.01427 0.11521 -0.124 0.901424
## [18,] 0.17026 0.10201 1.669 0.095115 .
## [19,] 0.34143 0.09617 3.550 0.000385 ***
## [20,] 0.18853 0.10581 1.782 0.074785 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.035078 -2.056357 -0.335307 -0.4031573
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3124 -0.156 -0.0293 -0.171
## [2,] -0.2836 0.279 -0.1427 -0.173
## [3,] 0.0511 0.220 0.6012 -0.187
## [4,] -0.0143 0.170 0.3414 0.189
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 111.63901 74.42614 -41.85585 -50.59916
## [2,] 74.42614 154.40806 -90.63831 -67.16861
## [3,] -41.85585 -90.63831 221.68341 132.64401
## [4,] -50.59916 -67.16861 132.64401 184.18137
## ----
## aic= 19.35053
## bic= 19.75194
## Number of parameters: 20
## initial estimates: -1.2671 -2.4416 -0.8111 0.0182 0.5423 -0.0332 -0.0383 -0.1329 0.0235 0.3913 -0.1038 0.2004 0.2397 0.0512 0.6267 -0.0822 -0.0719 -0.1743 0.1966 -0.0062
## Par. lower-bounds: -3.2165 -4.6282 -4.3572 -2.3919 0.3976 -0.2017 -0.1284 -0.2961 -0.1388 0.2022 -0.2049 0.0174 -0.0236 -0.2554 0.4628 -0.3791 -0.2508 -0.3827 0.0852 -0.208
## Par. upper-bounds: 0.6824 -0.255 2.7349 2.4283 0.6871 0.1354 0.0518 0.0303 0.1859 0.5804 -0.0027 0.3835 0.503 0.3579 0.7906 0.2147 0.1071 0.0341 0.308 0.1955
## Final Estimates: -1.210341 -2.340002 -0.6693642 -0.09220495 0.5369078 -0.02915865 -0.03639882 -0.1289149 0.01384006 0.39847 -0.100342 0.2075391 0.2261573 0.06124209 0.631488 -0.07228131 -0.06134771 -0.1820762 0.1928686 -0.01392773
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.21034 0.96963 -1.248 0.211939
## [2,] -2.34000 1.09036 -2.146 0.031866 *
## [3,] -0.66936 1.76642 -0.379 0.704734
## [4,] -0.09220 1.20169 -0.077 0.938839
## [5,] 0.53691 0.07183 7.474 7.77e-14 ***
## [6,] -0.02916 0.08394 -0.347 0.728322
## [7,] -0.03640 0.04489 -0.811 0.417484
## [8,] -0.12891 0.08126 -1.586 0.112643
## [9,] 0.01384 0.08077 0.171 0.863955
## [10,] 0.39847 0.09439 4.221 2.43e-05 ***
## [11,] -0.10034 0.05048 -1.988 0.046833 *
## [12,] 0.20754 0.09136 2.272 0.023113 *
## [13,] 0.22616 0.13086 1.728 0.083942 .
## [14,] 0.06124 0.15292 0.400 0.688799
## [15,] 0.63149 0.08177 7.722 1.13e-14 ***
## [16,] -0.07228 0.14800 -0.488 0.625268
## [17,] -0.06135 0.08903 -0.689 0.490757
## [18,] -0.18208 0.10403 -1.750 0.080072 .
## [19,] 0.19287 0.05563 3.467 0.000526 ***
## [20,] -0.01393 0.10066 -0.138 0.889948
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.210341 -2.340002 -0.6693642 -0.09220495
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.5369 -0.0292 -0.0364 -0.1289
## [2,] 0.0138 0.3985 -0.1003 0.2075
## [3,] 0.2262 0.0612 0.6315 -0.0723
## [4,] -0.0613 -0.1821 0.1929 -0.0139
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 125.60619 59.54849 -42.30820 -11.73438
## [2,] 59.54849 158.82097 -90.93729 -81.96256
## [3,] -42.30820 -90.93729 416.80367 150.25295
## [4,] -11.73438 -81.96256 150.25295 192.90056
## ----
## aic= 20.63077
## bic= 21.03219
## Number of parameters: 20
## initial estimates: -0.7363 -1.9244 -0.5741 -0.1789 -0.0304 0.0105 -0.0557 -0.1004 -0.4789 0.4701 -0.2054 -0.1587 0.096 -0.0498 -0.0061 0.2801 0.42 -0.1878 0.0786 0.1494
## Par. lower-bounds: -1.8225 -3.806 -2.4024 -1.6767 -0.2231 -0.0914 -0.1673 -0.2391 -0.8128 0.2935 -0.3987 -0.3989 -0.2284 -0.2214 -0.1939 0.0466 0.1543 -0.3284 -0.0752 -0.0419
## Par. upper-bounds: 0.3498 -0.0428 1.2542 1.3188 0.1623 0.1125 0.0558 0.0383 -0.1451 0.6467 -0.0122 0.0816 0.4204 0.1219 0.1817 0.5135 0.6857 -0.0472 0.2325 0.3406
## Final Estimates: -0.6947775 -1.824933 -0.5135342 -0.2506302 -0.03705968 0.01188982 -0.05238751 -0.09751407 -0.4948005 0.4733622 -0.1973973 -0.1517291 0.08635456 -0.04776932 -0.001205009 0.2842977 0.4314242 -0.1901159 0.07285154 0.1443805
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.694778 0.541225 -1.284 0.19924
## [2,] -1.824933 0.940240 -1.941 0.05227 .
## [3,] -0.513534 0.910275 -0.564 0.57265
## [4,] -0.250630 0.747638 -0.335 0.73745
## [5,] -0.037060 0.096078 -0.386 0.69970
## [6,] 0.011890 0.050948 0.233 0.81547
## [7,] -0.052388 0.055661 -0.941 0.34661
## [8,] -0.097514 0.069265 -1.408 0.15918
## [9,] -0.494800 0.166912 -2.964 0.00303 **
## [10,] 0.473362 0.088509 5.348 8.89e-08 ***
## [11,] -0.197397 0.096685 -2.042 0.04119 *
## [12,] -0.151729 0.120331 -1.261 0.20733
## [13,] 0.086355 0.161606 0.534 0.59310
## [14,] -0.047769 0.085691 -0.557 0.57721
## [15,] -0.001205 0.092980 -0.013 0.98966
## [16,] 0.284298 0.116372 2.443 0.01457 *
## [17,] 0.431424 0.132720 3.251 0.00115 **
## [18,] -0.190116 0.070377 -2.701 0.00690 **
## [19,] 0.072852 0.076778 0.949 0.34269
## [20,] 0.144380 0.095667 1.509 0.13125
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.6947775 -1.824933 -0.5135342 -0.2506302
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] -0.0371 0.0119 -0.05239 -0.0975
## [2,] -0.4948 0.4734 -0.19740 -0.1517
## [3,] 0.0864 -0.0478 -0.00121 0.2843
## [4,] 0.4314 -0.1901 0.07285 0.1444
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 41.25694 39.39010 -16.11324 -14.13986
## [2,] 39.39010 124.51314 -27.88763 -33.38446
## [3,] -16.11324 -27.88763 116.71596 47.73134
## [4,] -14.13986 -33.38446 47.73134 78.72315
## ----
## aic= 17.14787
## bic= 17.54929
## Number of parameters: 20
## initial estimates: -1.3835 -1.8746 -0.8987 -0.4209 0.4834 -0.261 0.064 0.0646 0.003 -0.0056 -0.0261 0.1031 -0.0517 0.5041 0.295 -0.3453 0.0898 0.0233 0.0656 0.014
## Par. lower-bounds: -3.5309 -3.3401 -3.498 -2.2364 0.3031 -0.5453 -0.0744 -0.146 -0.12 -0.1996 -0.1206 -0.0407 -0.2699 0.16 0.1274 -0.6003 -0.0627 -0.217 -0.0515 -0.1641
## Par. upper-bounds: 0.7639 -0.409 1.7006 1.3946 0.6637 0.0233 0.2025 0.2753 0.126 0.1884 0.0684 0.2468 0.1665 0.8482 0.4626 -0.0903 0.2422 0.2636 0.1827 0.1921
## Final Estimates: -1.316094 -1.799418 -0.7845015 -0.5035372 0.4775906 -0.2567172 0.0638669 0.07150372 -0.003484249 -0.0008183291 -0.02629186 0.1107478 -0.06159587 0.5113886 0.2947086 -0.3336374 0.09687756 0.01804152 0.06580929 0.005534808
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.3160945 1.0690853 -1.231 0.218305
## [2,] -1.7994179 0.7325006 -2.457 0.014028 *
## [3,] -0.7845015 1.2962700 -0.605 0.545047
## [4,] -0.5035372 0.9056022 -0.556 0.578194
## [5,] 0.4775906 0.0903337 5.287 1.24e-07 ***
## [6,] -0.2567172 0.1444281 -1.777 0.075490 .
## [7,] 0.0638669 0.0691582 0.923 0.355752
## [8,] 0.0715037 0.1048237 0.682 0.495155
## [9,] -0.0034842 0.0626859 -0.056 0.955674
## [10,] -0.0008183 0.1022392 -0.008 0.993614
## [11,] -0.0262919 0.0473745 -0.555 0.578909
## [12,] 0.1107478 0.0718021 1.542 0.122976
## [13,] -0.0615959 0.1088045 -0.566 0.571316
## [14,] 0.5113886 0.1720200 2.973 0.002951 **
## [15,] 0.2947086 0.0838712 3.514 0.000442 ***
## [16,] -0.3336374 0.1271377 -2.624 0.008685 **
## [17,] 0.0968776 0.0760208 1.274 0.202538
## [18,] 0.0180415 0.1201736 0.150 0.880663
## [19,] 0.0658093 0.0585953 1.123 0.261389
## [20,] 0.0055348 0.0888254 0.062 0.950315
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.316094 -1.799418 -0.7845015 -0.5035372
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.47759 -0.256717 0.0639 0.07150
## [2,] -0.00348 -0.000818 -0.0263 0.11075
## [3,] -0.06160 0.511389 0.2947 -0.33364
## [4,] 0.09688 0.018042 0.0658 0.00553
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 160.48743 64.4037607 -39.6738304 -19.46050
## [2,] 64.40376 75.2622153 -0.8706215 -10.08428
## [3,] -39.67383 -0.8706215 236.0603793 66.94759
## [4,] -19.46050 -10.0842752 66.9475888 115.23308
## ----
## aic= 19.19982
## bic= 19.60124
## Number of parameters: 20
## initial estimates: -1.0867 -1.9129 -0.3612 -0.0814 0.1417 0.3254 -0.055 -0.0211 -0.1698 0.534 -0.1046 0.148 0.3022 -0.3592 0.042 -0.0367 0.352 -0.2702 0.1013 0.087
## Par. lower-bounds: -2.8921 -3.9741 -2.8106 -2.8222 -0.0413 0.134 -0.2118 -0.1622 -0.3787 0.3155 -0.2836 -0.0131 0.0539 -0.6189 -0.1708 -0.2281 0.0742 -0.5607 -0.1367 -0.1272
## Par. upper-bounds: 0.7187 0.1483 2.0882 2.6594 0.3247 0.5168 0.1018 0.12 0.0391 0.7526 0.0744 0.3091 0.5504 -0.0995 0.2547 0.1547 0.6299 0.0204 0.3393 0.3012
## Final Estimates: -1.033929 -1.814336 -0.3089327 -0.2019872 0.1344272 0.331099 -0.05504045 -0.0155368 -0.1833585 0.5446394 -0.1047416 0.1584314 0.2949777 -0.3535579 0.04190146 -0.03119791 0.3686381 -0.2831207 0.1014418 0.07428138
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.03393 0.89850 -1.151 0.249841
## [2,] -1.81434 1.02887 -1.763 0.077828 .
## [3,] -0.30893 1.21757 -0.254 0.799705
## [4,] -0.20199 1.36683 -0.148 0.882518
## [5,] 0.13443 0.09083 1.480 0.138893
## [6,] 0.33110 0.09525 3.476 0.000509 ***
## [7,] -0.05504 0.07827 -0.703 0.481914
## [8,] -0.01554 0.07003 -0.222 0.824433
## [9,] -0.18336 0.10403 -1.763 0.077968 .
## [10,] 0.54464 0.10909 4.993 5.95e-07 ***
## [11,] -0.10474 0.08964 -1.169 0.242604
## [12,] 0.15843 0.08021 1.975 0.048250 *
## [13,] 0.29498 0.12313 2.396 0.016588 *
## [14,] -0.35356 0.12912 -2.738 0.006176 **
## [15,] 0.04190 0.10609 0.395 0.692869
## [16,] -0.03120 0.09494 -0.329 0.742452
## [17,] 0.36864 0.13822 2.667 0.007654 **
## [18,] -0.28312 0.14495 -1.953 0.050788 .
## [19,] 0.10144 0.11910 0.852 0.394357
## [20,] 0.07428 0.10658 0.697 0.485840
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.033929 -1.814336 -0.3089327 -0.2019872
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.134 0.331 -0.0550 -0.0155
## [2,] -0.183 0.545 -0.1047 0.1584
## [3,] 0.295 -0.354 0.0419 -0.0312
## [4,] 0.369 -0.283 0.1014 0.0743
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 110.96453 63.48483 -51.56871 -12.07883
## [2,] 63.48483 145.54072 -87.65589 -99.42988
## [3,] -51.56871 -87.65589 203.89400 128.89477
## [4,] -12.07883 -99.42988 128.89477 256.95187
## ----
## aic= 19.61805
## bic= 20.01947
## Number of parameters: 20
## initial estimates: -1.0874 -2.1257 -0.3419 -0.4055 0.4254 -0.2658 -0.1154 -0.2506 -0.0342 0.0231 -0.2578 -0.1647 -0.0786 0.0013 0.4108 0.1693 -0.1849 -0.007 0.1076 0.0884
## Par. lower-bounds: -2.8242 -3.9922 -2.2248 -2.0203 0.2684 -0.4308 -0.2775 -0.4473 -0.203 -0.1542 -0.432 -0.3761 -0.2489 -0.1776 0.235 -0.044 -0.331 -0.1604 -0.0431 -0.0945
## Par. upper-bounds: 0.6494 -0.2592 1.541 1.2093 0.5825 -0.1009 0.0467 -0.0539 0.1346 0.2004 -0.0836 0.0467 0.0917 0.1801 0.5865 0.3825 -0.0388 0.1463 0.2583 0.2713
## Final Estimates: -1.042591 -2.065888 -0.2741075 -0.4728572 0.4199915 -0.2661005 -0.1123927 -0.2469559 -0.04147036 0.02275697 -0.2538044 -0.1598224 -0.08688396 0.0008606153 0.41527 0.174797 -0.1766939 -0.006635909 0.1031081 0.08287226
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.0425912 0.8647111 -1.206 0.22793
## [2,] -2.0658885 0.9301706 -2.221 0.02635 *
## [3,] -0.2741075 0.9395657 -0.292 0.77049
## [4,] -0.4728572 0.8060957 -0.587 0.55747
## [5,] 0.4199915 0.0780517 5.381 7.41e-08 ***
## [6,] -0.2661005 0.0824482 -3.227 0.00125 **
## [7,] -0.1123927 0.0808142 -1.391 0.16430
## [8,] -0.2469559 0.0980673 -2.518 0.01179 *
## [9,] -0.0414704 0.0839732 -0.494 0.62141
## [10,] 0.0227570 0.0888890 0.256 0.79794
## [11,] -0.2538044 0.0869516 -2.919 0.00351 **
## [12,] -0.1598224 0.1054876 -1.515 0.12975
## [13,] -0.0868840 0.0850600 -1.021 0.30704
## [14,] 0.0008606 0.0926596 0.009 0.99259
## [15,] 0.4152700 0.0880545 4.716 2.40e-06 ***
## [16,] 0.1747970 0.1064915 1.641 0.10071
## [17,] -0.1766939 0.0727933 -2.427 0.01521 *
## [18,] -0.0066359 0.0770976 -0.086 0.93141
## [19,] 0.1031081 0.0753603 1.368 0.17125
## [20,] 0.0828723 0.0914298 0.906 0.36472
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.042591 -2.065888 -0.2741075 -0.4728572
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.4200 -0.266100 -0.112 -0.2470
## [2,] -0.0415 0.022757 -0.254 -0.1598
## [3,] -0.0869 0.000861 0.415 0.1748
## [4,] -0.1767 -0.006636 0.103 0.0829
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 107.15277 44.00728 -22.70327 -15.28888
## [2,] 44.00728 123.98007 -37.25175 -17.99227
## [3,] -22.70327 -37.25175 126.34932 50.01326
## [4,] -15.28888 -17.99227 50.01326 93.13967
## ----
## aic= 18.63095
## bic= 19.03237
## Number of parameters: 20
## initial estimates: -1.5731 -1.8005 -0.7813 -0.3538 0.3247 0.3159 -0.0198 -0.175 -0.0516 0.4298 0.0232 -0.1021 0.4041 -0.0972 0.5453 0.2885 0.0857 0.0616 -0.1588 0.8484
## Par. lower-bounds: -3.7911 -3.2582 -2.6553 -1.689 0.1389 0.0242 -0.1803 -0.4166 -0.1737 0.238 -0.0823 -0.2608 0.2471 -0.3436 0.4096 0.0844 -0.0261 -0.1141 -0.2554 0.703
## Par. upper-bounds: 0.6449 -0.3429 1.0927 0.9814 0.5105 0.6077 0.1407 0.0665 0.0706 0.6215 0.1287 0.0567 0.5611 0.1493 0.6809 0.4926 0.1976 0.2372 -0.0622 0.9938
## Final Estimates: -1.549502 -1.764398 -0.7295292 -0.4029657 0.3155295 0.3192928 -0.01192734 -0.1688441 -0.05845248 0.4328225 0.02940642 -0.09751018 0.3972628 -0.09365324 0.5516747 0.2929982 0.0897553 0.05898126 -0.1628412 0.8458628
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.54950 1.10392 -1.404 0.160429
## [2,] -1.76440 0.72630 -2.429 0.015128 *
## [3,] -0.72953 0.93198 -0.783 0.433762
## [4,] -0.40297 0.66345 -0.607 0.543602
## [5,] 0.31553 0.09252 3.411 0.000648 ***
## [6,] 0.31929 0.14578 2.190 0.028506 *
## [7,] -0.01193 0.07977 -0.150 0.881140
## [8,] -0.16884 0.12067 -1.399 0.161758
## [9,] -0.05845 0.06087 -0.960 0.336897
## [10,] 0.43282 0.09591 4.513 6.40e-06 ***
## [11,] 0.02941 0.05248 0.560 0.575270
## [12,] -0.09751 0.07939 -1.228 0.219383
## [13,] 0.39726 0.07811 5.086 3.65e-07 ***
## [14,] -0.09365 0.12307 -0.761 0.446684
## [15,] 0.55167 0.06735 8.191 2.22e-16 ***
## [16,] 0.29300 0.10189 2.876 0.004030 **
## [17,] 0.08976 0.05560 1.614 0.106476
## [18,] 0.05898 0.08761 0.673 0.500821
## [19,] -0.16284 0.04795 -3.396 0.000683 ***
## [20,] 0.84586 0.07253 11.662 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.549502 -1.764398 -0.7295292 -0.4029657
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3155 0.3193 -0.0119 -0.1688
## [2,] -0.0585 0.4328 0.0294 -0.0975
## [3,] 0.3973 -0.0937 0.5517 0.2930
## [4,] 0.0898 0.0590 -0.1628 0.8459
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 158.050869 60.642537 -2.689091 -15.158059
## [2,] 60.642537 68.414850 -5.738655 -4.111902
## [3,] -2.689091 -5.738655 112.652434 55.117600
## [4,] -15.158059 -4.111902 55.117600 57.088971
## ----
## aic= 17.21081
## bic= 17.61223
## Number of parameters: 20
## initial estimates: -1.5807 -1.9923 -0.6287 -0.0889 0.3908 -0.0094 0.2644 -0.5339 -0.0471 0.2265 0.0573 -0.2863 -0.0199 -0.0431 0.2143 0.1453 -0.1414 0.2456 0.0044 0.4084
## Par. lower-bounds: -4.3749 -3.8176 -3.4127 -2.1845 0.214 -0.3146 0.0779 -0.7968 -0.1626 0.0271 -0.0645 -0.4581 -0.1961 -0.3472 0.0285 -0.1166 -0.274 0.0167 -0.1355 0.2112
## Par. upper-bounds: 1.2135 -0.1671 2.1554 2.0068 0.5677 0.2959 0.4509 -0.271 0.0684 0.4259 0.1791 -0.1146 0.1562 0.261 0.4001 0.4073 -0.0088 0.4745 0.1442 0.6056
## Final Estimates: -1.493522 -1.920976 -0.5280884 -0.180497 0.3853356 -0.00879979 0.2677825 -0.5261661 -0.0516202 0.2269672 0.06005379 -0.2799955 -0.0263116 -0.04247072 0.2181482 0.1542545 -0.1355669 0.2449858 0.0008268483 0.4002315
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.4935216 1.3922549 -1.073 0.28339
## [2,] -1.9209761 0.9107587 -2.109 0.03493 *
## [3,] -0.5280884 1.3883722 -0.380 0.70367
## [4,] -0.1804970 1.0467762 -0.172 0.86310
## [5,] 0.3853356 0.0880991 4.374 1.22e-05 ***
## [6,] -0.0087998 0.1524918 -0.058 0.95398
## [7,] 0.2677825 0.0930246 2.879 0.00399 **
## [8,] -0.5261661 0.1310320 -4.016 5.93e-05 ***
## [9,] -0.0516202 0.0576312 -0.896 0.37041
## [10,] 0.2269672 0.0997496 2.275 0.02288 *
## [11,] 0.0600538 0.0608222 0.987 0.32346
## [12,] -0.2799955 0.0857126 -3.267 0.00109 **
## [13,] -0.0263116 0.0878523 -0.299 0.76456
## [14,] -0.0424707 0.1520247 -0.279 0.77996
## [15,] 0.2181482 0.0926966 2.353 0.01860 *
## [16,] 0.1542545 0.1306509 1.181 0.23774
## [17,] -0.1355669 0.0662328 -2.047 0.04068 *
## [18,] 0.2449858 0.1146211 2.137 0.03257 *
## [19,] 0.0008268 0.0696204 0.012 0.99052
## [20,] 0.4002315 0.0984331 4.066 4.78e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.493522 -1.920976 -0.5280884 -0.180497
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3853 -0.0088 0.267782 -0.526
## [2,] -0.0516 0.2270 0.060054 -0.280
## [3,] -0.0263 -0.0425 0.218148 0.154
## [4,] -0.1356 0.2450 0.000827 0.400
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 271.98068 104.63759 -65.62345 -82.45766
## [2,] 104.63759 116.38863 -56.55972 -61.09641
## [3,] -65.62345 -56.55972 270.46703 104.65140
## [4,] -82.45766 -61.09641 104.65140 153.72588
## ----
## aic= 20.25241
## bic= 20.65383
## Number of parameters: 20
## initial estimates: -0.2617 -1.7867 -0.4492 -0.238 0.0132 0.0998 0.0402 0.0104 -0.3469 0.4208 -0.0103 -0.1664 0.2236 -0.3032 0.0927 -0.1078 0.2526 -0.0986 0.0059 0.0867
## Par. lower-bounds: -1.5413 -3.4891 -2.2595 -1.8165 -0.2328 -0.0147 -0.1478 -0.1791 -0.6741 0.2684 -0.2604 -0.4185 -0.1244 -0.4652 -0.1733 -0.376 -0.0508 -0.2399 -0.226 -0.1471
## Par. upper-bounds: 1.0179 -0.0843 1.3612 1.3406 0.2592 0.2144 0.2282 0.1999 -0.0196 0.5732 0.2399 0.0857 0.5716 -0.1412 0.3587 0.1603 0.5561 0.0427 0.2379 0.3205
## Final Estimates: -0.2386331 -1.707172 -0.4145188 -0.296965 0.009958523 0.09999643 0.03862451 0.01291673 -0.3578243 0.4214118 -0.01563255 -0.1576549 0.2188939 -0.3029093 0.09042001 -0.1040606 0.2607904 -0.09903675 0.009923983 0.08018235
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.238633 0.636165 -0.375 0.707577
## [2,] -1.707172 0.849804 -2.009 0.044548 *
## [3,] -0.414519 0.900108 -0.461 0.645142
## [4,] -0.296965 0.786654 -0.378 0.705799
## [5,] 0.009959 0.122400 0.081 0.935155
## [6,] 0.099996 0.057111 1.751 0.079961 .
## [7,] 0.038625 0.093717 0.412 0.680235
## [8,] 0.012917 0.094340 0.137 0.891097
## [9,] -0.357824 0.163597 -2.187 0.028725 *
## [10,] 0.421412 0.076290 5.524 3.32e-08 ***
## [11,] -0.015633 0.125178 -0.125 0.900617
## [12,] -0.157655 0.126042 -1.251 0.211002
## [13,] 0.218894 0.173206 1.264 0.206310
## [14,] -0.302909 0.080805 -3.749 0.000178 ***
## [15,] 0.090420 0.132567 0.682 0.495194
## [16,] -0.104061 0.133487 -0.780 0.435652
## [17,] 0.260790 0.151380 1.723 0.084933 .
## [18,] -0.099037 0.070620 -1.402 0.160801
## [19,] 0.009924 0.115839 0.086 0.931729
## [20,] 0.080182 0.116661 0.687 0.491886
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.2386331 -1.707172 -0.4145188 -0.296965
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.00996 0.100 0.03862 0.0129
## [2,] -0.35782 0.421 -0.01563 -0.1577
## [3,] 0.21889 -0.303 0.09042 -0.1041
## [4,] 0.26079 -0.099 0.00992 0.0802
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 56.68086 13.83949 -59.51642 -42.85053
## [2,] 13.83949 101.14390 -15.83232 -19.58768
## [3,] -59.51642 -15.83232 113.46768 70.76042
## [4,] -42.85053 -19.58768 70.76042 86.66944
## ----
## aic= 16.51935
## bic= 16.92077
## Number of parameters: 20
## initial estimates: -0.8929 -2.427 -1.0777 0.0541 0.1577 0.0952 -0.1764 0.0258 0.0123 0.6396 -0.0914 -0.0341 0.0602 -0.0096 0.2688 0.0996 0.3937 -0.1242 0.3886 0.0913
## Par. lower-bounds: -2.547 -4.8963 -3.7674 -3.2482 -0.0197 -5e-04 -0.2982 -0.0782 -0.2525 0.4967 -0.2733 -0.1893 -0.2283 -0.1653 0.0708 -0.0694 0.0395 -0.3153 0.1454 -0.1163
## Par. upper-bounds: 0.7612 0.0423 1.6119 3.3564 0.3351 0.191 -0.0546 0.1297 0.2772 0.7826 0.0904 0.1211 0.3487 0.146 0.4668 0.2687 0.7479 0.0669 0.6318 0.2988
## Final Estimates: -0.8260335 -2.281141 -0.997559 -0.1152644 0.1513228 0.09669806 -0.1721447 0.02722998 -0.001544354 0.6428467 -0.08218344 -0.03092145 0.05255528 -0.007886693 0.2738831 0.1013755 0.409821 -0.1279186 0.3778572 0.0875907
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.826033 0.824331 -1.002 0.31631
## [2,] -2.281141 1.235225 -1.847 0.06478 .
## [3,] -0.997559 1.339228 -0.745 0.45635
## [4,] -0.115264 1.651664 -0.070 0.94436
## [5,] 0.151323 0.088302 1.714 0.08659 .
## [6,] 0.096698 0.047831 2.022 0.04321 *
## [7,] -0.172145 0.060733 -2.834 0.00459 **
## [8,] 0.027230 0.051960 0.524 0.60024
## [9,] -0.001544 0.130774 -0.012 0.99058
## [10,] 0.642847 0.071549 8.985 < 2e-16 ***
## [11,] -0.082183 0.090965 -0.903 0.36628
## [12,] -0.030921 0.077849 -0.397 0.69122
## [13,] 0.052555 0.143654 0.366 0.71448
## [14,] -0.007887 0.077779 -0.101 0.91923
## [15,] 0.273883 0.098620 2.777 0.00548 **
## [16,] 0.101376 0.084356 1.202 0.22945
## [17,] 0.409821 0.176664 2.320 0.02035 *
## [18,] -0.127919 0.095767 -1.336 0.18164
## [19,] 0.377857 0.121497 3.110 0.00187 **
## [20,] 0.087591 0.103932 0.843 0.39936
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.8260335 -2.281141 -0.997559 -0.1152644
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.15132 0.09670 -0.1721 0.0272
## [2,] -0.00154 0.64285 -0.0822 -0.0309
## [3,] 0.05256 -0.00789 0.2739 0.1014
## [4,] 0.40982 -0.12792 0.3779 0.0876
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 89.16085 54.23414 -35.06636 -62.27665
## [2,] 54.23414 200.17567 -44.18093 -112.02646
## [3,] -35.06636 -44.18093 235.04228 168.51928
## [4,] -62.27665 -112.02646 168.51928 356.79418
## ----
## aic= 20.55071
## bic= 20.95213
## Number of parameters: 20
## initial estimates: -1.3801 -3.0917 -0.9158 -0.4078 0.526 -0.0456 0.1058 0.017 0.2663 -0.0494 -0.0532 -0.044 0.2933 0.3046 0.5646 -0.171 0.2388 0.1561 -0.096 0.6346
## Par. lower-bounds: -3.5083 -5.5703 -3.4428 -2.5149 0.3665 -0.203 -0.0287 -0.1477 0.0806 -0.2327 -0.2099 -0.2358 0.1039 0.1177 0.4049 -0.3666 0.0809 4e-04 -0.2291 0.4715
## Par. upper-bounds: 0.748 -0.6131 1.6112 1.6993 0.6855 0.1117 0.2404 0.1817 0.4521 0.1338 0.1034 0.1478 0.4827 0.4914 0.7243 0.0246 0.3967 0.3119 0.0372 0.7976
## Final Estimates: -1.289429 -2.930818 -0.8109479 -0.5046956 0.5238312 -0.04636971 0.1065117 0.02744462 0.2624511 -0.05074148 -0.05203362 -0.02556146 0.2907818 0.3036988 0.5653579 -0.1589861 0.2411495 0.1569139 -0.09667249 0.6234268
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.28943 1.05703 -1.220 0.22252
## [2,] -2.93082 1.23472 -2.374 0.01761 *
## [3,] -0.81095 1.25501 -0.646 0.51817
## [4,] -0.50470 1.04700 -0.482 0.62978
## [5,] 0.52383 0.07961 6.580 4.71e-11 ***
## [6,] -0.04637 0.07857 -0.590 0.55508
## [7,] 0.10651 0.06718 1.586 0.11285
## [8,] 0.02744 0.08126 0.338 0.73556
## [9,] 0.26245 0.09299 2.822 0.00477 **
## [10,] -0.05074 0.09178 -0.553 0.58036
## [11,] -0.05203 0.07847 -0.663 0.50729
## [12,] -0.02556 0.09493 -0.269 0.78771
## [13,] 0.29078 0.09452 3.076 0.00210 **
## [14,] 0.30370 0.09328 3.256 0.00113 **
## [15,] 0.56536 0.07976 7.089 1.36e-12 ***
## [16,] -0.15899 0.09647 -1.648 0.09935 .
## [17,] 0.24115 0.07885 3.058 0.00223 **
## [18,] 0.15691 0.07782 2.016 0.04377 *
## [19,] -0.09667 0.06654 -1.453 0.14624
## [20,] 0.62343 0.08048 7.746 9.55e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.289429 -2.930818 -0.8109479 -0.5046956
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.524 -0.0464 0.1065 0.0274
## [2,] 0.262 -0.0507 -0.0520 -0.0256
## [3,] 0.291 0.3037 0.5654 -0.1590
## [4,] 0.241 0.1569 -0.0967 0.6234
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 144.82468 76.84110 -39.44521 -45.83409
## [2,] 76.84110 197.60492 -32.12907 -40.83450
## [3,] -39.44521 -32.12907 204.15388 119.16492
## [4,] -45.83409 -40.83450 119.16492 142.08266
## ----
## aic= 19.77829
## bic= 20.17971
## Number of parameters: 20
## initial estimates: -0.8991 -1.5562 -0.3613 0.0708 0.2621 -0.0805 -0.1257 0.1792 0.1367 -0.1605 -0.156 0.0699 -0.1575 0.2405 0.6136 -0.0679 0.1103 0.1404 0.3874 0.4016
## Par. lower-bounds: -2.1297 -2.9502 -1.2718 -1.4689 0.0519 -0.2786 -0.2992 0.0531 -0.1014 -0.385 -0.3525 -0.073 -0.313 0.0938 0.4852 -0.1613 -0.1527 -0.1076 0.1704 0.2438
## Par. upper-bounds: 0.3315 -0.1622 0.5492 1.6105 0.4723 0.1177 0.0478 0.3054 0.3748 0.064 0.0405 0.2128 -0.0019 0.3871 0.742 0.0254 0.3733 0.3884 0.6045 0.5595
## Final Estimates: -0.8375368 -1.454808 -0.2951202 -0.05409178 0.2612617 -0.07883847 -0.1212635 0.1886291 0.1352746 -0.1577973 -0.1486845 0.08537552 -0.1583913 0.2422265 0.6183767 -0.05782791 0.1120291 0.1370986 0.3784152 0.3825389
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.83754 0.61227 -1.368 0.171340
## [2,] -1.45481 0.69618 -2.090 0.036646 *
## [3,] -0.29512 0.45474 -0.649 0.516342
## [4,] -0.05409 0.77039 -0.070 0.944024
## [5,] 0.26126 0.10510 2.486 0.012928 *
## [6,] -0.07884 0.09908 -0.796 0.426215
## [7,] -0.12126 0.08664 -1.400 0.161627
## [8,] 0.18863 0.06239 3.023 0.002500 **
## [9,] 0.13527 0.11951 1.132 0.257656
## [10,] -0.15780 0.11266 -1.401 0.161317
## [11,] -0.14868 0.09851 -1.509 0.131225
## [12,] 0.08538 0.07094 1.203 0.228791
## [13,] -0.15839 0.07806 -2.029 0.042447 *
## [14,] 0.24223 0.07359 3.292 0.000996 ***
## [15,] 0.61838 0.06435 9.610 < 2e-16 ***
## [16,] -0.05783 0.04634 -1.248 0.212046
## [17,] 0.11203 0.13223 0.847 0.396862
## [18,] 0.13710 0.12465 1.100 0.271401
## [19,] 0.37842 0.10900 3.472 0.000517 ***
## [20,] 0.38254 0.07849 4.874 1.1e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.8375368 -1.454808 -0.2951202 -0.05409178
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.261 -0.0788 -0.121 0.1886
## [2,] 0.135 -0.1578 -0.149 0.0854
## [3,] -0.158 0.2422 0.618 -0.0578
## [4,] 0.112 0.1371 0.378 0.3825
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 52.375482 38.734065 -7.07308873 -21.28378730
## [2,] 38.734065 67.713317 -1.58085363 -32.94734950
## [3,] -7.073089 -1.580854 28.89057372 0.06085763
## [4,] -21.283787 -32.947349 0.06085763 82.89829159
## ----
## aic= 15.40699
## bic= 15.8084
## Number of parameters: 20
## initial estimates: -1.6158 -2.923 -0.1978 0.1261 0.2692 -0.2864 0.2197 -0.3246 -0.119 -0.0239 0.0362 -0.1585 -0.1097 0.0881 7e-04 0.2262 -0.0128 0.0063 0.0021 0.201
## Par. lower-bounds: -4.0893 -5.8949 -3.131 -2.5967 0.0777 -0.4763 0.0359 -0.5327 -0.3491 -0.252 -0.1847 -0.4085 -0.3368 -0.1371 -0.2173 -0.0206 -0.2236 -0.2028 -0.2003 -0.0281
## Par. upper-bounds: 0.8578 0.049 2.7354 2.8489 0.4608 -0.0965 0.4036 -0.1164 0.1112 0.2043 0.2571 0.0916 0.1174 0.3133 0.2187 0.473 0.1981 0.2153 0.2045 0.4301
## Final Estimates: -1.538283 -2.786686 -0.1301364 -0.01169653 0.2630566 -0.2827331 0.2229205 -0.3192578 -0.1298286 -0.01742013 0.04180688 -0.149161 -0.1150771 0.09129946 0.00347475 0.2307878 -0.001781035 -0.0002436693 -0.003604025 0.1915888
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.5382826 1.2270961 -1.254 0.20999
## [2,] -2.7866860 1.4724763 -1.893 0.05842 .
## [3,] -0.1301364 1.4491569 -0.090 0.92845
## [4,] -0.0116965 1.3351742 -0.009 0.99301
## [5,] 0.2630566 0.0939351 2.800 0.00510 **
## [6,] -0.2827331 0.0926954 -3.050 0.00229 **
## [7,] 0.2229205 0.0914521 2.438 0.01479 *
## [8,] -0.3192578 0.1036788 -3.079 0.00207 **
## [9,] -0.1298286 0.1110732 -1.169 0.24246
## [10,] -0.0174201 0.1084755 -0.161 0.87242
## [11,] 0.0418069 0.1098725 0.381 0.70357
## [12,] -0.1491610 0.1247030 -1.196 0.23165
## [13,] -0.1150771 0.1092728 -1.053 0.29229
## [14,] 0.0912995 0.1071922 0.852 0.39436
## [15,] 0.0034747 0.1078024 0.032 0.97429
## [16,] 0.2307878 0.1231542 1.874 0.06093 .
## [17,] -0.0017810 0.0963849 -0.018 0.98526
## [18,] -0.0002437 0.0931747 -0.003 0.99791
## [19,] -0.0036040 0.1004077 -0.036 0.97137
## [20,] 0.1915888 0.1141934 1.678 0.09339 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.538283 -2.786686 -0.1301364 -0.01169653
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.26306 -0.282733 0.22292 -0.319
## [2,] -0.12983 -0.017420 0.04181 -0.149
## [3,] -0.11508 0.091299 0.00347 0.231
## [4,] -0.00178 -0.000244 -0.00360 0.192
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 218.50642 154.1931 -119.6391 -99.99022
## [2,] 154.19312 316.8691 -167.9399 -179.20439
## [3,] -119.63911 -167.9399 306.6959 176.94510
## [4,] -99.99022 -179.2044 176.9451 266.47170
## ----
## aic= 21.2269
## bic= 21.62832
## Number of parameters: 20
## initial estimates: -2.2927 -3.0381 -0.2729 -0.4653 0.4497 0.1092 0.1009 -0.0708 0.1043 0.1181 -0.1875 0.0794 -0.0388 -0.1274 0.6721 -0.3245 -0.0476 -0.1108 -0.0888 0.5309
## Par. lower-bounds: -5.8349 -5.7114 -3.1722 -2.4979 0.2926 -0.1448 -0.094 -0.3473 -0.0142 -0.0736 -0.3346 -0.1292 -0.1674 -0.3354 0.5126 -0.5508 -0.1377 -0.2565 -0.2006 0.3722
## Par. upper-bounds: 1.2495 -0.3648 2.6265 1.5673 0.6068 0.3632 0.2958 0.2056 0.2229 0.3098 -0.0404 0.2881 0.0898 0.0805 0.8317 -0.0982 0.0425 0.035 0.0231 0.6895
## Final Estimates: -2.218224 -2.953938 -0.2167535 -0.5217663 0.4465662 0.1097143 0.09982242 -0.05944139 0.100774 0.1186636 -0.1887448 0.09234586 -0.04114732 -0.1270353 0.671304 -0.315921 -0.04523482 -0.1111663 -0.0879422 0.5222497
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -2.21822 1.76372 -1.258 0.20850
## [2,] -2.95394 1.33345 -2.215 0.02674 *
## [3,] -0.21675 1.44374 -0.150 0.88066
## [4,] -0.52177 1.01325 -0.515 0.60659
## [5,] 0.44657 0.07823 5.708 1.14e-08 ***
## [6,] 0.10971 0.12677 0.865 0.38677
## [7,] 0.09982 0.09726 1.026 0.30471
## [8,] -0.05944 0.13680 -0.435 0.66392
## [9,] 0.10077 0.05914 1.704 0.08840 .
## [10,] 0.11866 0.09584 1.238 0.21564
## [11,] -0.18874 0.07353 -2.567 0.01026 *
## [12,] 0.09235 0.10342 0.893 0.37191
## [13,] -0.04115 0.06402 -0.643 0.52040
## [14,] -0.12704 0.10374 -1.225 0.22074
## [15,] 0.67130 0.07959 8.435 < 2e-16 ***
## [16,] -0.31592 0.11195 -2.822 0.00477 **
## [17,] -0.04523 0.04494 -1.007 0.31411
## [18,] -0.11117 0.07282 -1.527 0.12684
## [19,] -0.08794 0.05586 -1.574 0.11544
## [20,] 0.52225 0.07858 6.646 3.01e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -2.218224 -2.953938 -0.2167535 -0.5217663
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.4466 0.110 0.0998 -0.0594
## [2,] 0.1008 0.119 -0.1887 0.0923
## [3,] -0.0411 -0.127 0.6713 -0.3159
## [4,] -0.0452 -0.111 -0.0879 0.5222
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 429.225533 114.31606 -52.94021 1.204533
## [2,] 114.316060 245.31479 -113.87447 -48.081017
## [3,] -52.940214 -113.87447 287.44466 133.399228
## [4,] 1.204533 -48.08102 133.39923 141.620853
## ----
## aic= 21.51478
## bic= 21.9162
## Number of parameters: 20
## initial estimates: -0.6249 -1.3691 -0.6741 -0.2233 0.0969 0.0557 0.0757 -0.189 -0.3376 0.2224 -0.0682 -0.1036 0.5442 0.0447 -0.1059 0.3417 -0.1001 0.2649 -0.133 0.0071
## Par. lower-bounds: -1.6954 -2.6624 -3.046 -2.1438 -0.0755 -0.091 -0.0032 -0.2875 -0.5459 0.0451 -0.1635 -0.2227 0.1623 -0.2804 -0.2806 0.1234 -0.4094 0.0017 -0.2745 -0.1697
## Par. upper-bounds: 0.4455 -0.0757 1.6977 1.6973 0.2693 0.2024 0.1546 -0.0904 -0.1294 0.3997 0.0271 0.0154 0.9262 0.3698 0.0689 0.56 0.2092 0.5282 0.0086 0.1838
## Final Estimates: -0.5855546 -1.311434 -0.5855395 -0.3074443 0.08779775 0.05669015 0.07719954 -0.1873609 -0.3509541 0.2238616 -0.0660308 -0.1012843 0.5236009 0.04696905 -0.1025312 0.3453271 -0.08061776 0.2628093 -0.1361162 0.003643277
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.585555 0.533769 -1.097 0.272633
## [2,] -1.311434 0.645906 -2.030 0.042318 *
## [3,] -0.585539 1.182850 -0.495 0.620583
## [4,] -0.307444 0.959019 -0.321 0.748527
## [5,] 0.087798 0.085702 1.024 0.305619
## [6,] 0.056690 0.073358 0.773 0.439648
## [7,] 0.077200 0.039410 1.959 0.050126 .
## [8,] -0.187361 0.049245 -3.805 0.000142 ***
## [9,] -0.350954 0.103707 -3.384 0.000714 ***
## [10,] 0.223862 0.088770 2.522 0.011675 *
## [11,] -0.066031 0.047690 -1.385 0.166177
## [12,] -0.101284 0.059597 -1.699 0.089230 .
## [13,] 0.523601 0.189917 2.757 0.005834 **
## [14,] 0.046969 0.162560 0.289 0.772632
## [15,] -0.102531 0.087336 -1.174 0.240400
## [16,] 0.345327 0.109140 3.164 0.001556 **
## [17,] -0.080618 0.153980 -0.524 0.600586
## [18,] 0.262809 0.131804 1.994 0.046159 *
## [19,] -0.136116 0.070817 -1.922 0.054594 .
## [20,] 0.003643 0.088562 0.041 0.967186
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.5855546 -1.311434 -0.5855395 -0.3074443
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.0878 0.0567 0.0772 -0.18736
## [2,] -0.3510 0.2239 -0.0660 -0.10128
## [3,] 0.5236 0.0470 -0.1025 0.34533
## [4,] -0.0806 0.2628 -0.1361 0.00364
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 40.80964 23.34549 -13.03029 -17.20507
## [2,] 23.34549 59.75802 -28.95292 -33.66208
## [3,] -13.03029 -28.95292 200.40720 72.72989
## [4,] -17.20507 -33.66208 72.72989 131.73656
## ----
## aic= 17.59727
## bic= 17.99869
## Number of parameters: 20
## initial estimates: -0.8487 -1.6621 -0.4157 -0.0211 0.3042 -0.1359 -0.0137 0.0841 -0.1305 -0.0067 -0.1677 0.0303 0.3046 -0.1203 0.3348 0.0033 0.1629 -0.0808 0.2077 0.3698
## Par. lower-bounds: -2.2192 -3.0698 -2.0263 -1.1169 0.1337 -0.3155 -0.1491 -0.1086 -0.3056 -0.1912 -0.3068 -0.1676 0.1043 -0.3313 0.1757 -0.2232 0.0267 -0.2244 0.0995 0.2157
## Par. upper-bounds: 0.5217 -0.2543 1.1948 1.0747 0.4746 0.0436 0.1217 0.2768 0.0445 0.1778 -0.0286 0.2282 0.5048 0.0908 0.4939 0.2297 0.2992 0.0628 0.316 0.5238
## Final Estimates: -0.8089268 -1.577564 -0.3284371 -0.09137409 0.3001879 -0.1328739 -0.01214987 0.09447999 -0.1389535 -0.0002051056 -0.1644283 0.05229807 0.2958541 -0.1135873 0.3381485 0.02600007 0.1699548 -0.08618856 0.2050193 0.3514687## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.8089268 0.6800473 -1.190 0.23424
## [2,] -1.5775640 0.6933326 -2.275 0.02289 *
## [3,] -0.3284371 0.8036843 -0.409 0.68279
## [4,] -0.0913741 0.5468413 -0.167 0.86730
## [5,] 0.3001879 0.0839609 3.575 0.00035 ***
## [6,] -0.1328739 0.0807111 -1.646 0.09970 .
## [7,] -0.0121499 0.0675388 -0.180 0.85724
## [8,] 0.0944800 0.0935888 1.010 0.31272
## [9,] -0.1389535 0.0808042 -1.720 0.08550 .
## [10,] -0.0002051 NaN NaN NaN
## [11,] -0.1644283 0.0697096 -2.359 0.01834 *
## [12,] 0.0522981 0.0877329 0.596 0.55110
## [13,] 0.2958541 0.1000335 2.958 0.00310 **
## [14,] -0.1135873 0.1050810 -1.081 0.27972
## [15,] 0.3381485 0.0796594 4.245 2.19e-05 ***
## [16,] 0.0260001 0.1119061 0.232 0.81628
## [17,] 0.1699548 0.0674511 2.520 0.01175 *
## [18,] -0.0861886 0.0643281 -1.340 0.18030
## [19,] 0.2050193 0.0543105 3.775 0.00016 ***
## [20,] 0.3514687 0.0751704 4.676 2.93e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.8089268 -1.577564 -0.3284371 -0.09137409
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.300 -0.132874 -0.0121 0.0945
## [2,] -0.139 -0.000205 -0.1644 0.0523
## [3,] 0.296 -0.113587 0.3381 0.0260
## [4,] 0.170 -0.086189 0.2050 0.3515
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 66.501471 25.847266 -25.241286 -6.771272
## [2,] 25.847266 70.864878 -6.931039 -21.579553
## [3,] -25.241286 -6.931039 92.532604 3.839240
## [4,] -6.771272 -21.579553 3.839240 43.014356
## ----
## aic= 16.58202
## bic= 16.98344
## Number of parameters: 20
## initial estimates: -0.974 -1.669 -0.5233 0.0798 0.2676 0.0886 -0.0094 0.0083 0.1896 -0.05 -0.2055 0.0025 -0.0086 0.5762 0.5148 0.1193 0.0103 0.2213 0.2255 0.3841
## Par. lower-bounds: -2.7086 -3.2559 -2.8933 -1.454 0.0729 -0.1468 -0.1416 -0.209 0.0115 -0.2654 -0.3264 -0.1963 -0.2746 0.2545 0.3343 -0.1775 -0.1619 0.0132 0.1087 0.192
## Par. upper-bounds: 0.7606 -0.082 1.8468 1.6137 0.4624 0.3241 0.1227 0.2256 0.3678 0.1654 -0.0846 0.2013 0.2575 0.8978 0.6954 0.4162 0.1825 0.4295 0.3424 0.5762
## Final Estimates: -0.9181888 -1.580723 -0.4151674 -0.00475854 0.2652185 0.08948049 -0.007998895 0.016977 0.185783 -0.04869096 -0.2032201 0.01615373 -0.01325947 0.5778381 0.5176105 0.1360466 0.01393445 0.2200624 0.2233761 0.3710059
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.918189 0.868616 -1.057 0.290479
## [2,] -1.580723 0.802176 -1.971 0.048776 *
## [3,] -0.415167 1.194610 -0.348 0.728190
## [4,] -0.004759 0.799799 -0.006 0.995253
## [5,] 0.265218 0.097136 2.730 0.006326 **
## [6,] 0.089480 0.117527 0.761 0.446442
## [7,] -0.007999 0.065991 -0.121 0.903524
## [8,] 0.016977 0.107700 0.158 0.874746
## [9,] 0.185783 0.089142 2.084 0.037149 *
## [10,] -0.048691 0.107887 -0.451 0.651763
## [11,] -0.203220 0.060552 -3.356 0.000790 ***
## [12,] 0.016154 0.098867 0.163 0.870212
## [13,] -0.013259 0.132998 -0.100 0.920585
## [14,] 0.577838 0.160815 3.593 0.000327 ***
## [15,] 0.517611 0.090285 5.733 9.86e-09 ***
## [16,] 0.136047 0.147388 0.923 0.355980
## [17,] 0.013934 0.086147 0.162 0.871501
## [18,] 0.220062 0.104374 2.108 0.034997 *
## [19,] 0.223376 0.058568 3.814 0.000137 ***
## [20,] 0.371006 0.095555 3.883 0.000103 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.9181888 -1.580723 -0.4151674 -0.00475854
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2652 0.0895 -0.008 0.0170
## [2,] 0.1858 -0.0487 -0.203 0.0162
## [3,] -0.0133 0.5778 0.518 0.1360
## [4,] 0.0139 0.2201 0.223 0.3710
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 101.04918 54.27457 -55.56105 -35.46064
## [2,] 54.27457 85.10577 -49.88840 -44.30683
## [3,] -55.56105 -49.88840 189.23773 64.47162
## [4,] -35.46064 -44.30683 64.47162 79.49318
## ----
## aic= 17.78029
## bic= 18.18171
## Number of parameters: 20
## initial estimates: -0.6174 -1.3863 -0.5196 -0.0927 0.2551 -0.1215 -0.1069 -0.0689 0.084 0.0183 -0.0444 -0.0647 -0.0279 -0.0725 0.5123 0.0056 0.3264 -0.1168 0.0043 0.5039
## Par. lower-bounds: -1.6969 -2.5672 -2.0828 -1.3042 0.0713 -0.2878 -0.2197 -0.2108 -0.1171 -0.1636 -0.1677 -0.2199 -0.2941 -0.3133 0.3491 -0.1998 0.1201 -0.3034 -0.1222 0.3447
## Par. upper-bounds: 0.4621 -0.2055 1.0437 1.1187 0.4389 0.0448 0.0058 0.073 0.2851 0.2002 0.0789 0.0905 0.2383 0.1684 0.6756 0.2111 0.5327 0.0698 0.1308 0.6631
## Final Estimates: -0.5865581 -1.319665 -0.4559873 -0.1492886 0.2503518 -0.1208771 -0.1056129 -0.06356781 0.07369335 0.01959893 -0.04151603 -0.05318841 -0.03773745 -0.07121663 0.5150531 0.01662876 0.3351242 -0.1179096 0.001904596 0.494129
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.586558 0.537265 -1.092 0.27494
## [2,] -1.319665 0.590768 -2.234 0.02550 *
## [3,] -0.455987 0.779445 -0.585 0.55854
## [4,] -0.149289 0.604715 -0.247 0.80501
## [5,] 0.250352 0.091528 2.735 0.00623 **
## [6,] -0.120877 0.083023 -1.456 0.14541
## [7,] -0.105613 0.056216 -1.879 0.06028 .
## [8,] -0.063568 0.070455 -0.902 0.36693
## [9,] 0.073693 0.100640 0.732 0.46402
## [10,] 0.019599 0.091281 0.215 0.82999
## [11,] -0.041516 0.061812 -0.672 0.50180
## [12,] -0.053188 0.077465 -0.687 0.49233
## [13,] -0.037737 0.132774 -0.284 0.77624
## [14,] -0.071217 0.120448 -0.591 0.55434
## [15,] 0.515053 0.081539 6.317 2.67e-10 ***
## [16,] 0.016629 0.102214 0.163 0.87077
## [17,] 0.335124 0.102937 3.256 0.00113 **
## [18,] -0.117910 0.093442 -1.262 0.20700
## [19,] 0.001905 0.062970 0.030 0.97587
## [20,] 0.494129 0.079277 6.233 4.58e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.5865581 -1.319665 -0.4559873 -0.1492886
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2504 -0.1209 -0.1056 -0.0636
## [2,] 0.0737 0.0196 -0.0415 -0.0532
## [3,] -0.0377 -0.0712 0.5151 0.0166
## [4,] 0.3351 -0.1179 0.0019 0.4941
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 41.07186 16.026070 -21.714109 -16.56802
## [2,] 16.02607 49.659365 -2.736875 -18.00875
## [3,] -21.71411 -2.736875 86.445342 29.58678
## [4,] -16.56802 -18.008750 29.586780 52.03456
## ----
## aic= 15.63033
## bic= 16.03175
## Number of parameters: 20
## initial estimates: -0.5197 -1.1962 -0.3636 -0.0148 0.0217 -0.1741 0.0435 0.0187 -0.3115 0.053 0.0411 -0.0134 0.1657 0.0209 0.9036 0.1481 0.1064 -0.0278 0.0015 0.8978
## Par. lower-bounds: -1.292 -2.253 -1.4677 -0.6274 -0.1483 -0.299 2e-04 -0.0712 -0.5441 -0.1178 -0.0181 -0.1365 -0.0773 -0.1576 0.8418 0.0195 -0.0285 -0.1269 -0.0328 0.8264
## Par. upper-bounds: 0.2526 -0.1394 0.7405 0.5977 0.1917 -0.0492 0.0868 0.1087 -0.0788 0.2239 0.1003 0.1096 0.4088 0.1994 0.9655 0.2767 0.2412 0.0712 0.0358 0.9691
## Final Estimates: -0.4971999 -1.160597 -0.3151278 -0.04713308 0.0170235 -0.1733282 0.04529326 0.02409615 -0.318823 0.05427758 0.04391033 -0.004920473 0.1556827 0.02260861 0.907488 0.1597588 0.1130368 -0.02893038 -0.001064322 0.8900406
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.497200 0.385281 -1.290 0.19688
## [2,] -1.160597 0.527742 -2.199 0.02787 *
## [3,] -0.315128 0.552938 -0.570 0.56874
## [4,] -0.047133 0.307733 -0.153 0.87827
## [5,] 0.017023 0.084833 0.201 0.84096
## [6,] -0.173328 0.062410 -2.777 0.00548 **
## [7,] 0.045293 0.021547 2.102 0.03555 *
## [8,] 0.024096 0.044600 0.540 0.58901
## [9,] -0.318823 0.116202 -2.744 0.00607 **
## [10,] 0.054278 0.085485 0.635 0.52547
## [11,] 0.043910 0.029515 1.488 0.13682
## [12,] -0.004920 0.061108 -0.081 0.93582
## [13,] 0.155683 0.121744 1.279 0.20098
## [14,] 0.022609 0.089568 0.252 0.80072
## [15,] 0.907488 0.030923 29.347 < 2e-16 ***
## [16,] 0.159759 0.064006 2.496 0.01256 *
## [17,] 0.113037 0.067748 1.668 0.09522 .
## [18,] -0.028930 0.049841 -0.580 0.56161
## [19,] -0.001064 0.017210 -0.062 0.95069
## [20,] 0.890041 0.035618 24.989 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.4971999 -1.160597 -0.3151278 -0.04713308
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.017 -0.1733 0.04529 0.02410
## [2,] -0.319 0.0543 0.04391 -0.00492
## [3,] 0.156 0.0226 0.90749 0.15976
## [4,] 0.113 -0.0289 -0.00106 0.89004
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 21.287331 10.435934 -0.775317 -1.026238
## [2,] 10.435934 39.939767 -4.082985 -3.912816
## [3,] -0.775317 -4.082985 43.840824 -6.634868
## [4,] -1.026238 -3.912816 -6.634868 13.576351
## ----
## aic= 13.1353
## bic= 13.53672
## Number of parameters: 20
## initial estimates: -0.8526 -1.8246 -0.9388 -0.31 0.1682 -0.0297 0.1439 -0.2038 -0.2026 0.1623 0.0454 0.0372 0.4737 -0.0874 0.6538 -0.0997 0.1389 0.1405 -0.0395 0.657
## Par. lower-bounds: -2.3701 -3.4278 -2.6727 -1.4527 0.0069 -0.1837 0.0312 -0.392 -0.373 -3e-04 -0.0737 -0.1617 0.2893 -0.2633 0.5249 -0.3148 0.0174 0.0246 -0.1244 0.5152
## Par. upper-bounds: 0.6649 -0.2214 0.7952 0.8327 0.3296 0.1242 0.2567 -0.0155 -0.0321 0.325 0.1645 0.2361 0.6581 0.0885 0.7826 0.1154 0.2604 0.2565 0.0454 0.7987
## Final Estimates: -0.793584 -1.710528 -0.8175497 -0.36837 0.1630566 -0.02734581 0.1454339 -0.1934114 -0.2125444 0.1669389 0.04827443 0.05727638 0.4630914 -0.08253289 0.6568088 -0.07836875 0.1440261 0.138197 -0.04094277 0.6466959
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.79358 0.75244 -1.055 0.29157
## [2,] -1.71053 0.79784 -2.144 0.03204 *
## [3,] -0.81755 0.86278 -0.948 0.34334
## [4,] -0.36837 0.56727 -0.649 0.51610
## [5,] 0.16306 0.08017 2.034 0.04197 *
## [6,] -0.02735 0.07676 -0.356 0.72164
## [7,] 0.14543 0.05624 2.586 0.00971 **
## [8,] -0.19341 0.09272 -2.086 0.03698 *
## [9,] -0.21254 0.08501 -2.500 0.01241 *
## [10,] 0.16694 0.08139 2.051 0.04025 *
## [11,] 0.04827 0.05963 0.810 0.41818
## [12,] 0.05728 0.09831 0.583 0.56017
## [13,] 0.46309 0.09193 5.038 4.71e-07 ***
## [14,] -0.08253 0.08801 -0.938 0.34837
## [15,] 0.65681 0.06448 10.186 < 2e-16 ***
## [16,] -0.07837 0.10631 -0.737 0.46103
## [17,] 0.14403 0.06044 2.383 0.01718 *
## [18,] 0.13820 0.05787 2.388 0.01693 *
## [19,] -0.04094 0.04240 -0.966 0.33418
## [20,] 0.64670 0.06990 9.252 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.793584 -1.710528 -0.8175497 -0.36837
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.163 -0.0273 0.1454 -0.1934
## [2,] -0.213 0.1669 0.0483 0.0573
## [3,] 0.463 -0.0825 0.6568 -0.0784
## [4,] 0.144 0.1382 -0.0409 0.6467
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 78.122969 18.217998 -5.300581 3.605247
## [2,] 18.217998 87.835973 5.642097 -12.650343
## [3,] -5.300581 5.642097 102.714612 35.363853
## [4,] 3.605247 -12.650343 35.363853 44.401934
## ----
## aic= 17.03456
## bic= 17.43598
## Number of parameters: 20
## initial estimates: -1.5217 -2.3883 -0.6088 -0.1474 0.5953 -0.2107 0.0559 -0.34 0.1501 0.0641 -0.1316 -0.1208 0.0178 0.0811 0.6593 0.0845 -0.049 -0.1418 0.176 0.3546
## Par. lower-bounds: -3.582 -4.2461 -2.5847 -2.0517 0.4463 -0.4233 -0.0806 -0.518 0.0157 -0.1277 -0.2547 -0.2813 -0.1252 -0.1229 0.5284 -0.0862 -0.1868 -0.3384 0.0498 0.1901
## Par. upper-bounds: 0.5386 -0.5306 1.3671 1.7568 0.7444 0.002 0.1925 -0.162 0.2845 0.2558 -0.0085 0.0397 0.1608 0.285 0.7903 0.2552 0.0887 0.0548 0.3022 0.5192
## Final Estimates: -1.470079 -2.313856 -0.5236731 -0.2299665 0.5898895 -0.2093762 0.059913 -0.3334013 0.1422158 0.06592769 -0.1258854 -0.1112293 0.008845113 0.08318437 0.6658656 0.09534412 -0.04032778 -0.1438449 0.1696451 0.3440737
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.470079 1.026390 -1.432 0.152063
## [2,] -2.313856 0.928271 -2.493 0.012679 *
## [3,] -0.523673 0.988081 -0.530 0.596119
## [4,] -0.229967 0.952296 -0.241 0.809178
## [5,] 0.589890 0.074076 7.963 1.78e-15 ***
## [6,] -0.209376 0.106170 -1.972 0.048600 *
## [7,] 0.059913 0.067967 0.882 0.378047
## [8,] -0.333401 0.088440 -3.770 0.000163 ***
## [9,] 0.142216 0.066994 2.123 0.033769 *
## [10,] 0.065928 0.096020 0.687 0.492333
## [11,] -0.125885 0.061469 -2.048 0.040566 *
## [12,] -0.111229 0.079985 -1.391 0.164341
## [13,] 0.008845 0.071309 0.124 0.901284
## [14,] 0.083184 0.102205 0.814 0.415706
## [15,] 0.665866 0.065428 10.177 < 2e-16 ***
## [16,] 0.095344 0.085137 1.120 0.262761
## [17,] -0.040328 0.068729 -0.587 0.557364
## [18,] -0.143845 0.098505 -1.460 0.144211
## [19,] 0.169645 0.063060 2.690 0.007140 **
## [20,] 0.344074 0.082055 4.193 2.75e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.470079 -2.313856 -0.5236731 -0.2299665
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.58989 -0.2094 0.0599 -0.3334
## [2,] 0.14222 0.0659 -0.1259 -0.1112
## [3,] 0.00885 0.0832 0.6659 0.0953
## [4,] -0.04033 -0.1438 0.1696 0.3441
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 144.552456 58.507251 -2.359146 -1.53409
## [2,] 58.507251 118.235396 -6.494945 -39.47002
## [3,] -2.359146 -6.494945 133.956927 33.23589
## [4,] -1.534090 -39.470025 33.235892 124.43408
## ----
## aic= 19.30231
## bic= 19.70373
## Number of parameters: 20
## initial estimates: -0.3433 -1.5803 -1.3542 -0.4326 0.2866 -0.1384 0.0333 -0.0558 -0.3187 0.2136 -0.1011 -0.0513 0.1211 0.0128 0.4286 0.004 0.6298 0.0286 0.0641 0.3931
## Par. lower-bounds: -1.1852 -3.2037 -4.5979 -2.5707 0.1317 -0.2297 -0.0174 -0.1373 -0.6174 0.0376 -0.1989 -0.2083 -0.4758 -0.339 0.2333 -0.3097 0.2363 -0.2032 -0.0646 0.1863
## Par. upper-bounds: 0.4986 0.0431 1.8894 1.7054 0.4416 -0.0471 0.084 0.0256 -0.0199 0.3897 -0.0034 0.1058 0.718 0.3646 0.6239 0.3178 1.0232 0.2605 0.1929 0.5999
## Final Estimates: -0.3206621 -1.490814 -1.209738 -0.51244 0.2817246 -0.1383419 0.03367325 -0.05321499 -0.3380598 0.213843 -0.09960087 -0.04096992 0.08973847 0.01314462 0.4310105 0.02067559 0.6470552 0.02846327 0.0627656 0.3839348
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.32066 0.41841 -0.766 0.443448
## [2,] -1.49081 0.81003 -1.840 0.065702 .
## [3,] -1.20974 1.61569 -0.749 0.454012
## [4,] -0.51244 1.06384 -0.482 0.630028
## [5,] 0.28172 0.07688 3.664 0.000248 ***
## [6,] -0.13834 0.04556 -3.037 0.002391 **
## [7,] 0.03367 0.02528 1.332 0.182920
## [8,] -0.05321 0.04041 -1.317 0.187834
## [9,] -0.33806 0.14884 -2.271 0.023129 *
## [10,] 0.21384 0.08819 2.425 0.015320 *
## [11,] -0.09960 0.04895 -2.035 0.041871 *
## [12,] -0.04097 0.07822 -0.524 0.600452
## [13,] 0.08974 0.29685 0.302 0.762420
## [14,] 0.01314 0.17606 0.075 0.940484
## [15,] 0.43101 0.09764 4.414 1.01e-05 ***
## [16,] 0.02068 0.15616 0.132 0.894670
## [17,] 0.64706 0.19547 3.310 0.000932 ***
## [18,] 0.02846 0.11587 0.246 0.805956
## [19,] 0.06277 0.06429 0.976 0.328905
## [20,] 0.38393 0.10277 3.736 0.000187 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.3206621 -1.490814 -1.209738 -0.51244
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2817 -0.1383 0.0337 -0.0532
## [2,] -0.3381 0.2138 -0.0996 -0.0410
## [3,] 0.0897 0.0131 0.4310 0.0207
## [4,] 0.6471 0.0285 0.0628 0.3839
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 24.770347 -5.489769 11.99482 5.42751
## [2,] -5.489769 92.838163 -33.62881 -51.56495
## [3,] 11.994823 -33.628811 369.29450 153.71860
## [4,] 5.427510 -51.564954 153.71860 160.12581
## ----
## aic= 18.24675
## bic= 18.64817
## Number of parameters: 20
## initial estimates: -0.9598 -2.5893 -0.0697 0.0801 0.2223 -0.0088 -0.0418 0.0479 -0.1014 0.0946 -0.297 -0.1221 0.3677 -0.0806 0.4267 0.2159 0.4365 -0.191 0.2914 -0.1577
## Par. lower-bounds: -2.0472 -5.0061 -1.9869 -1.2658 0.0243 -0.1192 -0.1586 -0.1346 -0.5414 -0.1507 -0.5566 -0.5277 0.0187 -0.2751 0.2208 -0.1059 0.1915 -0.3276 0.1468 -0.3836
## Par. upper-bounds: 0.1277 -0.1725 1.8476 1.426 0.4202 0.1015 0.0751 0.2304 0.3385 0.3399 -0.0374 0.2835 0.7167 0.114 0.6326 0.5376 0.6815 -0.0545 0.4359 0.0681
## Final Estimates: -0.9183752 -2.469359 -0.03892009 0.01992895 0.217726 -0.00797055 -0.03686188 0.04808904 -0.1146634 0.09703454 -0.282841 -0.1214589 0.3643505 -0.07995232 0.4302908 0.2160029 0.443111 -0.1922706 0.2842723 -0.1580569
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.918375 0.542525 -1.693 0.09050 .
## [2,] -2.469359 1.212151 -2.037 0.04163 *
## [3,] -0.038920 0.960700 -0.041 0.96768
## [4,] 0.019929 0.677988 0.029 0.97655
## [5,] 0.217726 0.098913 2.201 0.02772 *
## [6,] -0.007971 0.055194 -0.144 0.88518
## [7,] -0.036862 0.058219 -0.633 0.52663
## [8,] 0.048089 0.091269 0.527 0.59827
## [9,] -0.114663 0.220364 -0.520 0.60283
## [10,] 0.097035 0.122957 0.789 0.43001
## [11,] -0.282841 0.129706 -2.181 0.02921 *
## [12,] -0.121459 0.203332 -0.597 0.55028
## [13,] 0.364351 0.173864 2.096 0.03612 *
## [14,] -0.079952 0.097026 -0.824 0.40992
## [15,] 0.430291 0.102345 4.204 2.62e-05 ***
## [16,] 0.216003 0.160441 1.346 0.17820
## [17,] 0.443111 0.122575 3.615 0.00030 ***
## [18,] -0.192271 0.068402 -2.811 0.00494 **
## [19,] 0.284272 0.072152 3.940 8.15e-05 ***
## [20,] -0.158057 0.113110 -1.397 0.16230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.9183752 -2.469359 -0.03892009 0.01992895
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.218 -0.00797 -0.0369 0.0481
## [2,] -0.115 0.09703 -0.2828 -0.1215
## [3,] 0.364 -0.07995 0.4303 0.2160
## [4,] 0.443 -0.19227 0.2843 -0.1581
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 41.55785 53.52018 -15.54410 -10.51845
## [2,] 53.52018 206.28089 -83.08717 -65.66613
## [3,] -15.54410 -83.08717 128.42663 60.63750
## [4,] -10.51845 -65.66613 60.63750 63.83108
## ----
## aic= 16.85459
## bic= 17.25601
## Number of parameters: 20
## initial estimates: -1.8613 -2.6932 -1.1208 -0.3773 0.2202 -0.3178 -0.2325 0.077 -0.0233 0.0908 -0.3214 0.2298 0.1586 0.1276 0.5207 -0.0835 0.0423 -0.0394 0.0331 0.1889
## Par. lower-bounds: -5.0106 -5.0145 -4.286 -2.3371 0.0536 -0.5466 -0.4124 -0.2479 -0.1461 -0.0779 -0.4539 -0.0097 -0.0088 -0.1024 0.3399 -0.41 -0.0613 -0.1818 -0.0789 -0.0132
## Par. upper-bounds: 1.2879 -0.3719 2.0443 1.5826 0.3867 -0.0889 -0.0527 0.4018 0.0995 0.2595 -0.1888 0.4692 0.326 0.3576 0.7014 0.243 0.146 0.103 0.145 0.3911
## Final Estimates: -1.76358 -2.567075 -0.9909398 -0.45074 0.2146026 -0.3163322 -0.2307084 0.08687448 -0.03050518 0.09264094 -0.3189867 0.2425576 0.1511769 0.1294887 0.5230882 -0.07032905 0.04653156 -0.04049683 0.03170994 0.1814784
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.76358 1.56633 -1.126 0.26020
## [2,] -2.56707 1.15874 -2.215 0.02673 *
## [3,] -0.99094 1.57632 -0.629 0.52958
## [4,] -0.45074 0.97560 -0.462 0.64407
## [5,] 0.21460 0.08279 2.592 0.00954 **
## [6,] -0.31633 0.11422 -2.769 0.00562 **
## [7,] -0.23071 0.08976 -2.570 0.01016 *
## [8,] 0.08687 0.16160 0.538 0.59086
## [9,] -0.03051 0.06125 -0.498 0.61844
## [10,] 0.09264 0.08450 1.096 0.27294
## [11,] -0.31899 0.06640 -4.804 1.56e-06 ***
## [12,] 0.24256 0.11955 2.029 0.04246 *
## [13,] 0.15118 0.08332 1.814 0.06961 .
## [14,] 0.12949 0.11495 1.126 0.25997
## [15,] 0.52309 0.09034 5.790 7.02e-09 ***
## [16,] -0.07033 0.16264 -0.432 0.66543
## [17,] 0.04653 0.05157 0.902 0.36686
## [18,] -0.04050 0.07114 -0.569 0.56920
## [19,] 0.03171 0.05591 0.567 0.57060
## [20,] 0.18148 0.10066 1.803 0.07139 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.76358 -2.567075 -0.9909398 -0.45074
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2146 -0.3163 -0.2307 0.0869
## [2,] -0.0305 0.0926 -0.3190 0.2426
## [3,] 0.1512 0.1295 0.5231 -0.0703
## [4,] 0.0465 -0.0405 0.0317 0.1815
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 350.121173 85.33284 -14.27066 -6.063378
## [2,] 85.332840 191.61269 -41.06576 -44.693651
## [3,] -14.270658 -41.06576 354.59018 135.136279
## [4,] -6.063378 -44.69365 135.13628 135.823694
## ----
## aic= 21.48466
## bic= 21.88608
## Number of parameters: 20
## initial estimates: -0.4874 -1.3082 -0.3094 -0.1623 0.3067 0.0179 0.2102 -0.5816 0.0173 0.0016 -0.1835 0.2741 0.2134 0.0033 0.9379 0.1172 0.0311 -0.0304 0.0625 0.8588
## Par. lower-bounds: -1.4431 -2.3112 -0.9801 -0.5746 0.1519 -0.1369 0.0508 -0.8918 -0.1452 -0.1609 -0.3509 -0.0514 0.1048 -0.1054 0.826 -0.1005 -0.0357 -0.0972 -0.0062 0.725
## Par. upper-bounds: 0.4682 -0.3052 0.3613 0.25 0.4615 0.1727 0.3697 -0.2714 0.1798 0.164 -0.0162 0.5997 0.3221 0.1119 1.0498 0.3349 0.0979 0.0364 0.1313 0.9926
## Final Estimates: -0.4745276 -1.288848 -0.299729 -0.1682217 0.3037831 0.01628912 0.2107626 -0.5767467 0.01289562 -0.0007759329 -0.1827193 0.28142 0.2112273 0.002117133 0.9382717 0.1207367 0.03242179 -0.02972933 0.06232637 0.8566407
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.4745276 0.4766904 -0.995 0.319511
## [2,] -1.2888476 0.5023089 -2.566 0.010292 *
## [3,] -0.2997290 0.3345829 -0.896 0.370344
## [4,] -0.1682217 0.2056510 -0.818 0.413359
## [5,] 0.3037831 0.0771756 3.936 8.28e-05 ***
## [6,] 0.0162891 0.0773291 0.211 0.833163
## [7,] 0.2107626 0.0796024 2.648 0.008104 **
## [8,] -0.5767467 0.1546846 -3.729 0.000193 ***
## [9,] 0.0128956 0.0811845 0.159 0.873792
## [10,] -0.0007759 0.0858280 -0.009 0.992787
## [11,] -0.1827193 0.0837726 -2.181 0.029173 *
## [12,] 0.2814200 0.1627407 1.729 0.083764 .
## [13,] 0.2112273 0.0541747 3.899 9.66e-05 ***
## [14,] 0.0021171 0.0541978 0.039 0.968840
## [15,] 0.9382717 0.0558766 16.792 < 2e-16 ***
## [16,] 0.1207367 0.1085812 1.112 0.266160
## [17,] 0.0324218 0.0332979 0.974 0.330211
## [18,] -0.0297293 0.0333193 -0.892 0.372256
## [19,] 0.0623264 0.0343438 1.815 0.069558 .
## [20,] 0.8566407 0.0667381 12.836 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.4745276 -1.288848 -0.299729 -0.1682217
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3038 0.016289 0.2108 -0.577
## [2,] 0.0129 -0.000776 -0.1827 0.281
## [3,] 0.2112 0.002117 0.9383 0.121
## [4,] 0.0324 -0.029729 0.0623 0.857
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 30.881087 2.7364688 -2.386090 -1.0406813
## [2,] 2.736469 34.1393704 3.130081 0.9676614
## [3,] -2.386090 3.1300814 15.216502 6.8826407
## [4,] -1.040681 0.9676614 6.882641 5.7484830
## ----
## aic= 10.87483
## bic= 11.27625
## Number of parameters: 20
## initial estimates: -0.8193 -1.7462 -0.4115 -0.1194 0.284 0.1001 0.0058 0.0158 -0.0148 0.2029 -0.2729 0.121 0.4179 -0.3163 0.6434 -0.542 0.387 -0.2444 0.3063 -0.1834
## Par. lower-bounds: -2.2759 -3.4116 -2.7696 -1.8938 0.1106 -0.0694 -0.1275 -0.1823 -0.2131 0.0092 -0.4253 -0.1055 0.1371 -0.5906 0.4276 -0.8628 0.1757 -0.4508 0.1439 -0.4248
## Par. upper-bounds: 0.6373 -0.0808 1.9465 1.6549 0.4574 0.2695 0.1391 0.214 0.1835 0.3966 -0.1205 0.3476 0.6986 -0.042 0.8592 -0.2212 0.5982 -0.038 0.4686 0.0579
## Final Estimates: -0.792327 -1.672631 -0.3609789 -0.1769076 0.2807618 0.1001381 0.004823971 0.01943389 -0.02363718 0.203069 -0.2754864 0.1308719 0.4117905 -0.316182 0.6415966 -0.5351809 0.3938566 -0.2445324 0.3082967 -0.1911457
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.792327 0.724849 -1.093 0.274353
## [2,] -1.672631 0.832581 -2.009 0.044540 *
## [3,] -0.360979 1.173917 -0.307 0.758463
## [4,] -0.176908 0.884766 -0.200 0.841521
## [5,] 0.280762 0.086280 3.254 0.001138 **
## [6,] 0.100138 0.084516 1.185 0.236081
## [7,] 0.004824 0.066378 0.073 0.942066
## [8,] 0.019434 0.098516 0.197 0.843619
## [9,] -0.023637 0.099106 -0.239 0.811490
## [10,] 0.203069 0.097076 2.092 0.036451 *
## [11,] -0.275486 0.076325 -3.609 0.000307 ***
## [12,] 0.130872 0.113254 1.156 0.247861
## [13,] 0.411790 0.139744 2.947 0.003211 **
## [14,] -0.316182 0.136871 -2.310 0.020884 *
## [15,] 0.641597 0.107614 5.962 2.49e-09 ***
## [16,] -0.535181 0.159682 -3.352 0.000804 ***
## [17,] 0.393857 0.105327 3.739 0.000184 ***
## [18,] -0.244532 0.103162 -2.370 0.017770 *
## [19,] 0.308297 0.081118 3.801 0.000144 ***
## [20,] -0.191146 0.120364 -1.588 0.112272
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.792327 -1.672631 -0.3609789 -0.1769076
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2808 0.100 0.00482 0.0194
## [2,] -0.0236 0.203 -0.27549 0.1309
## [3,] 0.4118 -0.316 0.64160 -0.5352
## [4,] 0.3939 -0.245 0.30830 -0.1911
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 73.202154 24.76771 -33.57554 -6.395099
## [2,] 24.767711 96.57632 -52.38290 -54.042690
## [3,] -33.575542 -52.38290 191.98136 96.061247
## [4,] -6.395099 -54.04269 96.06125 109.060311
## ----
## aic= 17.96505
## bic= 18.36647
## Number of parameters: 20
## initial estimates: -0.7605 -1.9142 -0.3573 -0.3789 0.4659 -0.0746 0.0641 -0.1352 0.1464 -0.0648 0.03 -0.0575 -0.0305 0.0332 0.6177 0.1313 -0.1095 0.0762 -0.028 0.7268
## Par. lower-bounds: -2.0746 -3.5268 -1.7394 -1.9171 0.3087 -0.2138 -0.0917 -0.2796 -0.0466 -0.2357 -0.1612 -0.2347 -0.196 -0.1132 0.4539 -0.0206 -0.2936 -0.0867 -0.2104 0.5577
## Par. upper-bounds: 0.5536 -0.3016 1.0248 1.1593 0.6232 0.0646 0.2199 0.0092 0.3394 0.106 0.2212 0.1198 0.1349 0.1796 0.7816 0.2832 0.0746 0.2391 0.1544 0.8958
## Final Estimates: -0.7330536 -1.851878 -0.317602 -0.4412722 0.4633092 -0.07513311 0.06570851 -0.1319424 0.1404471 -0.06595122 0.03360488 -0.05007678 -0.0343198 0.0325332 0.6200365 0.1359792 -0.1035464 0.07729445 -0.0316652 0.7193532
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.73305 0.65342 -1.122 0.2619
## [2,] -1.85188 0.80366 -2.304 0.0212 *
## [3,] -0.31760 0.68778 -0.462 0.6442
## [4,] -0.44127 0.76680 -0.575 0.5650
## [5,] 0.46331 0.07829 5.918 3.27e-09 ***
## [6,] -0.07513 0.06942 -1.082 0.2791
## [7,] 0.06571 0.07767 0.846 0.3975
## [8,] -0.13194 0.07178 -1.838 0.0661 .
## [9,] 0.14045 0.09630 1.459 0.1447
## [10,] -0.06595 0.08539 -0.772 0.4399
## [11,] 0.03360 0.09553 0.352 0.7250
## [12,] -0.05008 0.08829 -0.567 0.5706
## [13,] -0.03432 0.08241 -0.416 0.6771
## [14,] 0.03253 0.07308 0.445 0.6562
## [15,] 0.62004 0.08175 7.584 3.33e-14 ***
## [16,] 0.13598 0.07556 1.800 0.0719 .
## [17,] -0.10355 0.09188 -1.127 0.2597
## [18,] 0.07729 0.08147 0.949 0.3428
## [19,] -0.03167 0.09115 -0.347 0.7283
## [20,] 0.71935 0.08424 8.539 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.7330536 -1.851878 -0.317602 -0.4412722
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.4633 -0.0751 0.0657 -0.1319
## [2,] 0.1404 -0.0660 0.0336 -0.0501
## [3,] -0.0343 0.0325 0.6200 0.1360
## [4,] -0.1035 0.0773 -0.0317 0.7194
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 60.12856 19.27543 -17.88276 -10.88833
## [2,] 19.27543 90.95862 -13.23238 -16.94822
## [3,] -17.88276 -13.23238 66.61860 47.92579
## [4,] -10.88833 -16.94822 47.92579 82.80713
## ----
## aic= 16.76877
## bic= 17.17019
## Number of parameters: 20
## initial estimates: -0.9818 -2.2728 -0.8724 -0.1099 0.2024 -0.0817 0.0051 -0.0314 -0.1393 0.1845 -0.0752 0.0435 0.5801 -0.0646 0.4844 -0.2405 -0.0119 -0.1943 0.2109 -0.1129
## Par. lower-bounds: -2.3733 -4.3403 -4.2649 -2.5002 0.0023 -0.223 -0.0831 -0.1764 -0.4367 -0.0253 -0.2063 -0.172 0.092 -0.4089 0.2693 -0.5941 -0.3557 -0.4369 0.0594 -0.3621
## Par. upper-bounds: 0.4097 -0.2054 2.5202 2.2804 0.4026 0.0595 0.0933 0.1137 0.1581 0.3944 0.0559 0.259 1.0681 0.2797 0.6995 0.1131 0.332 0.0482 0.3625 0.1362
## Final Estimates: -0.924064 -2.170991 -0.7774587 -0.1909514 0.193692 -0.07834081 0.005165002 -0.02634406 -0.1546874 0.1905381 -0.07504848 0.0523256 0.5658274 -0.05907771 0.4845182 -0.2323764 0.0004141723 -0.1991386 0.2107856 -0.119967
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.9240640 0.6939356 -1.332 0.18298
## [2,] -2.1709913 1.0326338 -2.102 0.03552 *
## [3,] -0.7774587 1.6883890 -0.460 0.64518
## [4,] -0.1909514 1.1905595 -0.160 0.87258
## [5,] 0.1936920 0.1015973 1.906 0.05659 .
## [6,] -0.0783408 0.0708125 -1.106 0.26859
## [7,] 0.0051650 0.0441046 0.117 0.90677
## [8,] -0.0263441 0.0724107 -0.364 0.71600
## [9,] -0.1546874 0.1521315 -1.017 0.30925
## [10,] 0.1905381 0.1054802 1.806 0.07086 .
## [11,] -0.0750485 0.0656641 -1.143 0.25307
## [12,] 0.0523256 0.1078860 0.485 0.62767
## [13,] 0.5658274 0.2555998 2.214 0.02685 *
## [14,] -0.0590777 0.1742970 -0.339 0.73465
## [15,] 0.4845182 0.1073755 4.512 6.41e-06 ***
## [16,] -0.2323764 0.1763130 -1.318 0.18751
## [17,] 0.0004142 0.1873568 0.002 0.99824
## [18,] -0.1991386 0.1240090 -1.606 0.10831
## [19,] 0.2107856 0.0757269 2.783 0.00538 **
## [20,] -0.1199670 0.1245425 -0.963 0.33542
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.924064 -2.170991 -0.7774587 -0.1909514
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.193692 -0.0783 0.00517 -0.0263
## [2,] -0.154687 0.1905 -0.07505 0.0523
## [3,] 0.565827 -0.0591 0.48452 -0.2324
## [4,] 0.000414 -0.1991 0.21079 -0.1200
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 67.56295 60.42469 -48.25210 -50.85071
## [2,] 60.42469 149.60932 -81.10519 -84.67737
## [3,] -48.25210 -81.10519 399.94135 205.46937
## [4,] -50.85071 -84.67737 205.46937 198.87272
## ----
## aic= 19.24513
## bic= 19.64655
## Number of parameters: 20
## initial estimates: -1.9001 -2.8292 0.1899 0.4427 0.0042 -0.0943 -0.1424 -0.2025 -0.3798 0.3009 -0.0722 -0.2346 0.4219 0.0574 0.1519 0.6148 0.142 0.1625 0.0819 0.3802
## Par. lower-bounds: -5.5911 -6.3148 -3.9408 -3.4888 -0.2476 -0.3835 -0.4133 -0.4827 -0.6176 0.0279 -0.328 -0.4991 0.1402 -0.2662 -0.1513 0.3013 -0.1262 -0.1455 -0.2066 0.0818
## Par. upper-bounds: 1.791 0.6565 4.3206 4.3742 0.2559 0.1949 0.1285 0.0777 -0.142 0.574 0.1836 0.03 0.7037 0.381 0.455 0.9283 0.4101 0.4705 0.3705 0.6786
## Final Estimates: -1.775312 -2.658751 0.2026494 0.2535095 -0.002635157 -0.0877623 -0.1374274 -0.1985968 -0.3890783 0.3099037 -0.06543015 -0.2292412 0.4212428 0.05808461 0.1523826 0.6152121 0.1522577 0.1525493 0.07440698 0.3742501
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.775312 1.835060 -0.967 0.33332
## [2,] -2.658751 1.736421 -1.531 0.12573
## [3,] 0.202649 2.048873 0.099 0.92121
## [4,] 0.253509 1.957778 0.129 0.89697
## [5,] -0.002635 0.124968 -0.021 0.98318
## [6,] -0.087762 0.143954 -0.610 0.54209
## [7,] -0.137427 0.135094 -1.017 0.30903
## [8,] -0.198597 0.139787 -1.421 0.15540
## [9,] -0.389078 0.118427 -3.285 0.00102 **
## [10,] 0.309904 0.136297 2.274 0.02298 *
## [11,] -0.065430 0.127852 -0.512 0.60882
## [12,] -0.229241 0.132291 -1.733 0.08312 .
## [13,] 0.421243 0.139768 3.014 0.00258 **
## [14,] 0.058085 0.160848 0.361 0.71801
## [15,] 0.152383 0.150889 1.010 0.31254
## [16,] 0.615212 0.156132 3.940 8.14e-05 ***
## [17,] 0.152258 0.133611 1.140 0.25447
## [18,] 0.152549 0.153738 0.992 0.32107
## [19,] 0.074407 0.144174 0.516 0.60579
## [20,] 0.374250 0.149193 2.508 0.01212 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.775312 -2.658751 0.2026494 0.2535095
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] -0.00264 -0.0878 -0.1374 -0.199
## [2,] -0.38908 0.3099 -0.0654 -0.229
## [3,] 0.42124 0.0581 0.1524 0.615
## [4,] 0.15226 0.1525 0.0744 0.374
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 472.4880 336.7614 -388.1796 -321.4242
## [2,] 336.7614 423.1696 -380.7592 -364.0119
## [3,] -388.1796 -380.7592 589.4427 467.6800
## [4,] -321.4242 -364.0119 467.6800 538.2099
## ----
## aic= 21.95795
## bic= 22.35937
## Number of parameters: 20
## initial estimates: -0.7302 -1.857 -0.0896 -0.1751 0.3851 0.0921 0.0689 0.0116 0.0747 0.1894 0.0159 0.1786 0.0965 -0.0611 0.1212 -0.0375 -0.0407 -0.1303 0.0304 0.1328
## Par. lower-bounds: -1.6876 -3.3575 -0.6512 -1.5431 0.2178 -0.0263 -0.2201 -0.105 -0.1875 0.0039 -0.4371 -0.004 -0.0016 -0.1305 -0.0484 -0.1059 -0.2797 -0.2994 -0.3826 -0.0337
## Par. upper-bounds: 0.2273 -0.3565 0.4719 1.1929 0.5524 0.2104 0.358 0.1281 0.3369 0.3749 0.4689 0.3613 0.1946 0.0083 0.2907 0.0308 0.1984 0.0388 0.4433 0.2993
## Final Estimates: -0.6968477 -1.789844 -0.07205796 -0.2417834 0.3795669 0.0950428 0.07288201 0.01608874 0.06352086 0.195418 0.02383418 0.1877019 0.09357136 -0.05952676 0.1232273 -0.03513581 -0.02954793 -0.1362289 0.02246172 0.1237713
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.69685 0.47723 -1.460 0.1442
## [2,] -1.78984 0.74938 -2.388 0.0169 *
## [3,] -0.07206 0.27975 -0.258 0.7967
## [4,] -0.24178 0.68384 -0.354 0.7237
## [5,] 0.37957 0.08342 4.550 5.37e-06 ***
## [6,] 0.09504 0.05907 1.609 0.1076
## [7,] 0.07288 0.14439 0.505 0.6137
## [8,] 0.01609 0.05806 0.277 0.7817
## [9,] 0.06352 0.13100 0.485 0.6277
## [10,] 0.19542 0.09275 2.107 0.0351 *
## [11,] 0.02383 0.22669 0.105 0.9163
## [12,] 0.18770 0.09116 2.059 0.0395 *
## [13,] 0.09357 0.04890 1.914 0.0557 .
## [14,] -0.05953 0.03462 -1.719 0.0856 .
## [15,] 0.12323 0.08464 1.456 0.1454
## [16,] -0.03514 0.03403 -1.033 0.3018
## [17,] -0.02955 0.11953 -0.247 0.8047
## [18,] -0.13623 0.08464 -1.610 0.1075
## [19,] 0.02246 0.20691 0.109 0.9136
## [20,] 0.12377 0.08319 1.488 0.1368
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.6968477 -1.789844 -0.07205796 -0.2417834
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3796 0.0950 0.0729 0.0161
## [2,] 0.0635 0.1954 0.0238 0.1877
## [3,] 0.0936 -0.0595 0.1232 -0.0351
## [4,] -0.0295 -0.1362 0.0225 0.1238
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 31.3317781 23.619679 -1.916328 -0.2642696
## [2,] 23.6196788 77.255754 -5.837174 -7.5097994
## [3,] -1.9163279 -5.837174 10.765258 7.3136635
## [4,] -0.2642696 -7.509799 7.313664 64.3309257
## ----
## aic= 14.20851
## bic= 14.60992
## Number of parameters: 20
## initial estimates: -2.2419 -2.7448 -0.4557 -0.0814 0.1418 -0.0381 -0.0971 -0.1717 -0.1747 0.3563 -0.1437 0.0227 0.1025 -0.1692 0.5496 -0.3453 0.2864 -0.3642 0.2332 -0.0264
## Par. lower-bounds: -5.1756 -5.3578 -3.2154 -2.6129 -0.1006 -0.3297 -0.2992 -0.409 -0.3906 0.0966 -0.3236 -0.1886 -0.1256 -0.4435 0.3596 -0.5685 0.0772 -0.6158 0.0589 -0.2312
## Par. upper-bounds: 0.6919 -0.1318 2.3039 2.45 0.3843 0.2535 0.1049 0.0656 0.0413 0.6161 0.0363 0.2341 0.3306 0.1052 0.7397 -0.1221 0.4956 -0.1125 0.4075 0.1783
## Final Estimates: -2.121773 -2.619359 -0.383955 -0.1927149 0.1278847 -0.02757984 -0.09716186 -0.1627839 -0.1892132 0.3672945 -0.1436979 0.03202481 0.09417266 -0.1628602 0.5496137 -0.339952 0.299281 -0.373899 0.2332157 -0.03465031
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -2.12177 1.46309 -1.450 0.14700
## [2,] -2.61936 1.30493 -2.007 0.04472 *
## [3,] -0.38396 1.37302 -0.280 0.77975
## [4,] -0.19271 1.26315 -0.153 0.87874
## [5,] 0.12788 0.12055 1.061 0.28878
## [6,] -0.02758 0.14554 -0.190 0.84970
## [7,] -0.09716 0.10105 -0.962 0.33630
## [8,] -0.16278 0.11840 -1.375 0.16918
## [9,] -0.18921 0.10753 -1.760 0.07846 .
## [10,] 0.36729 0.12981 2.830 0.00466 **
## [11,] -0.14370 0.09013 -1.594 0.11086
## [12,] 0.03202 0.10561 0.303 0.76171
## [13,] 0.09417 0.11315 0.832 0.40524
## [14,] -0.16286 0.13659 -1.192 0.23314
## [15,] 0.54961 0.09484 5.795 6.83e-09 ***
## [16,] -0.33995 0.11112 -3.059 0.00222 **
## [17,] 0.29928 0.10408 2.875 0.00403 **
## [18,] -0.37390 0.12565 -2.976 0.00292 **
## [19,] 0.23322 0.08724 2.673 0.00751 **
## [20,] -0.03465 0.10222 -0.339 0.73463
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -2.121773 -2.619359 -0.383955 -0.1927149
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.1279 -0.0276 -0.0972 -0.1628
## [2,] -0.1892 0.3673 -0.1437 0.0320
## [3,] 0.0942 -0.1629 0.5496 -0.3400
## [4,] 0.2993 -0.3739 0.2332 -0.0347
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 301.47945 207.8277 -97.01252 -87.92425
## [2,] 207.82773 239.8267 -103.84396 -103.64761
## [3,] -97.01252 -103.8440 265.56193 144.43291
## [4,] -87.92425 -103.6476 144.43291 224.70868
## ----
## aic= 20.84362
## bic= 21.24504
## Number of parameters: 20
## initial estimates: -0.9585 -2.0086 -0.2851 0.1204 0.2962 0.1816 -0.0693 0.1785 -0.0147 0.4659 -0.2156 0.1757 0.2732 -0.2841 0.5745 -0.068 0.0619 -0.1416 -0.0244 0.4541
## Par. lower-bounds: -2.4333 -3.875 -1.9303 -1.1886 0.1289 0.0327 -0.2091 -0.023 -0.2263 0.2775 -0.3925 -0.0793 0.0866 -0.4502 0.4187 -0.2929 -0.0865 -0.2738 -0.1485 0.2752
## Par. upper-bounds: 0.5162 -0.1421 1.36 1.4294 0.4634 0.3304 0.0704 0.3801 0.197 0.6543 -0.0388 0.4308 0.4597 -0.1181 0.7304 0.1568 0.2104 -0.0095 0.0996 0.633
## Final Estimates: -0.9121568 -1.922939 -0.245078 0.06519758 0.2922415 0.1857527 -0.06782295 0.1886116 -0.02192216 0.4736745 -0.2127993 0.1943433 0.269799 -0.2805209 0.5758536 -0.05938313 0.06660143 -0.1466373 -0.02624918 0.4420927
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.91216 0.73489 -1.241 0.214525
## [2,] -1.92294 0.93276 -2.062 0.039250 *
## [3,] -0.24508 0.81884 -0.299 0.764712
## [4,] 0.06520 0.65362 0.100 0.920544
## [5,] 0.29224 0.08344 3.503 0.000461 ***
## [6,] 0.18575 0.07422 2.503 0.012323 *
## [7,] -0.06782 0.06979 -0.972 0.331144
## [8,] 0.18861 0.10005 1.885 0.059394 .
## [9,] -0.02192 0.10591 -0.207 0.836016
## [10,] 0.47367 0.09420 5.028 4.95e-07 ***
## [11,] -0.21280 0.08858 -2.402 0.016294 *
## [12,] 0.19434 0.12698 1.530 0.125905
## [13,] 0.26980 0.09298 2.902 0.003711 **
## [14,] -0.28052 0.08271 -3.392 0.000694 ***
## [15,] 0.57585 0.07777 7.404 1.32e-13 ***
## [16,] -0.05938 0.11149 -0.533 0.594273
## [17,] 0.06660 0.07421 0.897 0.369472
## [18,] -0.14664 0.06601 -2.221 0.026320 *
## [19,] -0.02625 0.06207 -0.423 0.672379
## [20,] 0.44209 0.08898 4.968 6.75e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.9121568 -1.922939 -0.245078 0.06519758
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2922 0.186 -0.0678 0.1886
## [2,] -0.0219 0.474 -0.2128 0.1943
## [3,] 0.2698 -0.281 0.5759 -0.0594
## [4,] 0.0666 -0.147 -0.0262 0.4421
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 73.49221 36.66547 -12.98413 -10.27128
## [2,] 36.66547 118.40014 -36.73561 -38.40898
## [3,] -12.98413 -36.73561 91.26296 40.77947
## [4,] -10.27128 -38.40898 40.77947 58.13618
## ----
## aic= 17.11003
## bic= 17.51145
## Number of parameters: 20
## initial estimates: -1.5332 -2.5454 -0.3704 -0.0877 0.0296 0.0567 -0.2121 0.0734 -0.2135 0.4008 -0.1408 -0.0997 0.0736 -0.1628 0.8784 -0.1499 0.1218 -0.1767 0.1124 0.5522
## Par. lower-bounds: -3.5991 -4.8526 -1.8295 -1.465 -0.177 -0.1217 -0.4086 -0.1898 -0.4442 0.2016 -0.3601 -0.3936 -0.0723 -0.2887 0.7397 -0.3358 -0.0159 -0.2956 -0.0185 0.3767
## Par. upper-bounds: 0.5328 -0.2381 1.0887 1.2896 0.2361 0.235 -0.0157 0.3366 0.0172 0.5999 0.0786 0.1943 0.2194 -0.0368 1.0171 0.036 0.2595 -0.0578 0.2434 0.7276
## Final Estimates: -1.478963 -2.466214 -0.343012 -0.1189489 0.02442776 0.06007871 -0.2142509 0.09183878 -0.2207529 0.4056164 -0.1436874 -0.07354301 0.07162638 -0.1613773 0.877692 -0.1428216 0.1247553 -0.1786958 0.11361 0.5414607
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.47896 1.03142 -1.434 0.15160
## [2,] -2.46621 1.15435 -2.136 0.03264 *
## [3,] -0.34301 0.72662 -0.472 0.63688
## [4,] -0.11895 0.68688 -0.173 0.86252
## [5,] 0.02443 0.10316 0.237 0.81281
## [6,] 0.06008 0.08911 0.674 0.50016
## [7,] -0.21425 0.09821 -2.182 0.02913 *
## [8,] 0.09184 0.13039 0.704 0.48122
## [9,] -0.22075 0.11546 -1.912 0.05589 .
## [10,] 0.40562 0.09973 4.067 4.76e-05 ***
## [11,] -0.14369 0.10991 -1.307 0.19110
## [12,] -0.07354 0.14593 -0.504 0.61429
## [13,] 0.07163 0.07269 0.985 0.32446
## [14,] -0.16138 0.06279 -2.570 0.01016 *
## [15,] 0.87769 0.06919 12.685 < 2e-16 ***
## [16,] -0.14282 0.09187 -1.555 0.12004
## [17,] 0.12476 0.06872 1.815 0.06947 .
## [18,] -0.17870 0.05936 -3.011 0.00261 **
## [19,] 0.11361 0.06541 1.737 0.08243 .
## [20,] 0.54146 0.08685 6.234 4.54e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.478963 -2.466214 -0.343012 -0.1189489
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.0244 0.0601 -0.214 0.0918
## [2,] -0.2208 0.4056 -0.144 -0.0735
## [3,] 0.0716 -0.1614 0.878 -0.1428
## [4,] 0.1248 -0.1787 0.114 0.5415
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 147.19201 103.12701 -27.62719 -29.04680
## [2,] 103.12701 184.36603 -24.39721 -29.68667
## [3,] -27.62719 -24.39721 73.06970 48.40369
## [4,] -29.04680 -29.68667 48.40369 65.30627
## ----
## aic= 17.65996
## bic= 18.06138
## Number of parameters: 20
## initial estimates: -1.3303 -1.967 -0.3284 -0.4493 0.5138 0.1783 0.0993 -0.1159 0.0527 0.0682 -0.1112 -0.067 0.0294 -0.2272 0.3007 -0.3428 -7e-04 0.2234 0.3027 -0.1732
## Par. lower-bounds: -3.6496 -3.7861 -4.256 -2.8946 0.3402 -0.0883 -0.0395 -0.316 -0.0834 -0.1409 -0.22 -0.2241 -0.2645 -0.6787 0.0657 -0.6818 -0.1837 -0.0578 0.1564 -0.3842
## Par. upper-bounds: 0.989 -0.148 3.5992 1.996 0.6874 0.4449 0.238 0.0843 0.1889 0.2774 -0.0024 0.09 0.3234 0.2243 0.5356 -0.0038 0.1823 0.5045 0.449 0.0379
## Final Estimates: -1.294695 -1.917631 -0.2470266 -0.5120997 0.5105551 0.1771629 0.0981465 -0.1122972 0.04823665 0.06669137 -0.1127582 -0.06207934 0.02204128 -0.2297975 0.2980713 -0.3345944 0.005001491 0.2253268 0.3047035 -0.1794963
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.294695 1.154649 -1.121 0.2622
## [2,] -1.917631 0.907298 -2.114 0.0346 *
## [3,] -0.247027 1.957044 -0.126 0.8996
## [4,] -0.512100 1.219441 -0.420 0.6745
## [5,] 0.510555 0.086350 5.913 3.37e-09 ***
## [6,] 0.177163 0.132962 1.332 0.1827
## [7,] 0.098146 0.069167 1.419 0.1559
## [8,] -0.112297 0.099586 -1.128 0.2595
## [9,] 0.048237 0.067853 0.711 0.4771
## [10,] 0.066691 0.104476 0.638 0.5233
## [11,] -0.112758 0.054348 -2.075 0.0380 *
## [12,] -0.062079 0.078249 -0.793 0.4276
## [13,] 0.022041 0.146380 0.151 0.8803
## [14,] -0.229797 0.225347 -1.020 0.3078
## [15,] 0.298071 0.117218 2.543 0.0110 *
## [16,] -0.334594 0.168766 -1.983 0.0474 *
## [17,] 0.005001 0.091178 0.055 0.9563
## [18,] 0.225327 0.140401 1.605 0.1085
## [19,] 0.304704 0.073040 4.172 3.02e-05 ***
## [20,] -0.179496 0.105161 -1.707 0.0878 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.294695 -1.917631 -0.2470266 -0.5120997
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.5106 0.1772 0.0981 -0.1123
## [2,] 0.0482 0.0667 -0.1128 -0.0621
## [3,] 0.0220 -0.2298 0.2981 -0.3346
## [4,] 0.0050 0.2253 0.3047 -0.1795
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 185.27528 87.80687 -139.2850 -45.07647
## [2,] 87.80687 114.38869 -129.4549 -60.06443
## [3,] -139.28497 -129.45492 532.0835 217.14928
## [4,] -45.07647 -60.06443 217.1493 206.59574
## ----
## aic= 20.43951
## bic= 20.84093
## Number of parameters: 20
## initial estimates: -0.9361 -1.6275 -0.7803 -0.2384 0.776 -0.4676 -0.0427 0.0747 0.0461 0.0207 0.0192 0.0397 -0.0752 0.0836 0.1931 0.3135 -0.0554 -0.2132 0.1322 -0.0864
## Par. lower-bounds: -2.6557 -3.0894 -3.4545 -2.0201 0.6674 -0.6719 -0.1543 -0.1043 -0.0462 -0.1531 -0.0757 -0.1125 -0.244 -0.2342 0.0195 0.0351 -0.1679 -0.4249 0.0166 -0.2719
## Par. upper-bounds: 0.7835 -0.1656 1.8939 1.5433 0.8846 -0.2633 0.0689 0.2537 0.1384 0.1944 0.1141 0.1919 0.0936 0.4013 0.3666 0.5919 0.0571 -0.0015 0.2479 0.099
## Final Estimates: -0.8789069 -1.560643 -0.6682112 -0.3385401 0.7738307 -0.4659719 -0.03925249 0.07712571 0.04351383 0.02255496 0.02323393 0.04256857 -0.07946705 0.08676345 0.1998718 0.3182739 -0.05158493 -0.2160479 0.1261338 -0.09069115
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.87891 0.85558 -1.027 0.3043
## [2,] -1.56064 0.72869 -2.142 0.0322 *
## [3,] -0.66821 1.33212 -0.502 0.6159
## [4,] -0.33854 0.88982 -0.380 0.7036
## [5,] 0.77383 0.05414 14.293 < 2e-16 ***
## [6,] -0.46597 0.10201 -4.568 4.93e-06 ***
## [7,] -0.03925 0.05556 -0.706 0.4799
## [8,] 0.07713 0.08934 0.863 0.3880
## [9,] 0.04351 0.04611 0.944 0.3453
## [10,] 0.02255 0.08689 0.260 0.7952
## [11,] 0.02323 0.04732 0.491 0.6234
## [12,] 0.04257 0.07609 0.559 0.5759
## [13,] -0.07947 0.08430 -0.943 0.3458
## [14,] 0.08676 0.15884 0.546 0.5849
## [15,] 0.19987 0.08651 2.310 0.0209 *
## [16,] 0.31827 0.13910 2.288 0.0221 *
## [17,] -0.05158 0.05631 -0.916 0.3596
## [18,] -0.21605 0.10610 -2.036 0.0417 *
## [19,] 0.12613 0.05778 2.183 0.0290 *
## [20,] -0.09069 0.09292 -0.976 0.3290
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.8789069 -1.560643 -0.6682112 -0.3385401
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.7738 -0.4660 -0.0393 0.0771
## [2,] 0.0435 0.0226 0.0232 0.0426
## [3,] -0.0795 0.0868 0.1999 0.3183
## [4,] -0.0516 -0.2160 0.1261 -0.0907
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 104.72880 18.36232 -21.36860 -34.02285
## [2,] 18.36232 75.96952 -35.88953 -30.47392
## [3,] -21.36860 -35.88953 253.89772 76.80685
## [4,] -34.02285 -30.47392 76.80685 113.28076
## ----
## aic= 19.03757
## bic= 19.43899
## Number of parameters: 20
## initial estimates: -0.8294 -1.7377 -0.6543 -0.1915 0.26 -0.121 -0.0041 -0.056 -0.2378 0.1931 -0.0244 -0.1377 0.0765 -0.3924 0.4025 -0.4033 0.1176 -0.1641 0.1282 0.0474
## Par. lower-bounds: -2.0921 -3.6091 -4.0484 -2.3289 0.0714 -0.2692 -0.0861 -0.1992 -0.5174 -0.0266 -0.1459 -0.35 -0.4306 -0.7909 0.1821 -0.7883 -0.2018 -0.4151 -0.0106 -0.1951
## Par. upper-bounds: 0.4333 0.1336 2.7399 1.946 0.4487 0.0273 0.0778 0.0873 0.0418 0.4128 0.0971 0.0746 0.5836 0.0061 0.6228 -0.0182 0.4369 0.0868 0.2669 0.2899
## Final Estimates: -0.7900987 -1.667547 -0.5651175 -0.2605592 0.253387 -0.1198469 -0.004795346 -0.05128533 -0.249677 0.1951545 -0.02557121 -0.1293408 0.06135508 -0.3898261 0.4009364 -0.3925724 0.1293076 -0.1661241 0.1293363 0.03912785
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.790099 0.629088 -1.256 0.209137
## [2,] -1.667547 0.933335 -1.787 0.073993 .
## [3,] -0.565118 1.689686 -0.334 0.738039
## [4,] -0.260559 1.065065 -0.245 0.806734
## [5,] 0.253387 0.093914 2.698 0.006974 **
## [6,] -0.119847 0.074044 -1.619 0.105536
## [7,] -0.004795 0.040949 -0.117 0.906777
## [8,] -0.051285 0.071353 -0.719 0.472293
## [9,] -0.249677 0.139336 -1.792 0.073148 .
## [10,] 0.195154 0.109853 1.777 0.075649 .
## [11,] -0.025571 0.060744 -0.421 0.673781
## [12,] -0.129341 0.105862 -1.222 0.221786
## [13,] 0.061355 0.252269 0.243 0.807841
## [14,] -0.389826 0.198884 -1.960 0.049988 *
## [15,] 0.400936 0.109971 3.646 0.000267 ***
## [16,] -0.392572 0.191660 -2.048 0.040533 *
## [17,] 0.129308 0.159006 0.813 0.416088
## [18,] -0.166124 0.125359 -1.325 0.185110
## [19,] 0.129336 0.069317 1.866 0.062061 .
## [20,] 0.039128 0.120808 0.324 0.746026
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.7900987 -1.667547 -0.5651175 -0.2605592
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2534 -0.120 -0.0048 -0.0513
## [2,] -0.2497 0.195 -0.0256 -0.1293
## [3,] 0.0614 -0.390 0.4009 -0.3926
## [4,] 0.1293 -0.166 0.1293 0.0391
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 56.64372 49.20863 -55.16236 -38.32463
## [2,] 49.20863 124.68552 -118.04594 -82.93150
## [3,] -55.16236 -118.04594 408.69770 178.95407
## [4,] -38.32463 -82.93150 178.95407 162.37440
## ----
## aic= 18.68731
## bic= 19.08873
## Number of parameters: 20
## initial estimates: -0.8229 -1.664 -0.4863 -0.1205 0.3184 -0.0233 -0.2011 0.0562 0.0628 0.1945 -0.3038 0.1025 0.1606 -0.1528 0.6012 -0.0172 0.2247 -0.1257 -0.1621 0.5663
## Par. lower-bounds: -1.9886 -3.0107 -1.7169 -1.4104 0.1359 -0.1782 -0.335 -0.0706 -0.1481 0.0154 -0.4585 -0.044 -0.0321 -0.3164 0.4598 -0.1511 0.0228 -0.2972 -0.3104 0.4259
## Par. upper-bounds: 0.3427 -0.3172 0.7444 1.1693 0.5009 0.1317 -0.0671 0.183 0.2737 0.3736 -0.149 0.249 0.3533 0.0109 0.7426 0.1167 0.4267 0.0458 -0.0139 0.7066
## Final Estimates: -0.7816445 -1.591738 -0.4372188 -0.1770112 0.3115927 -0.02163555 -0.197785 0.06293461 0.05084359 0.1973517 -0.2980011 0.114277 0.1525171 -0.1508306 0.6051123 -0.009214282 0.2340616 -0.1279579 -0.1666306 0.5570706
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.781644 0.580961 -1.345 0.178485
## [2,] -1.591738 0.673823 -2.362 0.018164 *
## [3,] -0.437219 0.613841 -0.712 0.476299
## [4,] -0.177011 0.643827 -0.275 0.783365
## [5,] 0.311593 0.090938 3.426 0.000612 ***
## [6,] -0.021636 0.077440 -0.279 0.779949
## [7,] -0.197785 0.066863 -2.958 0.003096 **
## [8,] 0.062935 0.062992 0.999 0.317749
## [9,] 0.050844 0.105473 0.482 0.629769
## [10,] 0.197352 0.089822 2.197 0.028011 *
## [11,] -0.298001 0.077550 -3.843 0.000122 ***
## [12,] 0.114277 0.073061 1.564 0.117786
## [13,] 0.152517 0.096085 1.587 0.112443
## [14,] -0.150831 0.081827 -1.843 0.065287 .
## [15,] 0.605112 0.070645 8.566 < 2e-16 ***
## [16,] -0.009214 0.066527 -0.139 0.889842
## [17,] 0.234062 0.100789 2.322 0.020217 *
## [18,] -0.127958 0.085832 -1.491 0.136017
## [19,] -0.166631 0.074105 -2.249 0.024539 *
## [20,] 0.557071 0.069810 7.980 1.55e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.7816445 -1.591738 -0.4372188 -0.1770112
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3116 -0.0216 -0.198 0.06293
## [2,] 0.0508 0.1974 -0.298 0.11428
## [3,] 0.1525 -0.1508 0.605 -0.00921
## [4,] 0.2341 -0.1280 -0.167 0.55707
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 47.560049 27.030546 -7.884341 -11.52987
## [2,] 27.030546 63.978516 2.919959 -13.78048
## [3,] -7.884341 2.919959 53.095816 23.89462
## [4,] -11.529871 -13.780478 23.894619 58.42044
## ----
## aic= 15.72273
## bic= 16.12415
## Number of parameters: 20
## initial estimates: -1.6154 -2.4826 -0.64 0.2361 0.4419 -0.2752 0.1276 -0.1446 -0.017 -0.0397 -0.0431 -0.0127 0.3631 0.0313 -0.0074 0.3654 0.1869 0.0383 0.0688 0.039
## Par. lower-bounds: -4.0672 -4.713 -3.4582 -2.0062 0.2711 -0.5262 -0.0165 -0.3802 -0.1724 -0.2681 -0.1743 -0.2271 0.1667 -0.2573 -0.173 0.0945 0.0307 -0.1914 -0.0631 -0.1765
## Par. upper-bounds: 0.8364 -0.2522 2.1781 2.4784 0.6127 -0.0241 0.2718 0.0911 0.1384 0.1887 0.088 0.2017 0.5594 0.3199 0.1583 0.6363 0.3431 0.2679 0.2006 0.2545
## Final Estimates: -1.530088 -2.351417 -0.5224368 0.1009559 0.4353581 -0.2718679 0.1311649 -0.1396124 -0.02705402 -0.03464888 -0.03768464 -0.005056413 0.354076 0.03582057 -0.002481423 0.3722221 0.1972087 0.03305042 0.06315031 0.03114079
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.530088 1.220982 -1.253 0.210147
## [2,] -2.351417 1.116014 -2.107 0.035119 *
## [3,] -0.522437 1.404920 -0.372 0.709995
## [4,] 0.100956 1.122399 0.090 0.928330
## [5,] 0.435358 0.085005 5.122 3.03e-07 ***
## [6,] -0.271868 0.125406 -2.168 0.030167 *
## [7,] 0.131165 0.071955 1.823 0.068324 .
## [8,] -0.139612 0.117697 -1.186 0.235541
## [9,] -0.027054 0.077690 -0.348 0.727666
## [10,] -0.034649 0.114640 -0.302 0.762468
## [11,] -0.037685 0.065769 -0.573 0.566658
## [12,] -0.005056 0.107668 -0.047 0.962543
## [13,] 0.354076 0.097814 3.620 0.000295 ***
## [14,] 0.035821 0.144306 0.248 0.803959
## [15,] -0.002481 0.083042 -0.030 0.976161
## [16,] 0.372222 0.135459 2.748 0.005999 **
## [17,] 0.197209 0.078136 2.524 0.011605 *
## [18,] 0.033050 0.115297 0.287 0.774377
## [19,] 0.063150 0.066169 0.954 0.339895
## [20,] 0.031141 0.108264 0.288 0.773624
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.530088 -2.351417 -0.5224368 0.1009559
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.4354 -0.2719 0.13116 -0.13961
## [2,] -0.0271 -0.0346 -0.03768 -0.00506
## [3,] 0.3541 0.0358 -0.00248 0.37222
## [4,] 0.1972 0.0331 0.06315 0.03114
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 209.36703 101.29283 -71.49847 -77.62338
## [2,] 101.29283 174.88581 -46.07884 -111.38384
## [3,] -71.49847 -46.07884 277.21395 75.28832
## [4,] -77.62338 -111.38384 75.28832 176.88643
## ----
## aic= 20.55729
## bic= 20.9587
## Number of parameters: 20
## initial estimates: -1.3609 -2.3005 -0.273 -0.2244 0.2874 0.0645 0.3208 -0.0275 -0.0626 0.1657 0.0277 0.104 0.1774 -0.0077 0.1619 -0.0551 0.1805 -0.1744 -0.0039 0.1279
## Par. lower-bounds: -3.3518 -4.2695 -2.4902 -1.9272 0.1121 -0.138 0.1364 -0.2565 -0.236 -0.0345 -0.1547 -0.1226 -0.0178 -0.2332 -0.0435 -0.3102 0.0306 -0.3476 -0.1617 -0.068
## Par. upper-bounds: 0.6301 -0.3314 1.9442 1.4784 0.4627 0.267 0.5053 0.2016 0.1108 0.366 0.2102 0.3305 0.3726 0.2178 0.3674 0.2 0.3305 -0.0012 0.1539 0.3238
## Final Estimates: -1.285348 -2.209176 -0.2162209 -0.2993782 0.2835562 0.0683098 0.3226807 -0.01932025 -0.06721766 0.1703015 0.02993472 0.1138269 0.1745055 -0.004831554 0.1633067 -0.04903288 0.1843511 -0.1781714 -0.005741684 0.1198145
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.285348 0.991493 -1.296 0.194846
## [2,] -2.209176 0.981969 -2.250 0.024465 *
## [3,] -0.216221 1.102355 -0.196 0.844497
## [4,] -0.299378 0.848780 -0.353 0.724301
## [5,] 0.283556 0.087498 3.241 0.001192 **
## [6,] 0.068310 0.101094 0.676 0.499228
## [7,] 0.322681 0.092169 3.501 0.000464 ***
## [8,] -0.019320 0.114117 -0.169 0.865559
## [9,] -0.067218 0.086658 -0.776 0.437945
## [10,] 0.170302 0.100124 1.701 0.088960 .
## [11,] 0.029935 0.091282 0.328 0.742959
## [12,] 0.113827 0.113024 1.007 0.313884
## [13,] 0.174506 0.097277 1.794 0.072828 .
## [14,] -0.004832 0.112350 -0.043 0.965698
## [15,] 0.163307 0.102498 1.593 0.111100
## [16,] -0.049033 0.126910 -0.386 0.699231
## [17,] 0.184351 0.074908 2.461 0.013854 *
## [18,] -0.178171 0.086544 -2.059 0.039519 *
## [19,] -0.005742 0.078933 -0.073 0.942012
## [20,] 0.119814 0.097715 1.226 0.220139
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.285348 -2.209176 -0.2162209 -0.2993782
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2836 0.06831 0.32268 -0.0193
## [2,] -0.0672 0.17030 0.02993 0.1138
## [3,] 0.1745 -0.00483 0.16331 -0.0490
## [4,] 0.1844 -0.17817 -0.00574 0.1198
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 137.09335 74.36176 -42.83507 -32.24889
## [2,] 74.36176 134.47461 -59.67153 -32.57801
## [3,] -42.83507 -59.67153 169.50401 75.26847
## [4,] -32.24889 -32.57801 75.26847 100.48535
## ----
## aic= 18.87279
## bic= 19.27421
## Number of parameters: 20
## initial estimates: -1.7517 -3.2264 -0.5938 0.2889 0.2647 0.1548 0.1011 -0.1236 -0.1343 0.3412 0.0108 0.0221 0.4997 -0.2329 0.0407 0.2551 0.3783 -0.203 -0.0609 0.2363
## Par. lower-bounds: -4.1871 -6.0919 -3.2172 -2.8281 0.0822 -0.0313 -0.0571 -0.285 -0.3491 0.1222 -0.1754 -0.1679 0.3031 -0.4333 -0.1298 0.0812 0.1447 -0.4411 -0.2634 0.0296
## Par. upper-bounds: 0.6837 -0.361 2.0297 3.4059 0.4472 0.3408 0.2594 0.0379 0.0804 0.5601 0.197 0.2121 0.6963 -0.0324 0.2112 0.429 0.6119 0.0352 0.1417 0.4429
## Final Estimates: -1.73726 -3.206886 -0.5516254 0.2581486 0.2535847 0.1607324 0.1050392 -0.1179696 -0.150467 0.3498892 0.01640452 0.03018906 0.4909975 -0.2275195 0.04386666 0.2597512 0.3949862 -0.2121364 -0.06680413 0.2277759
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.73726 1.21544 -1.429 0.152911
## [2,] -3.20689 1.43346 -2.237 0.025276 *
## [3,] -0.55163 1.30648 -0.422 0.672862
## [4,] 0.25815 1.55833 0.166 0.868427
## [5,] 0.25358 0.09092 2.789 0.005283 **
## [6,] 0.16073 0.09292 1.730 0.083679 .
## [7,] 0.10504 0.07913 1.327 0.184359
## [8,] -0.11797 0.08064 -1.463 0.143496
## [9,] -0.15047 0.10722 -1.403 0.160523
## [10,] 0.34989 0.10959 3.193 0.001410 **
## [11,] 0.01640 0.09331 0.176 0.860443
## [12,] 0.03019 0.09510 0.317 0.750906
## [13,] 0.49100 0.09773 5.024 5.06e-07 ***
## [14,] -0.22752 0.09988 -2.278 0.022737 *
## [15,] 0.04387 0.08506 0.516 0.606047
## [16,] 0.25975 0.08668 2.997 0.002731 **
## [17,] 0.39499 0.11657 3.389 0.000703 ***
## [18,] -0.21214 0.11914 -1.781 0.074985 .
## [19,] -0.06680 0.10145 -0.659 0.510214
## [20,] 0.22778 0.10339 2.203 0.027592 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.73726 -3.206886 -0.5516254 0.2581486
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.254 0.161 0.1050 -0.1180
## [2,] -0.150 0.350 0.0164 0.0302
## [3,] 0.491 -0.228 0.0439 0.2598
## [4,] 0.395 -0.212 -0.0668 0.2278
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 201.56734 145.46222 -53.77287 -103.7343
## [2,] 145.46222 280.35835 -68.17429 -165.3122
## [3,] -53.77287 -68.17429 232.89773 124.1555
## [4,] -103.73426 -165.31224 124.15552 331.3486
## ----
## aic= 21.40409
## bic= 21.80551
## Number of parameters: 20
## initial estimates: -2.6015 -4.4706 0.1899 0.3472 0.2461 -0.2301 -0.653 0.3039 -0.1463 0.0276 -0.9836 0.4333 0.0496 -0.0015 0.6432 -0.1527 -0.0864 0.0132 0.4097 -0.156
## Par. lower-bounds: -6.4836 -8.6984 -2.263 -2.2671 0.031 -0.4315 -1.1233 -0.1774 -0.3805 -0.1918 -1.4957 -0.0909 -0.0862 -0.1288 0.3461 -0.4568 -0.2312 -0.1225 0.093 -0.4802
## Par. upper-bounds: 1.2805 -0.2428 2.6428 2.9615 0.4611 -0.0286 -0.1827 0.7853 0.0879 0.247 -0.4714 0.9575 0.1855 0.1259 0.9404 0.1515 0.0584 0.1489 0.7264 0.1681
## Final Estimates: -2.454333 -4.265021 0.1858162 0.2356843 0.2399486 -0.2253734 -0.6434303 0.3106577 -0.1548374 0.03415976 -0.9702388 0.4426904 0.04981302 -0.001586601 0.642959 -0.1528506 -0.08178046 0.009648058 0.4024906 -0.1611115
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -2.454333 1.934783 -1.269 0.204608
## [2,] -4.265021 2.111398 -2.020 0.043384 *
## [3,] 0.185816 1.218562 0.152 0.878802
## [4,] 0.235684 1.303958 0.181 0.856567
## [5,] 0.239949 0.107293 2.236 0.025326 *
## [6,] -0.225373 0.100417 -2.244 0.024809 *
## [7,] -0.643430 0.234859 -2.740 0.006151 **
## [8,] 0.310658 0.240518 1.292 0.196488
## [9,] -0.154837 0.117095 -1.322 0.186063
## [10,] 0.034160 0.109616 0.312 0.755320
## [11,] -0.970239 0.256310 -3.785 0.000153 ***
## [12,] 0.442690 0.262470 1.687 0.091674 .
## [13,] 0.049813 0.067546 0.737 0.460841
## [14,] -0.001587 0.062974 -0.025 0.979900
## [15,] 0.642959 0.147893 4.347 1.38e-05 ***
## [16,] -0.152851 0.151484 -1.009 0.312965
## [17,] -0.081780 0.072290 -1.131 0.257935
## [18,] 0.009648 0.067463 0.143 0.886281
## [19,] 0.402491 0.158269 2.543 0.010988 *
## [20,] -0.161111 0.162103 -0.994 0.320279
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -2.454333 -4.265021 0.1858162 0.2356843
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2399 -0.22537 -0.643 0.311
## [2,] -0.1548 0.03416 -0.970 0.443
## [3,] 0.0498 -0.00159 0.643 -0.153
## [4,] -0.0818 0.00965 0.402 -0.161
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 538.4192 367.6197 -190.4079 -218.9600
## [2,] 367.6197 641.2111 -220.6066 -241.1472
## [3,] -190.4079 -220.6066 213.5985 197.5824
## [4,] -218.9600 -241.1472 197.5824 244.5902
## ----
## aic= 21.37674
## bic= 21.77816
## Number of parameters: 20
## initial estimates: -1.8338 -2.3276 -0.3146 -0.1485 0.5998 -0.0679 0.1389 -0.2723 0.2277 0.1343 -0.0406 0.1091 -0.3342 0.249 0.1171 0.0396 -0.2174 0.1804 -0.1977 0.6511
## Par. lower-bounds: -4.3844 -4.2814 -2.8968 -1.6983 0.3792 -0.3611 -0.0706 -0.5505 0.0587 -0.0903 -0.2011 -0.104 -0.5576 -0.0479 -0.095 -0.242 -0.3515 0.0022 -0.3251 0.4821
## Par. upper-bounds: 0.7168 -0.3738 2.2675 1.4014 0.8204 0.2254 0.3484 0.0059 0.3967 0.3589 0.1199 0.3222 -0.1109 0.5458 0.3292 0.3212 -0.0834 0.3586 -0.0704 0.8202
## Final Estimates: -1.778467 -2.261592 -0.2516125 -0.1982157 0.595912 -0.06507539 0.1387788 -0.2631448 0.2230158 0.1376276 -0.04076212 0.1201147 -0.3386904 0.2521373 0.1169503 0.05012199 -0.2138957 0.1779026 -0.1976248 0.6428564
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.77847 1.26972 -1.401 0.16131
## [2,] -2.26159 0.97449 -2.321 0.02030 *
## [3,] -0.25161 1.28581 -0.196 0.84486
## [4,] -0.19822 0.77275 -0.257 0.79756
## [5,] 0.59591 0.10991 5.422 5.9e-08 ***
## [6,] -0.06508 0.14625 -0.445 0.65635
## [7,] 0.13878 0.10456 1.327 0.18440
## [8,] -0.26314 0.13805 -1.906 0.05664 .
## [9,] 0.22302 0.08435 2.644 0.00820 **
## [10,] 0.13763 0.11224 1.226 0.22015
## [11,] -0.04076 0.08024 -0.508 0.61147
## [12,] 0.12011 0.10595 1.134 0.25694
## [13,] -0.33869 0.11131 -3.043 0.00234 **
## [14,] 0.25214 0.14811 1.702 0.08869 .
## [15,] 0.11695 0.10588 1.105 0.26936
## [16,] 0.05012 0.13981 0.359 0.71996
## [17,] -0.21390 0.06689 -3.198 0.00139 **
## [18,] 0.17790 0.08901 1.999 0.04564 *
## [19,] -0.19762 0.06363 -3.106 0.00190 **
## [20,] 0.64286 0.08402 7.651 2.0e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.778467 -2.261592 -0.2516125 -0.1982157
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.596 -0.0651 0.1388 -0.2631
## [2,] 0.223 0.1376 -0.0408 0.1201
## [3,] -0.339 0.2521 0.1170 0.0501
## [4,] -0.214 0.1779 -0.1976 0.6429
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 218.33754 121.63592 -101.96772 -42.64939
## [2,] 121.63592 128.60548 -59.47408 -31.86064
## [3,] -101.96772 -59.47408 223.92509 89.27680
## [4,] -42.64939 -31.86064 89.27680 80.87224
## ----
## aic= 18.72662
## bic= 19.12804
## Number of parameters: 20
## initial estimates: -1.3323 -2.2839 -0.9149 -0.3078 0.1261 -0.0408 0.0311 0.0216 -0.1786 0.2243 -0.0941 0.025 0.1253 0.2311 0.217 -0.0168 0.1215 0.157 -0.016 0.3525
## Par. lower-bounds: -3.4516 -4.4273 -4.1695 -3.2317 -0.0921 -0.2585 -0.1146 -0.1413 -0.3992 0.0041 -0.2415 -0.1397 -0.2097 -0.1033 -0.0067 -0.2669 -0.1794 -0.1434 -0.217 0.1278
## Par. upper-bounds: 0.787 -0.1405 2.3397 2.616 0.3443 0.177 0.1768 0.1844 0.042 0.4445 0.0532 0.1897 0.4603 0.5655 0.4408 0.2333 0.4225 0.4574 0.185 0.5771
## Final Estimates: -1.266498 -2.160686 -0.8219451 -0.4298681 0.1214041 -0.03832691 0.03039817 0.02786938 -0.1873785 0.2288691 -0.0954711 0.03676137 0.118677 0.2345315 0.2160208 -0.007909852 0.1302322 0.1525085 -0.01468001 0.3408219
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.26650 1.05410 -1.202 0.22956
## [2,] -2.16069 1.07068 -2.018 0.04359 *
## [3,] -0.82195 1.61830 -0.508 0.61152
## [4,] -0.42987 1.45628 -0.295 0.76785
## [5,] 0.12140 0.10871 1.117 0.26411
## [6,] -0.03833 0.10863 -0.353 0.72421
## [7,] 0.03040 0.07270 0.418 0.67584
## [8,] 0.02787 0.08080 0.345 0.73015
## [9,] -0.18738 0.11043 -1.697 0.08972 .
## [10,] 0.22887 0.11034 2.074 0.03806 *
## [11,] -0.09547 0.07385 -1.293 0.19607
## [12,] 0.03676 0.08208 0.448 0.65425
## [13,] 0.11868 0.16690 0.711 0.47705
## [14,] 0.23453 0.16676 1.406 0.15961
## [15,] 0.21602 0.11157 1.936 0.05284 .
## [16,] -0.00791 0.12396 -0.064 0.94912
## [17,] 0.13023 0.15020 0.867 0.38592
## [18,] 0.15251 0.15008 1.016 0.30954
## [19,] -0.01468 0.10042 -0.146 0.88377
## [20,] 0.34082 0.11159 3.054 0.00226 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.266498 -2.160686 -0.8219451 -0.4298681
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.121 -0.0383 0.0304 0.02787
## [2,] -0.187 0.2289 -0.0955 0.03676
## [3,] 0.119 0.2345 0.2160 -0.00791
## [4,] 0.130 0.1525 -0.0147 0.34082
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 156.39160 102.11589 -92.76773 -61.25277
## [2,] 102.11589 161.35122 -72.01679 -96.02287
## [3,] -92.76773 -72.01679 368.63198 222.29452
## [4,] -61.25277 -96.02287 222.29452 298.53630
## ----
## aic= 20.54442
## bic= 20.94584
## Number of parameters: 20
## initial estimates: -1.3632 -1.6616 -1.2465 -0.8172 0.5109 -0.2875 -0.2199 0.0679 0.1589 -0.0276 -0.183 0.142 0.2878 0.3785 0.5835 -0.2008 0.0606 0.3609 0.4077 -0.1321
## Par. lower-bounds: -3.3735 -3.1985 -5.0112 -4.0534 0.3383 -0.5556 -0.4077 -0.1668 0.027 -0.2325 -0.3266 -0.0374 -0.0353 -0.1234 0.2319 -0.6402 -0.2172 -0.0706 0.1055 -0.5099
## Par. upper-bounds: 0.6471 -0.1247 2.5182 2.419 0.6834 -0.0195 -0.0321 0.3025 0.2908 0.1774 -0.0395 0.3214 0.6109 0.8805 0.9351 0.2387 0.3383 0.7924 0.71 0.2456
## Final Estimates: -1.280382 -1.58549 -1.164612 -0.8875637 0.5009099 -0.2839428 -0.2183971 0.0711865 0.1497323 -0.02425295 -0.1816409 0.1450326 0.2780912 0.3820866 0.5849643 -0.1975226 0.06914261 0.3578103 0.4064427 -0.1349747
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.28038 1.00101 -1.279 0.20086
## [2,] -1.58549 0.76633 -2.069 0.03855 *
## [3,] -1.16461 1.87047 -0.623 0.53353
## [4,] -0.88756 1.60797 -0.552 0.58096
## [5,] 0.50091 0.08560 5.852 4.86e-09 ***
## [6,] -0.28394 0.13393 -2.120 0.03399 *
## [7,] -0.21840 0.09384 -2.327 0.01995 *
## [8,] 0.07119 0.11724 0.607 0.54372
## [9,] 0.14973 0.06553 2.285 0.02232 *
## [10,] -0.02425 0.10253 -0.237 0.81301
## [11,] -0.18164 0.07184 -2.528 0.01146 *
## [12,] 0.14503 0.08975 1.616 0.10611
## [13,] 0.27809 0.15995 1.739 0.08210 .
## [14,] 0.38209 0.25025 1.527 0.12681
## [15,] 0.58496 0.17535 3.336 0.00085 ***
## [16,] -0.19752 0.21907 -0.902 0.36724
## [17,] 0.06914 0.13750 0.503 0.61507
## [18,] 0.35781 0.21513 1.663 0.09627 .
## [19,] 0.40644 0.15074 2.696 0.00701 **
## [20,] -0.13497 0.18832 -0.717 0.47355
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.280382 -1.58549 -1.164612 -0.8875637
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.5009 -0.2839 -0.218 0.0712
## [2,] 0.1497 -0.0243 -0.182 0.1450
## [3,] 0.2781 0.3821 0.585 -0.1975
## [4,] 0.0691 0.3578 0.406 -0.1350
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 140.00912 56.40640 -40.38715 -49.59317
## [2,] 56.40640 82.05611 -75.97198 -73.65689
## [3,] -40.38715 -75.97198 488.85420 377.02358
## [4,] -49.59317 -73.65689 377.02358 361.27215
## ----
## aic= 19.52481
## bic= 19.92623
## Number of parameters: 20
## initial estimates: -0.9179 -2.2246 -0.5266 -0.0075 0.3395 0.1575 0.1262 -0.1102 -0.079 0.3666 -0.0698 0.0878 0.1572 -0.1668 0.2683 0.0519 0.1398 -0.404 0.0888 0.0459
## Par. lower-bounds: -2.2932 -4.1442 -2.9911 -1.8599 0.1677 0.0159 0.0113 -0.2672 -0.3189 0.1688 -0.2302 -0.1313 -0.1507 -0.4207 0.0625 -0.2294 -0.0916 -0.5948 -0.0659 -0.1656
## Par. upper-bounds: 0.4574 -0.3051 1.9378 1.8449 0.5113 0.2992 0.2411 0.0468 0.1608 0.5643 0.0905 0.307 0.4651 0.0871 0.4742 0.3333 0.3712 -0.2132 0.2435 0.2574
## Final Estimates: -0.8749031 -2.136017 -0.4713097 -0.0752181 0.3343462 0.1606716 0.1280686 -0.1068307 -0.08965674 0.3730062 -0.06603896 0.09477695 0.1505407 -0.162768 0.2707048 0.05626536 0.1479069 -0.4089093 0.08589782 0.0406058
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.87490 0.68559 -1.276 0.201908
## [2,] -2.13602 0.96002 -2.225 0.026083 *
## [3,] -0.47131 1.22736 -0.384 0.700977
## [4,] -0.07522 0.92526 -0.081 0.935208
## [5,] 0.33435 0.08566 3.903 9.50e-05 ***
## [6,] 0.16067 0.07070 2.272 0.023059 *
## [7,] 0.12807 0.05736 2.233 0.025570 *
## [8,] -0.10683 0.07836 -1.363 0.172788
## [9,] -0.08966 0.11994 -0.747 0.454765
## [10,] 0.37301 0.09900 3.768 0.000165 ***
## [11,] -0.06604 0.08032 -0.822 0.410936
## [12,] 0.09478 0.10972 0.864 0.387696
## [13,] 0.15054 0.15330 0.982 0.326096
## [14,] -0.16277 0.12653 -1.286 0.198321
## [15,] 0.27070 0.10265 2.637 0.008361 **
## [16,] 0.05627 0.14024 0.401 0.688257
## [17,] 0.14791 0.11549 1.281 0.200320
## [18,] -0.40891 0.09533 -4.289 1.79e-05 ***
## [19,] 0.08590 0.07734 1.111 0.266703
## [20,] 0.04061 0.10565 0.384 0.700735
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.8749031 -2.136017 -0.4713097 -0.0752181
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3343 0.161 0.1281 -0.1068
## [2,] -0.0897 0.373 -0.0660 0.0948
## [3,] 0.1505 -0.163 0.2707 0.0563
## [4,] 0.1479 -0.409 0.0859 0.0406
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 64.23329 49.58714 -34.44715 -23.74071
## [2,] 49.58714 125.92822 -45.54835 -47.26614
## [3,] -34.44715 -45.54835 205.71778 99.19824
## [4,] -23.74071 -47.26614 99.19824 116.76483
## ----
## aic= 18.26081
## bic= 18.66223
## Number of parameters: 20
## initial estimates: -0.9729 -1.7968 -0.6796 -0.3137 0.3824 0.1732 -0.1634 0.154 -0.1131 0.2234 -0.3967 0.2691 0.0664 -0.0433 0.8475 -0.2692 0.016 0.1251 0.2057 0.3433
## Par. lower-bounds: -2.6294 -3.2981 -2.7006 -2.072 0.2226 -0.0115 -0.305 -0.039 -0.2579 0.056 -0.525 0.0942 -0.1285 -0.2686 0.6748 -0.5047 -0.1537 -0.071 0.0554 0.1384
## Par. upper-bounds: 0.6835 -0.2955 1.3413 1.4445 0.5422 0.3579 -0.0218 0.347 0.0317 0.3908 -0.2684 0.4441 0.2614 0.1821 1.0202 -0.0337 0.1856 0.3211 0.356 0.5482
## Final Estimates: -0.9287883 -1.722795 -0.6066592 -0.36546 0.3779034 0.1754592 -0.16387 0.1627394 -0.1207338 0.227224 -0.397508 0.2837839 0.05886705 -0.03949033 0.8467046 -0.2547126 0.02124882 0.1223985 0.2062267 0.3331295
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.92879 0.82383 -1.127 0.25957
## [2,] -1.72280 0.74925 -2.299 0.02148 *
## [3,] -0.60666 1.00633 -0.603 0.54661
## [4,] -0.36546 0.87470 -0.418 0.67608
## [5,] 0.37790 0.07944 4.757 1.96e-06 ***
## [6,] 0.17546 0.09210 1.905 0.05678 .
## [7,] -0.16387 0.07064 -2.320 0.02036 *
## [8,] 0.16274 0.09539 1.706 0.08800 .
## [9,] -0.12073 0.07225 -1.671 0.09471 .
## [10,] 0.22722 0.08377 2.713 0.00668 **
## [11,] -0.39751 0.06425 -6.187 6.13e-10 ***
## [12,] 0.28378 0.08675 3.271 0.00107 **
## [13,] 0.05887 0.09705 0.607 0.54413
## [14,] -0.03949 0.11251 -0.351 0.72560
## [15,] 0.84670 0.08629 9.812 < 2e-16 ***
## [16,] -0.25471 0.11652 -2.186 0.02882 *
## [17,] 0.02125 0.08436 0.252 0.80113
## [18,] 0.12240 0.09780 1.252 0.21072
## [19,] 0.20623 0.07501 2.749 0.00597 **
## [20,] 0.33313 0.10128 3.289 0.00101 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.9287883 -1.722795 -0.6066592 -0.36546
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3779 0.1755 -0.164 0.163
## [2,] -0.1207 0.2272 -0.398 0.284
## [3,] 0.0589 -0.0395 0.847 -0.255
## [4,] 0.0212 0.1224 0.206 0.333
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 94.781265 32.08880 -6.836294 7.522588
## [2,] 32.088800 78.39654 -13.644422 -23.246507
## [3,] -6.836294 -13.64442 141.423544 83.744504
## [4,] 7.522588 -23.24651 83.744504 106.848462
## ----
## aic= 17.88578
## bic= 18.2872
## Number of parameters: 20
## initial estimates: -0.7109 -1.7708 -0.6821 -0.0635 0.4562 -0.0042 -0.0196 0.2254 -0.0143 0.1982 -0.0336 -0.0061 0.0277 0.2688 0.5469 -0.0875 -0.0043 0.1959 -0.1332 0.7384
## Par. lower-bounds: -2.6131 -3.3452 -2.7177 -1.2895 0.3098 -0.2022 -0.1572 0.0278 -0.1354 0.0343 -0.1475 -0.1696 -0.1289 0.057 0.3996 -0.2989 -0.0987 0.0683 -0.2219 0.611
## Par. upper-bounds: 1.1913 -0.1965 1.3535 1.1626 0.6026 0.1937 0.1181 0.423 0.1068 0.362 0.0804 0.1574 0.1843 0.4807 0.6942 0.124 0.09 0.3235 -0.0445 0.8657
## Final Estimates: -0.6770366 -1.6883 -0.5869893 -0.125814 0.454404 -0.004028985 -0.01786041 0.2305971 -0.01867253 0.198648 -0.02937775 0.006481811 0.02264397 0.2693732 0.5516929 -0.07294432 -0.00104415 0.1955366 -0.1363583 0.7288569
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.677037 0.944609 -0.717 0.4735
## [2,] -1.688300 0.785195 -2.150 0.0315 *
## [3,] -0.586989 1.014313 -0.579 0.5628
## [4,] -0.125814 0.611472 -0.206 0.8370
## [5,] 0.454404 0.072840 6.238 4.42e-10 ***
## [6,] -0.004029 0.098693 -0.041 0.9674
## [7,] -0.017860 0.068514 -0.261 0.7943
## [8,] 0.230597 0.097692 2.360 0.0183 *
## [9,] -0.018673 0.060520 -0.309 0.7577
## [10,] 0.198648 0.082036 2.421 0.0155 *
## [11,] -0.029378 0.056947 -0.516 0.6059
## [12,] 0.006482 0.081139 0.080 0.9363
## [13,] 0.022644 0.078151 0.290 0.7720
## [14,] 0.269373 0.105977 2.542 0.0110 *
## [15,] 0.551693 0.073556 7.500 6.37e-14 ***
## [16,] -0.072944 0.104880 -0.696 0.4867
## [17,] -0.001044 0.047070 -0.022 0.9823
## [18,] 0.195537 0.063875 3.061 0.0022 **
## [19,] -0.136358 0.044339 -3.075 0.0021 **
## [20,] 0.728857 0.063212 11.530 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.6770366 -1.6883 -0.5869893 -0.125814
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.45440 -0.00403 -0.0179 0.23060
## [2,] -0.01867 0.19865 -0.0294 0.00648
## [3,] 0.02264 0.26937 0.5517 -0.07294
## [4,] -0.00104 0.19554 -0.1364 0.72886
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 121.882676 4.204335 -28.65709 -10.98735
## [2,] 4.204335 84.193873 -10.76546 -20.21863
## [3,] -28.657085 -10.765461 140.48358 43.08901
## [4,] -10.987347 -20.218631 43.08901 51.03599
## ----
## aic= 17.9254
## bic= 18.32682
## Number of parameters: 20
## initial estimates: -0.6472 -1.4137 -0.6036 -0.1492 0.197 -0.2356 -0.0543 -0.0863 0.3008 0.0723 -0.1022 -0.0859 0.0957 -0.0686 0.6722 -0.1164 -0.0789 -0.1013 0.1035 0.2523
## Par. lower-bounds: -1.6586 -2.7252 -2.4465 -1.6894 0.0331 -0.3744 -0.1297 -0.2068 0.0883 -0.1076 -0.2 -0.2422 -0.203 -0.3215 0.5348 -0.3359 -0.3285 -0.3126 -0.0113 0.0688
## Par. upper-bounds: 0.3641 -0.1023 1.2392 1.391 0.3609 -0.0969 0.0211 0.0342 0.5133 0.2523 -0.0045 0.0704 0.3944 0.1842 0.8096 0.1032 0.1707 0.11 0.2183 0.4358
## Final Estimates: -0.6178991 -1.351522 -0.5222204 -0.2198159 0.1917218 -0.2361815 -0.05319232 -0.08193465 0.289564 0.07118855 -0.09996031 -0.07666862 0.08100422 -0.0701549 0.6751952 -0.1042936 -0.06613856 -0.09998487 0.1009406 0.2418367
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.61790 0.50359 -1.227 0.219823
## [2,] -1.35152 0.65520 -2.063 0.039137 *
## [3,] -0.52222 0.92003 -0.568 0.570298
## [4,] -0.21982 0.76917 -0.286 0.775045
## [5,] 0.19172 0.08156 2.351 0.018739 *
## [6,] -0.23618 0.06929 -3.408 0.000654 ***
## [7,] -0.05319 0.03762 -1.414 0.157340
## [8,] -0.08193 0.05991 -1.368 0.171424
## [9,] 0.28956 0.10612 2.729 0.006358 **
## [10,] 0.07119 0.09016 0.790 0.429758
## [11,] -0.09996 0.04894 -2.042 0.041109 *
## [12,] -0.07667 0.07795 -0.984 0.325314
## [13,] 0.08100 0.14901 0.544 0.586703
## [14,] -0.07015 0.12660 -0.554 0.579473
## [15,] 0.67520 0.06873 9.825 < 2e-16 ***
## [16,] -0.10429 0.10945 -0.953 0.340666
## [17,] -0.06614 0.12458 -0.531 0.595502
## [18,] -0.09998 0.10585 -0.945 0.344849
## [19,] 0.10094 0.05746 1.757 0.078961 .
## [20,] 0.24184 0.09151 2.643 0.008225 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.6178991 -1.351522 -0.5222204 -0.2198159
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.1917 -0.2362 -0.0532 -0.0819
## [2,] 0.2896 0.0712 -0.1000 -0.0767
## [3,] 0.0810 -0.0702 0.6752 -0.1043
## [4,] -0.0661 -0.1000 0.1009 0.2418
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 35.999875 13.77875 -6.716286 -9.475427
## [2,] 13.778749 60.94098 -14.861159 -30.514987
## [3,] -6.716286 -14.86116 120.166412 35.908046
## [4,] -9.475427 -30.51499 35.908046 83.996192
## ----
## aic= 16.74667
## bic= 17.14809
## Number of parameters: 20
## initial estimates: -1.3284 -2.3427 -1.2735 -0.3598 0.5163 0.0339 0.0247 -0.1498 -0.0119 0.2777 -0.0184 -0.0616 -0.0134 -0.0645 0.1462 -0.0976 -0.156 0.0598 -0.0027 0.0037
## Par. lower-bounds: -3.425 -4.245 -5.0867 -2.1176 0.3637 -0.1558 -0.084 -0.3889 -0.1505 0.1056 -0.117 -0.2785 -0.2911 -0.4095 -0.0514 -0.5325 -0.284 -0.0992 -0.0938 -0.1967
## Par. upper-bounds: 0.7682 -0.4404 2.5397 1.3979 0.669 0.2235 0.1333 0.0893 0.1266 0.4498 0.0802 0.1553 0.2643 0.2804 0.3439 0.3372 -0.028 0.2188 0.0884 0.2041
## Final Estimates: -1.270925 -2.270936 -1.142932 -0.4088817 0.5110295 0.03429453 0.02580267 -0.1447802 -0.01857096 0.2782714 -0.01698768 -0.05534558 -0.02545398 -0.06357486 0.1488382 -0.08626178 -0.1514418 0.05942146 -0.003714956 -0.0005699302
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.2709254 1.0452172 -1.216 0.22401
## [2,] -2.2709365 0.9504636 -2.389 0.01688 *
## [3,] -1.1429320 1.9038204 -0.600 0.54828
## [4,] -0.4088817 0.8764909 -0.466 0.64086
## [5,] 0.5110295 0.0760163 6.723 1.78e-11 ***
## [6,] 0.0342945 0.0947493 0.362 0.71739
## [7,] 0.0258027 0.0542565 0.476 0.63438
## [8,] -0.1447802 0.1192469 -1.214 0.22470
## [9,] -0.0185710 0.0691181 -0.269 0.78817
## [10,] 0.2782714 0.0861607 3.230 0.00124 **
## [11,] -0.0169877 0.0493349 -0.344 0.73060
## [12,] -0.0553456 0.1083928 -0.511 0.60963
## [13,] -0.0254540 0.1384944 -0.184 0.85418
## [14,] -0.0635749 0.1725619 -0.368 0.71256
## [15,] 0.1488382 0.0984922 1.511 0.13075
## [16,] -0.0862618 0.2152536 -0.401 0.68861
## [17,] -0.1514418 0.0637276 -2.376 0.01748 *
## [18,] 0.0594215 0.0794348 0.748 0.45443
## [19,] -0.0037150 0.0450833 -0.082 0.93433
## [20,] -0.0005699 0.0976523 -0.006 0.99534
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.270925 -2.270936 -1.142932 -0.4088817
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.5110 0.0343 0.02580 -0.14478
## [2,] -0.0186 0.2783 -0.01699 -0.05535
## [3,] -0.0255 -0.0636 0.14884 -0.08626
## [4,] -0.1514 0.0594 -0.00371 -0.00057
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 150.122129 58.13885 -1.663988 -15.91661
## [2,] 58.138845 124.13529 -10.107900 -17.25556
## [3,] -1.663988 -10.10790 497.979870 132.34873
## [4,] -15.916612 -17.25556 132.348735 105.53357
## ----
## aic= 20.32817
## bic= 20.72959
## Number of parameters: 20
## initial estimates: -1.3659 -1.6721 -0.6081 -0.3662 0.3736 -0.1394 0.1494 -0.1313 0.06 -0.1932 -0.0485 0.0177 0.1284 -0.1056 0.539 -0.0101 0.1641 -0.051 0.1749 0.309
## Par. lower-bounds: -3.0885 -3.1199 -2.5806 -2.1166 0.194 -0.3739 -0.0055 -0.3159 -0.091 -0.3903 -0.1786 -0.1375 -0.0773 -0.374 0.3616 -0.2215 -0.0184 -0.2892 0.0176 0.1214
## Par. upper-bounds: 0.3568 -0.2244 1.3645 1.3841 0.5532 0.095 0.3043 0.0533 0.2109 0.0038 0.0817 0.1728 0.3341 0.1629 0.7164 0.2013 0.3466 0.1872 0.3323 0.4966
## Final Estimates: -1.294934 -1.59838 -0.5280496 -0.4380183 0.3647014 -0.1343516 0.1528569 -0.1206291 0.05069547 -0.1879508 -0.04483882 0.02883564 0.1184051 -0.0998605 0.5429147 0.001944139 0.1731592 -0.05619365 0.1713905 0.2981587
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.294934 0.858193 -1.509 0.13132
## [2,] -1.598380 0.722476 -2.212 0.02694 *
## [3,] -0.528050 0.982502 -0.537 0.59095
## [4,] -0.438018 0.871886 -0.502 0.61540
## [5,] 0.364701 0.089343 4.082 4.46e-05 ***
## [6,] -0.134352 0.117097 -1.147 0.25124
## [7,] 0.152857 0.077357 1.976 0.04815 *
## [8,] -0.120629 0.091655 -1.316 0.18813
## [9,] 0.050695 0.075214 0.674 0.50030
## [10,] -0.187951 0.098582 -1.907 0.05658 .
## [11,] -0.044839 0.065152 -0.688 0.49132
## [12,] 0.028836 0.077225 0.373 0.70885
## [13,] 0.118405 0.102306 1.157 0.24713
## [14,] -0.099860 0.134148 -0.744 0.45663
## [15,] 0.542915 0.088875 6.109 1.00e-09 ***
## [16,] 0.001944 0.105979 0.018 0.98536
## [17,] 0.173159 0.090780 1.907 0.05646 .
## [18,] -0.056194 0.119004 -0.472 0.63678
## [19,] 0.171390 0.078681 2.178 0.02938 *
## [20,] 0.298159 0.093401 3.192 0.00141 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.294934 -1.59838 -0.5280496 -0.4380183
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3647 -0.1344 0.1529 -0.12063
## [2,] 0.0507 -0.1880 -0.0448 0.02884
## [3,] 0.1184 -0.0999 0.5429 0.00194
## [4,] 0.1732 -0.0562 0.1714 0.29816
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 105.082636 42.30305 10.25729 2.264304
## [2,] 42.303046 74.47788 -29.19692 -33.160257
## [3,] 10.257293 -29.19692 137.75422 65.430791
## [4,] 2.264304 -33.16026 65.43079 108.481883
## ----
## aic= 17.99561
## bic= 18.39703
## Number of parameters: 20
## initial estimates: -0.4789 -1.9055 -1.0797 -0.5106 0.0491 0.0336 -0.0405 0.021 -0.1952 0.0447 -0.2303 -0.0272 0.3268 0.0887 0.7227 -0.4506 0.3736 0.1809 0.2135 0.2017
## Par. lower-bounds: -1.3444 -3.6316 -3.6467 -2.2744 -0.1193 -0.0501 -0.1042 -0.0798 -0.5309 -0.1223 -0.3573 -0.2282 -0.1725 -0.1596 0.5338 -0.7495 0.0306 0.0104 0.0838 -0.0037
## Par. upper-bounds: 0.3866 -0.1794 1.4873 1.2531 0.2174 0.1173 0.0231 0.1218 0.1406 0.2116 -0.1033 0.1738 0.8261 0.3369 0.9115 -0.1516 0.7167 0.3515 0.3433 0.4071
## Final Estimates: -0.4490655 -1.805072 -0.9730718 -0.5714475 0.04534945 0.03365173 -0.04123269 0.02526538 -0.2077008 0.04473175 -0.2326892 -0.01280618 0.3135044 0.08872952 0.7201824 -0.4352536 0.3812174 0.1809005 0.2149654 0.1929516
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.44907 0.43041 -1.043 0.296787
## [2,] -1.80507 0.86154 -2.095 0.036156 *
## [3,] -0.97307 1.27773 -0.762 0.446320
## [4,] -0.57145 0.87713 -0.651 0.514726
## [5,] 0.04535 0.08392 0.540 0.588914
## [6,] 0.03365 0.04179 0.805 0.420687
## [7,] -0.04123 0.03178 -1.297 0.194538
## [8,] 0.02527 0.05001 0.505 0.613440
## [9,] -0.20770 0.16797 -1.237 0.216264
## [10,] 0.04473 0.08365 0.535 0.592837
## [11,] -0.23269 0.06363 -3.657 0.000255 ***
## [12,] -0.01281 0.10015 -0.128 0.898250
## [13,] 0.31350 0.24912 1.258 0.208223
## [14,] 0.08873 0.12406 0.715 0.474484
## [15,] 0.72018 0.09436 7.633 2.31e-14 ***
## [16,] -0.43525 0.14847 -2.932 0.003372 **
## [17,] 0.38122 0.17101 2.229 0.025802 *
## [18,] 0.18090 0.08517 2.124 0.033661 *
## [19,] 0.21497 0.06477 3.319 0.000904 ***
## [20,] 0.19295 0.10192 1.893 0.058344 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.4490655 -1.805072 -0.9730718 -0.5714475
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.0453 0.0337 -0.0412 0.0253
## [2,] -0.2077 0.0447 -0.2327 -0.0128
## [3,] 0.3135 0.0887 0.7202 -0.4353
## [4,] 0.3812 0.1809 0.2150 0.1930
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 26.2401967 12.25613 -1.657844 -0.8431626
## [2,] 12.2561309 105.13552 -18.789439 -26.7059092
## [3,] -1.6578441 -18.78944 231.247817 105.8010386
## [4,] -0.8431626 -26.70591 105.801039 108.9746243
## ----
## aic= 17.60922
## bic= 18.01064
## Number of parameters: 20
## initial estimates: -1.9275 -2.9894 -1.0674 -0.351 0.2402 0.0141 -0.0721 0.0076 -0.2437 0.3399 -0.096 -0.0391 0.4078 -0.0908 0.3386 0.1006 0.2655 0.1281 0.2277 0.205
## Par. lower-bounds: -4.9669 -5.7808 -4.7331 -3.4964 0.0601 -0.1933 -0.2425 -0.1976 -0.409 0.1495 -0.2525 -0.2275 0.1907 -0.3409 0.1332 -0.1469 0.0791 -0.0865 0.0514 -0.0073
## Par. upper-bounds: 1.1118 -0.198 2.5982 2.7945 0.4203 0.2214 0.0982 0.2127 -0.0783 0.5304 0.0605 0.1494 0.625 0.1594 0.5441 0.348 0.4518 0.3427 0.404 0.4173
## Final Estimates: -1.796351 -2.830351 -0.9410375 -0.4949074 0.2319905 0.01806613 -0.06920902 0.01489965 -0.2535808 0.3447669 -0.09247172 -0.03020402 0.3999654 -0.08690687 0.341415 0.1076057 0.2744562 0.1237192 0.224552 0.1970133
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.79635 1.51329 -1.187 0.235208
## [2,] -2.83035 1.39301 -2.032 0.042171 *
## [3,] -0.94104 1.82298 -0.516 0.605710
## [4,] -0.49491 1.56663 -0.316 0.752075
## [5,] 0.23199 0.08962 2.589 0.009634 **
## [6,] 0.01807 0.10360 0.174 0.861563
## [7,] -0.06921 0.08511 -0.813 0.416125
## [8,] 0.01490 0.10229 0.146 0.884194
## [9,] -0.25358 0.08249 -3.074 0.002113 **
## [10,] 0.34477 0.09536 3.616 0.000300 ***
## [11,] -0.09247 0.07834 -1.180 0.237868
## [12,] -0.03020 0.09415 -0.321 0.748363
## [13,] 0.39997 0.10796 3.705 0.000212 ***
## [14,] -0.08691 0.12479 -0.696 0.486146
## [15,] 0.34142 0.10253 3.330 0.000868 ***
## [16,] 0.10761 0.12321 0.873 0.382463
## [17,] 0.27446 0.09278 2.958 0.003094 **
## [18,] 0.12372 0.10724 1.154 0.248636
## [19,] 0.22455 0.08811 2.549 0.010817 *
## [20,] 0.19701 0.10588 1.861 0.062795 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.796351 -2.830351 -0.9410375 -0.4949074
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.232 0.0181 -0.0692 0.0149
## [2,] -0.254 0.3448 -0.0925 -0.0302
## [3,] 0.400 -0.0869 0.3414 0.1076
## [4,] 0.274 0.1237 0.2246 0.1970
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 316.98035 152.0753 -52.51796 -73.95045
## [2,] 152.07535 268.6061 -113.65517 -127.48877
## [3,] -52.51796 -113.6552 460.03639 251.15300
## [4,] -73.95045 -127.4888 251.15300 339.75993
## ----
## aic= 22.53943
## bic= 22.94085
## Number of parameters: 20
## initial estimates: -1.7897 -2.5191 -0.1651 0.3273 0.6924 0.1865 -0.2336 0.3154 0.369 0.2341 -0.253 0.1207 -0.1178 -0.1481 0.2977 0.1043 -0.2432 0.1168 0.1415 0.1165
## Par. lower-bounds: -4.275 -4.9688 -2.6205 -1.5981 0.4841 -0.0781 -0.4401 0.0607 0.1637 -0.0267 -0.4566 -0.1304 -0.3235 -0.4095 0.0937 -0.1474 -0.4046 -0.0881 -0.0184 -0.0809
## Par. upper-bounds: 0.6957 -0.0694 2.2902 2.2527 0.9006 0.451 -0.0271 0.5702 0.5743 0.4949 -0.0495 0.3718 0.088 0.1133 0.5017 0.356 -0.0819 0.3218 0.3015 0.3138
## Final Estimates: -1.712492 -2.41283 -0.1252251 0.2397139 0.6935655 0.1890313 -0.2296585 0.3239539 0.3706847 0.2376255 -0.2476352 0.1324262 -0.1171472 -0.146763 0.2997215 0.1086817 -0.2446446 0.1139274 0.1371273 0.1067982
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.71249 1.23863 -1.383 0.166799
## [2,] -2.41283 1.22393 -1.971 0.048681 *
## [3,] -0.12523 1.22097 -0.103 0.918311
## [4,] 0.23971 0.96232 0.249 0.803284
## [5,] 0.69357 0.10405 6.666 2.63e-11 ***
## [6,] 0.18903 0.13216 1.430 0.152630
## [7,] -0.22966 0.10309 -2.228 0.025902 *
## [8,] 0.32395 0.12694 2.552 0.010712 *
## [9,] 0.37068 0.10282 3.605 0.000312 ***
## [10,] 0.23763 0.13059 1.820 0.068822 .
## [11,] -0.24764 0.10187 -2.431 0.015061 *
## [12,] 0.13243 0.12544 1.056 0.291093
## [13,] -0.11715 0.10259 -1.142 0.253503
## [14,] -0.14676 0.13031 -1.126 0.260053
## [15,] 0.29972 0.10165 2.949 0.003193 **
## [16,] 0.10868 0.12517 0.868 0.385226
## [17,] -0.24464 0.08085 -3.026 0.002480 **
## [18,] 0.11393 0.10270 1.109 0.267269
## [19,] 0.13713 0.08011 1.712 0.086944 .
## [20,] 0.10680 0.09864 1.083 0.278950
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.712492 -2.41283 -0.1252251 0.2397139
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.694 0.189 -0.230 0.324
## [2,] 0.371 0.238 -0.248 0.132
## [3,] -0.117 -0.147 0.300 0.109
## [4,] -0.245 0.114 0.137 0.107
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 185.04292 140.38146 -89.41627 -57.20577
## [2,] 140.38146 180.67764 -90.52662 -62.55231
## [3,] -89.41627 -90.52662 179.89924 78.51828
## [4,] -57.20577 -62.55231 78.51828 111.73417
## ----
## aic= 18.95642
## bic= 19.35784
## Number of parameters: 20
## initial estimates: -0.8789 -2.4391 -0.2958 -0.2012 0.3105 0.053 0.0557 0.008 -0.1521 0.2208 0.097 -0.2758 -0.0305 -0.0863 0.1441 0.135 0.3496 -0.4185 -0.152 0.0471
## Par. lower-bounds: -2.2675 -4.626 -2.4125 -1.9795 0.1437 -0.0617 -0.0669 -0.1255 -0.4147 0.0401 -0.096 -0.4861 -0.2847 -0.2612 -0.0427 -0.0686 0.136 -0.5654 -0.3089 -0.1239
## Par. upper-bounds: 0.5097 -0.2523 1.8209 1.5771 0.4773 0.1678 0.1782 0.1415 0.1106 0.4015 0.29 -0.0655 0.2237 0.0886 0.3309 0.3386 0.5632 -0.2715 0.0049 0.2181
## Final Estimates: -0.84634 -2.348626 -0.2500166 -0.2733945 0.3078696 0.05270975 0.05831917 0.008823867 -0.1594605 0.2199454 0.1043787 -0.2735064 -0.0342279 -0.08670469 0.1478015 0.136174 0.3554941 -0.417805 -0.1578738 0.04527513
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.846340 0.691521 -1.224 0.220997
## [2,] -2.348626 1.092767 -2.149 0.031615 *
## [3,] -0.250017 1.053763 -0.237 0.812454
## [4,] -0.273395 0.888420 -0.308 0.758287
## [5,] 0.307870 0.083160 3.702 0.000214 ***
## [6,] 0.052710 0.057276 0.920 0.357426
## [7,] 0.058319 0.061041 0.955 0.339371
## [8,] 0.008824 0.066645 0.132 0.894668
## [9,] -0.159461 0.131413 -1.213 0.224964
## [10,] 0.219945 0.090507 2.430 0.015093 *
## [11,] 0.104379 0.096461 1.082 0.279217
## [12,] -0.273506 0.105312 -2.597 0.009401 **
## [13,] -0.034228 0.126729 -0.270 0.787093
## [14,] -0.086705 0.087280 -0.993 0.320512
## [15,] 0.147801 0.093023 1.589 0.112092
## [16,] 0.136174 0.101556 1.341 0.179963
## [17,] 0.355494 0.106841 3.327 0.000877 ***
## [18,] -0.417805 0.073584 -5.678 1.36e-08 ***
## [19,] -0.157874 0.078425 -2.013 0.044108 *
## [20,] 0.045275 0.085620 0.529 0.596952
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.84634 -2.348626 -0.2500166 -0.2733945
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3079 0.0527 0.0583 0.00882
## [2,] -0.1595 0.2199 0.1044 -0.27351
## [3,] -0.0342 -0.0867 0.1478 0.13617
## [4,] 0.3555 -0.4178 -0.1579 0.04528
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 67.261552 40.81739 -22.01308 -7.652877
## [2,] 40.817388 167.96337 -57.67996 -39.744217
## [3,] -22.013078 -57.67996 156.20555 67.212289
## [4,] -7.652877 -39.74422 67.21229 111.023718
## ----
## aic= 18.73033
## bic= 19.13175
## Number of parameters: 20
## initial estimates: -1.52 -2.2338 -0.3562 -0.0459 0.2464 0.0484 -0.0436 -0.0047 -0.1742 0.239 -0.1437 0.0113 0.1027 0.0412 0.4084 0.2646 0.1196 0.1355 0.1268 0.3936
## Par. lower-bounds: -3.9779 -4.566 -3.5755 -2.115 0.0284 -0.2069 -0.2221 -0.2829 -0.381 -0.0032 -0.3131 -0.2526 -0.1828 -0.2931 0.1745 -0.0998 -0.0638 -0.0794 -0.0235 0.1595
## Par. upper-bounds: 0.9379 0.0983 2.863 2.0232 0.4643 0.3037 0.1349 0.2735 0.0326 0.4813 0.0257 0.2753 0.3881 0.3756 0.6422 0.629 0.3031 0.3504 0.2771 0.6278
## Final Estimates: -1.440964 -2.123759 -0.270183 -0.1339046 0.2410644 0.05366287 -0.04122754 0.004135821 -0.1816184 0.2463343 -0.1403848 0.02362585 0.09687662 0.04692344 0.4109537 0.2742068 0.1255584 0.1296685 0.1241333 0.3838091
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.440964 1.222028 -1.179 0.238335
## [2,] -2.123759 1.161867 -1.828 0.067567 .
## [3,] -0.270183 1.600017 -0.169 0.865905
## [4,] -0.133905 1.030408 -0.130 0.896604
## [5,] 0.241064 0.108543 2.221 0.026357 *
## [6,] 0.053663 0.127265 0.422 0.673273
## [7,] -0.041228 0.089104 -0.463 0.643586
## [8,] 0.004136 0.138563 0.030 0.976188
## [9,] -0.181618 0.103188 -1.760 0.078394 .
## [10,] 0.246334 0.120990 2.036 0.041752 *
## [11,] -0.140385 0.084723 -1.657 0.097524 .
## [12,] 0.023626 0.131779 0.179 0.857714
## [13,] 0.096877 0.142094 0.682 0.495380
## [14,] 0.046923 0.166612 0.282 0.778225
## [15,] 0.410954 0.116610 3.524 0.000425 ***
## [16,] 0.274207 0.181286 1.513 0.130390
## [17,] 0.125558 0.091484 1.372 0.169920
## [18,] 0.129669 0.107258 1.209 0.226687
## [19,] 0.124133 0.075079 1.653 0.098256 .
## [20,] 0.383809 0.116698 3.289 0.001006 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.440964 -2.123759 -0.270183 -0.1339046
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2411 0.0537 -0.0412 0.00414
## [2,] -0.1816 0.2463 -0.1404 0.02363
## [3,] 0.0969 0.0469 0.4110 0.27421
## [4,] 0.1256 0.1297 0.1241 0.38381
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 208.20106 138.42438 -138.8607 -72.92649
## [2,] 138.42438 188.17094 -148.1779 -96.29939
## [3,] -138.86067 -148.17792 356.7942 165.40162
## [4,] -72.92649 -96.29939 165.4016 147.91785
## ----
## aic= 19.78202
## bic= 20.18344
## Number of parameters: 20
## initial estimates: -0.8721 -1.997 0.0539 0.128 -0.0213 0.1475 0.1353 -0.3473 -0.3715 0.6129 -0.0333 -0.1832 0.563 -0.2305 0.383 0.3621 0.2801 -0.2056 0.1869 0.2507
## Par. lower-bounds: -2.6329 -4.2457 -2.4479 -2.1909 -0.2493 -0.015 -0.0516 -0.5323 -0.6627 0.4054 -0.2721 -0.4195 0.239 -0.4614 0.1174 0.0992 -0.0202 -0.4196 -0.0593 0.0071
## Par. upper-bounds: 0.8887 0.2518 2.5556 2.4468 0.2067 0.31 0.3223 -0.1623 -0.0803 0.8205 0.2054 0.053 0.8869 4e-04 0.6486 0.6249 0.5804 0.0084 0.4331 0.4943
## Final Estimates: -0.8194161 -1.902257 0.06859969 0.02692338 -0.02737799 0.1518548 0.1379649 -0.3440049 -0.382642 0.6208144 -0.02855891 -0.1771153 0.5606502 -0.2290629 0.3837256 0.3634457 0.2920119 -0.2139305 0.182025 0.2441114
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.81942 0.87541 -0.936 0.349256
## [2,] -1.90226 1.11991 -1.699 0.089399 .
## [3,] 0.06860 1.24042 0.055 0.955896
## [4,] 0.02692 1.15028 0.023 0.981326
## [5,] -0.02738 0.11351 -0.241 0.809406
## [6,] 0.15185 0.08092 1.877 0.060571 .
## [7,] 0.13796 0.09326 1.479 0.139060
## [8,] -0.34400 0.09223 -3.730 0.000192 ***
## [9,] -0.38264 0.14524 -2.635 0.008426 **
## [10,] 0.62081 0.10354 5.996 2.02e-09 ***
## [11,] -0.02856 0.11933 -0.239 0.810857
## [12,] -0.17712 0.11802 -1.501 0.133412
## [13,] 0.56065 0.16100 3.482 0.000497 ***
## [14,] -0.22906 0.11477 -1.996 0.045957 *
## [15,] 0.38373 0.13228 2.901 0.003722 **
## [16,] 0.36345 0.13083 2.778 0.005468 **
## [17,] 0.29201 0.14979 1.949 0.051245 .
## [18,] -0.21393 0.10676 -2.004 0.045090 *
## [19,] 0.18202 0.12306 1.479 0.139106
## [20,] 0.24411 0.12172 2.005 0.044911 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.8194161 -1.902257 0.06859969 0.02692338
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] -0.0274 0.152 0.1380 -0.344
## [2,] -0.3826 0.621 -0.0286 -0.177
## [3,] 0.5607 -0.229 0.3837 0.363
## [4,] 0.2920 -0.214 0.1820 0.244
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 103.83693 85.97826 -104.8184 -76.03688
## [2,] 85.97826 170.00127 -126.4311 -98.53236
## [3,] -104.81836 -126.43105 208.9123 142.74779
## [4,] -76.03688 -98.53236 142.7478 180.84803
## ----
## aic= 18.37376
## bic= 18.77518
## Number of parameters: 20
## initial estimates: -1.5761 -2.8615 -0.5411 -0.0893 0.4162 0.1979 0.0517 -0.0338 0.1541 0.159 0.0339 -0.1297 -0.4832 0.5626 0.0065 0.358 -0.1407 0.0269 0.1566 0.1991
## Par. lower-bounds: -4.1293 -5.5214 -4.4537 -3.0404 0.21 -0.0208 -0.1049 -0.248 -0.0606 -0.0689 -0.1293 -0.3528 -0.7991 0.2274 -0.2336 0.0297 -0.3789 -0.2259 -0.0245 -0.0485
## Par. upper-bounds: 0.977 -0.2017 3.3715 2.8618 0.6223 0.4166 0.2084 0.1804 0.3689 0.3868 0.1972 0.0935 -0.1673 0.8978 0.2467 0.6863 0.0976 0.2797 0.3377 0.4467
## Final Estimates: -1.568047 -2.833247 -0.4969298 -0.1363898 0.4133951 0.1979285 0.05458891 -0.03012947 0.150138 0.159268 0.03818724 -0.1242338 -0.4852728 0.5632062 0.009068742 0.3612556 -0.1373797 0.02614597 0.1530249 0.1944297
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.568047 1.272263 -1.232 0.217767
## [2,] -2.833247 1.328443 -2.133 0.032945 *
## [3,] -0.496930 1.946849 -0.255 0.798531
## [4,] -0.136390 1.471676 -0.093 0.926161
## [5,] 0.413395 0.102923 4.017 5.91e-05 ***
## [6,] 0.197928 0.109247 1.812 0.070025 .
## [7,] 0.054589 0.078184 0.698 0.485044
## [8,] -0.030129 0.106896 -0.282 0.778053
## [9,] 0.150138 0.107468 1.397 0.162398
## [10,] 0.159268 0.114071 1.396 0.162649
## [11,] 0.038187 0.081636 0.468 0.639945
## [12,] -0.124234 0.111616 -1.113 0.265688
## [13,] -0.485273 0.157466 -3.082 0.002058 **
## [14,] 0.563206 0.167150 3.369 0.000753 ***
## [15,] 0.009069 0.119726 0.076 0.939621
## [16,] 0.361256 0.163611 2.208 0.027243 *
## [17,] -0.137380 0.119001 -1.154 0.248321
## [18,] 0.026146 0.126322 0.207 0.836026
## [19,] 0.153025 0.090436 1.692 0.090631 .
## [20,] 0.194430 0.123616 1.573 0.115754
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.568047 -2.833247 -0.4969298 -0.1363898
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.413 0.1979 0.05459 -0.0301
## [2,] 0.150 0.1593 0.03819 -0.1242
## [3,] -0.485 0.5632 0.00907 0.3613
## [4,] -0.137 0.0261 0.15302 0.1944
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 219.7542 157.9736 -152.8694 -121.8349
## [2,] 157.9736 239.5883 -152.7974 -119.6477
## [3,] -152.8694 -152.7974 514.3689 304.1592
## [4,] -121.8349 -119.6477 304.1592 293.7578
## ----
## aic= 21.14864
## bic= 21.55006
## Number of parameters: 20
## initial estimates: -1.4046 -2.1167 -1.1711 -0.0785 0.244 -0.0251 -0.0831 0.3221 0.0164 0.1404 -0.1529 0.1851 -0.4861 -0.0697 0.5452 -0.5734 -0.1317 -0.0906 0.1698 -0.3446
## Par. lower-bounds: -3.2127 -4.0629 -4.6864 -1.819 0.044 -0.2181 -0.1705 0.1214 -0.1988 -0.0675 -0.247 -0.031 -0.8749 -0.4451 0.3752 -0.9636 -0.3242 -0.2765 0.0857 -0.5378
## Par. upper-bounds: 0.4035 -0.1706 2.3442 1.6619 0.444 0.168 0.0044 0.5228 0.2317 0.3482 -0.0588 0.4011 -0.0973 0.3057 0.7152 -0.1832 0.0608 0.0952 0.254 -0.1514
## Final Estimates: -1.343211 -2.033978 -1.084982 -0.1703267 0.2404433 -0.02457292 -0.08159625 0.3254807 0.01227649 0.1412262 -0.1511646 0.1890705 -0.4918843 -0.06913992 0.5475539 -0.5680925 -0.1278719 -0.09183508 0.1682622 -0.3484425
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.34321 0.90306 -1.487 0.13691
## [2,] -2.03398 0.97275 -2.091 0.03653 *
## [3,] -1.08498 1.75282 -0.619 0.53592
## [4,] -0.17033 0.87010 -0.196 0.84480
## [5,] 0.24044 0.10011 2.402 0.01631 *
## [6,] -0.02457 0.09671 -0.254 0.79943
## [7,] -0.08160 0.04378 -1.864 0.06234 .
## [8,] 0.32548 0.10049 3.239 0.00120 **
## [9,] 0.01228 0.10782 0.114 0.90935
## [10,] 0.14123 0.10416 1.356 0.17516
## [11,] -0.15116 0.04716 -3.206 0.00135 **
## [12,] 0.18907 0.10825 1.747 0.08071 .
## [13,] -0.49188 0.19435 -2.531 0.01138 *
## [14,] -0.06914 0.18774 -0.368 0.71266
## [15,] 0.54755 0.08498 6.444 1.17e-10 ***
## [16,] -0.56809 0.19507 -2.912 0.00359 **
## [17,] -0.12787 0.09646 -1.326 0.18497
## [18,] -0.09184 0.09318 -0.986 0.32436
## [19,] 0.16826 0.04218 3.989 6.63e-05 ***
## [20,] -0.34844 0.09683 -3.599 0.00032 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.343211 -2.033978 -1.084982 -0.1703267
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2404 -0.0246 -0.0816 0.325
## [2,] 0.0123 0.1412 -0.1512 0.189
## [3,] -0.4919 -0.0691 0.5476 -0.568
## [4,] -0.1279 -0.0918 0.1683 -0.348
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 116.26429 72.53108 19.31043 -34.15727
## [2,] 72.53108 134.90579 -51.15530 -49.97635
## [3,] 19.31043 -51.15530 438.06865 84.79460
## [4,] -34.15727 -49.97635 84.79460 107.93232
## ----
## aic= 19.8173
## bic= 20.21872
## Number of parameters: 20
## initial estimates: -1.1103 -1.6105 -0.7852 -0.3579 0.2609 -0.496 -0.1162 0.2249 0.004 -0.0374 -0.1026 0.1497 -0.2878 0.2661 0.02 -0.2156 -0.1769 0.3128 0.0082 0.0063
## Par. lower-bounds: -3.5488 -3.3609 -4.5707 -2.1377 0.0533 -0.7775 -0.2717 -0.0869 -0.1451 -0.2394 -0.2143 -0.0741 -0.6102 -0.1709 -0.2213 -0.6996 -0.3285 0.1073 -0.1053 -0.2213
## Par. upper-bounds: 1.3281 0.1399 3.0004 1.4219 0.4686 -0.2145 0.0393 0.5367 0.1531 0.1647 0.009 0.3735 0.0346 0.7032 0.2614 0.2684 -0.0253 0.5182 0.1217 0.2338
## Final Estimates: -1.056326 -1.545251 -0.667975 -0.4238577 0.2585196 -0.4951582 -0.1161297 0.230101 0.001097784 -0.03635323 -0.1025646 0.155984 -0.2930104 0.2679348 0.02017858 -0.2043748 -0.1739667 0.3117347 0.008148324 -9.841258e-05
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.056e+00 1.211e+00 -0.872 0.382969
## [2,] -1.545e+00 8.707e-01 -1.775 0.075955 .
## [3,] -6.680e-01 1.880e+00 -0.355 0.722344
## [4,] -4.239e-01 8.831e-01 -0.480 0.631233
## [5,] 2.585e-01 1.026e-01 2.520 0.011740 *
## [6,] -4.952e-01 1.403e-01 -3.529 0.000417 ***
## [7,] -1.161e-01 7.483e-02 -1.552 0.120681
## [8,] 2.301e-01 1.360e-01 1.692 0.090680 .
## [9,] 1.098e-03 7.352e-02 0.015 0.988087
## [10,] -3.635e-02 1.008e-01 -0.361 0.718371
## [11,] -1.026e-01 5.432e-02 -1.888 0.059024 .
## [12,] 1.560e-01 1.017e-01 1.534 0.124977
## [13,] -2.930e-01 1.586e-01 -1.848 0.064602 .
## [14,] 2.679e-01 2.180e-01 1.229 0.219087
## [15,] 2.018e-02 1.127e-01 0.179 0.857844
## [16,] -2.044e-01 1.817e-01 -1.125 0.260780
## [17,] -1.740e-01 7.352e-02 -2.366 0.017973 *
## [18,] 3.117e-01 1.026e-01 3.039 0.002377 **
## [19,] 8.148e-03 4.838e-02 0.168 0.866256
## [20,] -9.841e-05 3.287e-02 -0.003 0.997611
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.056326 -1.545251 -0.667975 -0.4238577
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2585 -0.4952 -0.11613 2.30e-01
## [2,] 0.0011 -0.0364 -0.10256 1.56e-01
## [3,] -0.2930 0.2679 0.02018 -2.04e-01
## [4,] -0.1740 0.3117 0.00815 -9.84e-05
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 210.05159 84.32052 -174.8719 -77.42182
## [2,] 84.32052 108.58992 -119.1861 -47.59641
## [3,] -174.87186 -119.18606 507.0938 164.51630
## [4,] -77.42182 -47.59641 164.5163 112.26112
## ----
## aic= 19.7489
## bic= 20.15032
## Number of parameters: 20
## initial estimates: -3.1253 -4.3768 -1.1853 -0.1558 0.2314 -0.0463 -0.3064 0.2034 -0.2387 0.3632 -0.2841 0.1314 0.5819 -0.457 0.6057 0.1006 0.2333 -0.1608 0.3764 0.1539
## Par. lower-bounds: -7.4082 -8.3345 -5.3798 -3.8512 0.0332 -0.2786 -0.4797 -0.0455 -0.4219 0.1485 -0.4443 -0.0986 0.3878 -0.6845 0.4359 -0.1432 0.0623 -0.3612 0.2269 -0.0609
## Par. upper-bounds: 1.1576 -0.419 3.0092 3.5396 0.4296 0.186 -0.133 0.4523 -0.0555 0.5778 -0.1239 0.3614 0.776 -0.2296 0.7754 0.3443 0.4043 0.0396 0.526 0.3686
## Final Estimates: -2.944473 -4.132316 -1.04889 -0.3298259 0.2233039 -0.03795865 -0.3055635 0.2159198 -0.2496788 0.3744464 -0.283002 0.1482564 0.5758033 -0.4507665 0.6063057 0.109975 0.2411354 -0.1688113 0.3756389 0.1418507
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -2.94447 2.13314 -1.380 0.167481
## [2,] -4.13232 1.97838 -2.089 0.036732 *
## [3,] -1.04889 2.08633 -0.503 0.615145
## [4,] -0.32983 1.84176 -0.179 0.857873
## [5,] 0.22330 0.09874 2.262 0.023725 *
## [6,] -0.03796 0.11580 -0.328 0.743076
## [7,] -0.30556 0.08666 -3.526 0.000422 ***
## [8,] 0.21592 0.12378 1.744 0.081082 .
## [9,] -0.24968 0.09158 -2.726 0.006402 **
## [10,] 0.37445 0.10741 3.486 0.000490 ***
## [11,] -0.28300 0.08037 -3.521 0.000430 ***
## [12,] 0.14826 0.11480 1.291 0.196546
## [13,] 0.57580 0.09657 5.962 2.49e-09 ***
## [14,] -0.45077 0.11327 -3.980 6.90e-05 ***
## [15,] 0.60631 0.08476 7.154 8.46e-13 ***
## [16,] 0.10997 0.12106 0.908 0.363650
## [17,] 0.24114 0.08526 2.828 0.004682 **
## [18,] -0.16881 0.10000 -1.688 0.091386 .
## [19,] 0.37564 0.07483 5.020 5.17e-07 ***
## [20,] 0.14185 0.10688 1.327 0.184444
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -2.944473 -4.132316 -1.04889 -0.3298259
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.223 -0.038 -0.306 0.216
## [2,] -0.250 0.374 -0.283 0.148
## [3,] 0.576 -0.451 0.606 0.110
## [4,] 0.241 -0.169 0.376 0.142
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 641.9485 393.2524 -166.3924 -171.2955
## [2,] 393.2524 552.1968 -148.2440 -230.9374
## [3,] -166.3924 -148.2440 614.1067 322.1184
## [4,] -171.2955 -230.9374 322.1184 478.6636
## ----
## aic= 24.3795
## bic= 24.78092
## Number of parameters: 20
## initial estimates: -1.562 -3.2963 -0.3288 0.2503 0.3001 -0.0473 -0.2645 0.0703 0.2571 0.222 -0.3134 -0.0159 0.0695 -0.0939 0.3921 0.0255 0.0416 0.0196 0.1805 0.1259
## Par. lower-bounds: -3.8792 -6.7726 -3.9706 -3.6366 0.0938 -0.1944 -0.4126 -0.0775 -0.0523 0.0014 -0.5355 -0.2376 -0.2546 -0.3249 0.1594 -0.2068 -0.3043 -0.227 -0.0678 -0.1221
## Par. upper-bounds: 0.7553 0.18 3.3129 4.1373 0.5063 0.0997 -0.1165 0.2181 0.5665 0.4425 -0.0913 0.2059 0.3937 0.1372 0.6248 0.2579 0.3876 0.2662 0.4289 0.3739
## Final Estimates: -1.48836 -3.14078 -0.2819952 0.09887588 0.2936316 -0.04629285 -0.2626144 0.07332727 0.2434818 0.2241877 -0.3093826 -0.009465707 0.06542335 -0.09321403 0.3933119 0.02748095 0.05486315 0.01746852 0.1766416 0.119663
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.488360 1.155020 -1.289 0.197537
## [2,] -3.140780 1.737300 -1.808 0.070630 .
## [3,] -0.281995 1.809534 -0.156 0.876160
## [4,] 0.098876 1.938471 0.051 0.959320
## [5,] 0.293632 0.102834 2.855 0.004298 **
## [6,] -0.046293 0.073465 -0.630 0.528609
## [7,] -0.262614 0.073953 -3.551 0.000384 ***
## [8,] 0.073327 0.073788 0.994 0.320345
## [9,] 0.243482 0.154706 1.574 0.115524
## [10,] 0.224188 0.110531 2.028 0.042532 *
## [11,] -0.309383 0.111244 -2.781 0.005417 **
## [12,] -0.009466 0.110984 -0.085 0.932032
## [13,] 0.065423 0.161230 0.406 0.684907
## [14,] -0.093214 0.115192 -0.809 0.418398
## [15,] 0.393312 0.115941 3.392 0.000693 ***
## [16,] 0.027481 0.115677 0.238 0.812218
## [17,] 0.054863 0.172740 0.318 0.750785
## [18,] 0.017469 0.123431 0.142 0.887456
## [19,] 0.176642 0.124221 1.422 0.155027
## [20,] 0.119663 0.123942 0.965 0.334308
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.48836 -3.14078 -0.2819952 0.09887588
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2936 -0.0463 -0.263 0.07333
## [2,] 0.2435 0.2242 -0.309 -0.00947
## [3,] 0.0654 -0.0932 0.393 0.02748
## [4,] 0.0549 0.0175 0.177 0.11966
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 184.8351 176.8557 -129.9668 -139.1110
## [2,] 176.8557 418.3496 -242.5197 -312.8081
## [3,] -129.9668 -242.5197 454.3506 355.1011
## [4,] -139.1110 -312.8081 355.1011 521.5814
## ----
## aic= 21.98197
## bic= 22.38339
## Number of parameters: 20
## initial estimates: -0.9054 -2.1186 -0.831 -0.0159 0.2729 0.1369 0.0324 -0.2733 -0.0649 0.3073 -0.0765 -0.0241 0.0268 0.1817 0.6358 -0.1442 -0.0849 0.0798 0.2038 0.1821
## Par. lower-bounds: -2.3916 -4.0777 -3.6898 -1.9589 0.1063 -0.0061 -0.0628 -0.4431 -0.2845 0.1188 -0.2019 -0.2479 -0.2936 -0.0933 0.4528 -0.4706 -0.3027 -0.1072 0.0794 -0.0398
## Par. upper-bounds: 0.5808 -0.1596 2.0279 1.9271 0.4394 0.2799 0.1275 -0.1036 0.1546 0.4958 0.0489 0.1996 0.3472 0.4567 0.8188 0.1823 0.1328 0.2667 0.3282 0.404
## Final Estimates: -0.8377151 -2.03549 -0.7151032 -0.09136513 0.2623445 0.1407147 0.03464708 -0.2670268 -0.07780734 0.3119439 -0.07375387 -0.01636905 0.008767644 0.1882203 0.6397249 -0.1333725 -0.07323006 0.07553005 0.2013014 0.1750865
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.837715 0.741708 -1.129 0.258712
## [2,] -2.035490 0.977152 -2.083 0.037244 *
## [3,] -0.715103 1.425727 -0.502 0.615969
## [4,] -0.091365 0.968984 -0.094 0.924879
## [5,] 0.262344 0.082891 3.165 0.001551 **
## [6,] 0.140715 0.071499 1.968 0.049061 *
## [7,] 0.034647 0.047587 0.728 0.466566
## [8,] -0.267027 0.084795 -3.149 0.001638 **
## [9,] -0.077807 0.109221 -0.712 0.476226
## [10,] 0.311944 0.094189 3.312 0.000927 ***
## [11,] -0.073754 0.062700 -1.176 0.239474
## [12,] -0.016369 0.111747 -0.146 0.883540
## [13,] 0.008768 0.159489 0.055 0.956160
## [14,] 0.188220 0.137410 1.370 0.170758
## [15,] 0.639725 0.091462 6.994 2.66e-12 ***
## [16,] -0.133373 0.163012 -0.818 0.413258
## [17,] -0.073230 0.108280 -0.676 0.498847
## [18,] 0.075530 0.093355 0.809 0.418478
## [19,] 0.201301 0.062139 3.240 0.001197 **
## [20,] 0.175086 0.110740 1.581 0.113865
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.8377151 -2.03549 -0.7151032 -0.09136513
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.26234 0.1407 0.0346 -0.2670
## [2,] -0.07781 0.3119 -0.0738 -0.0164
## [3,] 0.00877 0.1882 0.6397 -0.1334
## [4,] -0.07323 0.0755 0.2013 0.1751
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 75.19211 48.58839 -17.34359 -38.93721
## [2,] 48.58839 130.49626 -54.89779 -57.23942
## [3,] -17.34359 -54.89779 277.72053 109.67972
## [4,] -38.93721 -57.23942 109.67972 128.20032
## ----
## aic= 18.94457
## bic= 19.34599
## Number of parameters: 20
## initial estimates: -1.4397 -2.1536 -0.4738 -0.1817 0.2692 -0.0619 -0.047 0.0442 0.0726 -0.0883 -0.1331 0.0798 0.0343 0.0459 0.2181 -0.003 4e-04 0.1652 -0.0235 0.5696
## Par. lower-bounds: -3.563 -4.0832 -2.5247 -1.7722 0.0656 -0.2921 -0.2534 -0.183 -0.1125 -0.2975 -0.3207 -0.1267 -0.1624 -0.1764 0.0187 -0.2225 -0.1522 -0.0072 -0.1781 0.3993
## Par. upper-bounds: 0.6836 -0.224 1.577 1.4088 0.4729 0.1682 0.1594 0.2715 0.2576 0.1208 0.0545 0.2864 0.231 0.2682 0.4175 0.2165 0.1529 0.3376 0.1311 0.7398
## Final Estimates: -1.364305 -2.057668 -0.3960981 -0.2536405 0.2648659 -0.05995387 -0.04722351 0.05791924 0.06699656 -0.08580538 -0.1333579 0.09726504 0.02982467 0.0479218 0.2178768 0.01109929 0.004552503 0.1633431 -0.02330857 0.5564883
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.364305 1.056067 -1.292 0.19640
## [2,] -2.057668 0.961684 -2.140 0.03238 *
## [3,] -0.396098 1.020333 -0.388 0.69786
## [4,] -0.253641 0.792104 -0.320 0.74881
## [5,] 0.264866 0.101534 2.609 0.00909 **
## [6,] -0.059954 0.114905 -0.522 0.60183
## [7,] -0.047224 0.103075 -0.458 0.64685
## [8,] 0.057919 0.112164 0.516 0.60559
## [9,] 0.066997 0.092458 0.725 0.46869
## [10,] -0.085805 0.104635 -0.820 0.41219
## [11,] -0.133358 0.093862 -1.421 0.15538
## [12,] 0.097265 0.102143 0.952 0.34097
## [13,] 0.029825 0.098081 0.304 0.76106
## [14,] 0.047922 0.111027 0.432 0.66601
## [15,] 0.217877 0.099569 2.188 0.02866 *
## [16,] 0.011099 0.108340 0.102 0.91840
## [17,] 0.004553 0.076134 0.060 0.95232
## [18,] 0.163343 0.086188 1.895 0.05807 .
## [19,] -0.023309 0.077299 -0.302 0.76301
## [20,] 0.556488 0.084121 6.615 3.71e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.364305 -2.057668 -0.3960981 -0.2536405
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.26487 -0.0600 -0.0472 0.0579
## [2,] 0.06700 -0.0858 -0.1334 0.0973
## [3,] 0.02982 0.0479 0.2179 0.0111
## [4,] 0.00455 0.1633 -0.0233 0.5565
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 157.71898 88.55821 -49.66863 -36.56695
## [2,] 88.55821 130.78644 -42.62459 -39.07155
## [3,] -49.66863 -42.62459 147.22683 69.23030
## [4,] -36.56695 -39.07155 69.23030 88.73348
## ----
## aic= 18.55404
## bic= 18.95546
## Number of parameters: 20
## initial estimates: -0.6631 -1.682 -0.7276 -0.4296 0.53 -0.1465 -0.1218 0.1721 0.2617 0.0475 -0.1597 0.1912 0.3781 -0.0018 0.7738 -0.7661 0.343 -0.032 0.3125 -0.3326
## Par. lower-bounds: -1.8532 -3.1967 -3.7188 -2.4406 0.3815 -0.2835 -0.2113 0.03 0.0727 -0.1269 -0.2736 0.0104 0.0049 -0.3462 0.5489 -1.1232 0.0921 -0.2635 0.1613 -0.5727
## Par. upper-bounds: 0.5271 -0.1674 2.2635 1.5813 0.6785 -0.0095 -0.0324 0.3142 0.4507 0.2219 -0.0459 0.3721 0.7513 0.3427 0.9986 -0.4089 0.5939 0.1996 0.4636 -0.0925
## Final Estimates: -0.6231995 -1.622999 -0.6490313 -0.4916231 0.5250703 -0.1460126 -0.1221975 0.1745229 0.2544635 0.04823613 -0.1603111 0.1948843 0.3684419 -0.0008027081 0.7729823 -0.7612135 0.3506297 -0.03270853 0.3130954 -0.336377
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.6231995 0.5928171 -1.051 0.29314
## [2,] -1.6229989 0.7549613 -2.150 0.03157 *
## [3,] -0.6490313 1.4847906 -0.437 0.66202
## [4,] -0.4916231 0.9998101 -0.492 0.62292
## [5,] 0.5250703 0.0739780 7.098 1.27e-12 ***
## [6,] -0.1460126 0.0683573 -2.136 0.03268 *
## [7,] -0.1221975 0.0446877 -2.734 0.00625 **
## [8,] 0.1745229 0.0709385 2.460 0.01389 *
## [9,] 0.2544635 0.0941936 2.701 0.00690 **
## [10,] 0.0482361 0.0865370 0.557 0.57725
## [11,] -0.1603111 0.0569091 -2.817 0.00485 **
## [12,] 0.1948843 0.0903597 2.157 0.03102 *
## [13,] 0.3684419 0.1849845 1.992 0.04640 *
## [14,] -0.0008027 0.1621013 -0.005 0.99605
## [15,] 0.7729823 0.1119636 6.904 5.06e-12 ***
## [16,] -0.7612135 0.1780832 -4.274 1.92e-05 ***
## [17,] 0.3506297 0.1246780 2.812 0.00492 **
## [18,] -0.0327085 0.1120852 -0.292 0.77043
## [19,] 0.3130954 0.0753893 4.153 3.28e-05 ***
## [20,] -0.3363770 0.1198036 -2.808 0.00499 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.6231995 -1.622999 -0.6490313 -0.4916231
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.525 -0.146013 -0.122 0.175
## [2,] 0.254 0.048236 -0.160 0.195
## [3,] 0.368 -0.000803 0.773 -0.761
## [4,] 0.351 -0.032709 0.313 -0.336
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 49.27284 13.93355 -20.19093 -24.76680
## [2,] 13.93355 79.94789 -56.16885 -38.26985
## [3,] -20.19093 -56.16885 310.61388 154.07873
## [4,] -24.76680 -38.26985 154.07873 140.55544
## ----
## aic= 18.16334
## bic= 18.56476
## Number of parameters: 20
## initial estimates: -1.3777 -2.634 -0.6423 -0.1329 0.2463 -0.1885 -0.1631 -0.2851 -0.2538 0.2078 -0.124 -0.4337 0.1161 0.2319 0.3077 0.5782 0.1315 0.1872 0.3047 0.2529
## Par. lower-bounds: -3.7508 -4.9979 -2.6571 -2.5629 0.058 -0.3656 -0.3548 -0.4724 -0.4414 0.0314 -0.315 -0.6203 -0.0437 0.0815 0.1449 0.4191 -0.0612 0.0058 0.1084 0.061
## Par. upper-bounds: 0.9954 -0.27 1.3725 2.2971 0.4345 -0.0113 0.0287 -0.0977 -0.0663 0.3843 0.0671 -0.2471 0.276 0.3823 0.4705 0.7372 0.3243 0.3686 0.5011 0.4447
## Final Estimates: -1.285833 -2.481212 -0.5450946 -0.2906465 0.2408793 -0.1887552 -0.1556946 -0.2832359 -0.2627823 0.2073564 -0.1116875 -0.4306662 0.1104327 0.2315892 0.3154869 0.5801131 0.140794 0.1877214 0.2920415 0.2497262
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.28583 1.17928 -1.090 0.27556
## [2,] -2.48121 1.17907 -2.104 0.03535 *
## [3,] -0.54509 1.00235 -0.544 0.58657
## [4,] -0.29065 1.21201 -0.240 0.81048
## [5,] 0.24088 0.09376 2.569 0.01020 *
## [6,] -0.18876 0.08846 -2.134 0.03287 *
## [7,] -0.15569 0.09530 -1.634 0.10232
## [8,] -0.28324 0.09353 -3.028 0.00246 **
## [9,] -0.26278 0.09375 -2.803 0.00506 **
## [10,] 0.20736 0.08845 2.344 0.01906 *
## [11,] -0.11169 0.09529 -1.172 0.24114
## [12,] -0.43067 0.09351 -4.605 4.12e-06 ***
## [13,] 0.11043 0.07970 1.386 0.16585
## [14,] 0.23159 0.07519 3.080 0.00207 **
## [15,] 0.31549 0.08100 3.895 9.83e-05 ***
## [16,] 0.58011 0.07950 7.297 2.94e-13 ***
## [17,] 0.14079 0.09637 1.461 0.14404
## [18,] 0.18772 0.09093 2.064 0.03897 *
## [19,] 0.29204 0.09796 2.981 0.00287 **
## [20,] 0.24973 0.09613 2.598 0.00938 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.285833 -2.481212 -0.5450946 -0.2906465
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.241 -0.189 -0.156 -0.283
## [2,] -0.263 0.207 -0.112 -0.431
## [3,] 0.110 0.232 0.315 0.580
## [4,] 0.141 0.188 0.292 0.250
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 194.17328 106.91919 -62.79955 -54.92311
## [2,] 106.91919 194.10953 -34.70523 -74.70773
## [3,] -62.79955 -34.70523 140.28642 83.38314
## [4,] -54.92311 -74.70773 83.38314 205.14195
## ----
## aic= 20.16522
## bic= 20.56664
## Number of parameters: 20
## initial estimates: -2.0559 -3.3813 -0.5362 -0.54 0.4363 -0.232 -0.2832 0.2396 -0.0879 -0.0775 -0.3099 0.2196 0.1258 0.0473 1.0219 -0.1468 0.0352 0.0934 0.0889 0.8396
## Par. lower-bounds: -4.8637 -6.1902 -2.6946 -1.8895 0.2584 -0.4189 -0.4469 0.0389 -0.2659 -0.2645 -0.4737 0.0189 -0.011 -0.0964 0.8961 -0.3011 -0.0503 0.0036 0.0102 0.7432
## Par. upper-bounds: 0.7519 -0.5724 1.6221 0.8094 0.6142 -0.0452 -0.1195 0.4402 0.0901 0.1094 -0.1461 0.4203 0.2625 0.1909 1.1477 0.0074 0.1207 0.1832 0.1676 0.936
## Final Estimates: -1.985867 -3.293542 -0.4768689 -0.5700614 0.4324804 -0.2329508 -0.2845682 0.2494794 -0.09270955 -0.07869508 -0.3116795 0.232034 0.1225482 0.0464786 1.020706 -0.1384213 0.03683452 0.0938296 0.08950674 0.8353494
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.98587 1.39673 -1.422 0.155085
## [2,] -3.29354 1.39835 -2.355 0.018508 *
## [3,] -0.47687 1.07397 -0.444 0.657025
## [4,] -0.57006 0.67109 -0.849 0.395631
## [5,] 0.43248 0.08857 4.883 1.04e-06 ***
## [6,] -0.23295 0.09323 -2.499 0.012466 *
## [7,] -0.28457 0.08166 -3.485 0.000492 ***
## [8,] 0.24948 0.09890 2.523 0.011648 *
## [9,] -0.09271 0.08867 -1.046 0.295765
## [10,] -0.07870 0.09334 -0.843 0.399156
## [11,] -0.31168 0.08175 -3.813 0.000138 ***
## [12,] 0.23203 0.09901 2.344 0.019102 *
## [13,] 0.12255 0.06810 1.800 0.071935 .
## [14,] 0.04648 0.07168 0.648 0.516738
## [15,] 1.02071 0.06279 16.257 < 2e-16 ***
## [16,] -0.13842 0.07604 -1.820 0.068711 .
## [17,] 0.03683 0.04255 0.866 0.386706
## [18,] 0.09383 0.04479 2.095 0.036195 *
## [19,] 0.08951 0.03923 2.281 0.022526 *
## [20,] 0.83535 0.04752 17.580 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.985867 -3.293542 -0.4768689 -0.5700614
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.4325 -0.2330 -0.2846 0.249
## [2,] -0.0927 -0.0787 -0.3117 0.232
## [3,] 0.1225 0.0465 1.0207 -0.138
## [4,] 0.0368 0.0938 0.0895 0.835
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 276.053593 156.2290847 -51.66284 -3.1210476
## [2,] 156.229085 276.6923620 -27.87208 0.9030307
## [3,] -51.662843 -27.8720850 163.20927 79.3802836
## [4,] -3.121048 0.9030307 79.38028 63.7266281
## ----
## aic= 19.30465
## bic= 19.70607
## Number of parameters: 20
## initial estimates: -1.8492 -3.3896 0.1769 0.227 0.2946 -0.0015 -0.3184 0.1804 -0.1431 0.3481 -0.3199 0.1301 0.3392 -0.123 0.585 -0.0608 0.1663 -0.0316 0.1498 0.3341
## Par. lower-bounds: -4.2952 -6.8543 -3.1873 -2.5493 0.0552 -0.1983 -0.5233 -0.0575 -0.4823 0.0693 -0.6102 -0.2069 0.0098 -0.3937 0.3031 -0.388 -0.1055 -0.2551 -0.0828 0.0641
## Par. upper-bounds: 0.5968 0.0751 3.541 3.0032 0.5341 0.1954 -0.1135 0.4183 0.1961 0.6269 -0.0297 0.4671 0.6686 0.1478 0.8668 0.2663 0.4381 0.1918 0.3823 0.6041
## Final Estimates: -1.756422 -3.240718 0.2072521 0.125329 0.2859883 0.0046495 -0.3187504 0.191414 -0.1569915 0.3579135 -0.3204663 0.1478186 0.3363556 -0.1209597 0.5848499 -0.05722252 0.1757675 -0.03832925 0.1501305 0.3219692
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.756422 1.219942 -1.440 0.14994
## [2,] -3.240718 1.729694 -1.874 0.06099 .
## [3,] 0.207252 1.674410 0.124 0.90149
## [4,] 0.125329 1.385668 0.090 0.92793
## [5,] 0.285988 0.119469 2.394 0.01667 *
## [6,] 0.004649 0.098472 0.047 0.96234
## [7,] -0.318750 0.102435 -3.112 0.00186 **
## [8,] 0.191414 0.118339 1.618 0.10577
## [9,] -0.156991 0.169299 -0.927 0.35377
## [10,] 0.357913 0.139457 2.566 0.01027 *
## [11,] -0.320466 0.145215 -2.207 0.02733 *
## [12,] 0.147819 0.167766 0.881 0.37826
## [13,] 0.336356 0.163738 2.054 0.03995 *
## [14,] -0.120960 0.134825 -0.897 0.36963
## [15,] 0.584850 0.140486 4.163 3.14e-05 ***
## [16,] -0.057223 0.162298 -0.353 0.72441
## [17,] 0.175767 0.135470 1.297 0.19447
## [18,] -0.038329 0.111537 -0.344 0.73111
## [19,] 0.150130 0.116238 1.292 0.19650
## [20,] 0.321969 0.134284 2.398 0.01650 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.756422 -3.240718 0.2072521 0.125329
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.286 0.00465 -0.319 0.1914
## [2,] -0.157 0.35791 -0.320 0.1478
## [3,] 0.336 -0.12096 0.585 -0.0572
## [4,] 0.176 -0.03833 0.150 0.3220
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 204.6670 228.4744 -164.2643 -125.2303
## [2,] 228.4744 411.3484 -264.8718 -207.1944
## [3,] -164.2643 -264.8718 384.9773 260.7599
## [4,] -125.2303 -207.1944 260.7599 263.5625
## ----
## aic= 20.41565
## bic= 20.81707
## Number of parameters: 20
## initial estimates: -0.9133 -1.875 -0.7049 -0.3421 0.1075 -0.0803 0.1201 -0.0295 -0.326 0.1235 -0.0566 -0.0061 0.4933 -0.0525 0.3203 -0.0509 0.044 0.098 0.1312 0.4617
## Par. lower-bounds: -2.1132 -3.5497 -2.897 -2.3878 -0.0715 -0.2165 0.0322 -0.1215 -0.5758 -0.0666 -0.1793 -0.1346 0.1662 -0.3014 0.1596 -0.2192 -0.2612 -0.1342 -0.0187 0.3047
## Par. upper-bounds: 0.2865 -0.2004 1.4873 1.7036 0.2865 0.056 0.208 0.0626 -0.0761 0.3136 0.0661 0.1224 0.8203 0.1964 0.4809 0.1173 0.3492 0.3303 0.2811 0.6187
## Final Estimates: -0.86911 -1.784615 -0.5780512 -0.4632399 0.1017503 -0.07792541 0.1216249 -0.0234869 -0.3378134 0.1283231 -0.05350293 0.006146317 0.4767088 -0.04573143 0.3245571 -0.03379057 0.05991881 0.09159588 0.1270945 0.4452825
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.869110 0.596547 -1.457 0.14514
## [2,] -1.784615 0.834623 -2.138 0.03250 *
## [3,] -0.578051 1.093221 -0.529 0.59697
## [4,] -0.463240 1.020455 -0.454 0.64986
## [5,] 0.101750 0.089090 1.142 0.25341
## [6,] -0.077925 0.067962 -1.147 0.25155
## [7,] 0.121625 0.043858 2.773 0.00555 **
## [8,] -0.023487 0.045348 -0.518 0.60451
## [9,] -0.337813 0.124646 -2.710 0.00672 **
## [10,] 0.128323 0.095086 1.350 0.17716
## [11,] -0.053503 0.061360 -0.872 0.38324
## [12,] 0.006146 0.063428 0.097 0.92280
## [13,] 0.476709 0.163269 2.920 0.00350 **
## [14,] -0.045731 0.124550 -0.367 0.71349
## [15,] 0.324557 0.080376 4.038 5.39e-05 ***
## [16,] -0.033791 0.083113 -0.407 0.68433
## [17,] 0.059919 0.152405 0.393 0.69420
## [18,] 0.091596 0.116263 0.788 0.43079
## [19,] 0.127094 0.075026 1.694 0.09026 .
## [20,] 0.445282 0.077583 5.739 9.50e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.86911 -1.784615 -0.5780512 -0.4632399
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.1018 -0.0779 0.1216 -0.02349
## [2,] -0.3378 0.1283 -0.0535 0.00615
## [3,] 0.4767 -0.0457 0.3246 -0.03379
## [4,] 0.0599 0.0916 0.1271 0.44528
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 50.489632 33.14194 -2.837411 6.321091
## [2,] 33.141940 98.83017 -25.847644 -33.704408
## [3,] -2.837411 -25.84764 169.570957 37.736320
## [4,] 6.321091 -33.70441 37.736320 147.750183
## ----
## aic= 18.44152
## bic= 18.84294
## Number of parameters: 20
## initial estimates: -1.0647 -1.913 -1.1323 -0.3365 0.2615 -0.2067 -0.0523 -0.0932 -0.1517 0.1303 -0.0346 0.066 0.1672 -0.0794 0.6315 -0.1496 0.1252 0.036 0.1223 0.2484
## Par. lower-bounds: -2.4099 -3.5391 -3.5534 -1.6324 0.0673 -0.3703 -0.1466 -0.2932 -0.3864 -0.0674 -0.1485 -0.1758 -0.1822 -0.3738 0.4619 -0.5096 -0.0618 -0.1216 0.0315 0.0557
## Par. upper-bounds: 0.2805 -0.287 1.2888 0.9593 0.4556 -0.0431 0.0419 0.1069 0.083 0.328 0.0793 0.3078 0.5166 0.215 0.8012 0.2105 0.3123 0.1935 0.2131 0.4411
## Final Estimates: -0.998136 -1.816159 -0.9912428 -0.3911011 0.2507217 -0.2016112 -0.05170708 -0.08364852 -0.1673582 0.1377613 -0.03369711 0.07988447 0.1443823 -0.06857982 0.6328416 -0.1294229 0.1340178 0.03179017 0.1218361 0.24054
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.99814 0.66970 -1.490 0.13611
## [2,] -1.81616 0.81083 -2.240 0.02510 *
## [3,] -0.99124 1.20706 -0.821 0.41153
## [4,] -0.39110 0.64449 -0.607 0.54396
## [5,] 0.25072 0.09655 2.597 0.00941 **
## [6,] -0.20161 0.08165 -2.469 0.01354 *
## [7,] -0.05171 0.04714 -1.097 0.27267
## [8,] -0.08365 0.09962 -0.840 0.40109
## [9,] -0.16736 0.11689 -1.432 0.15222
## [10,] 0.13776 0.09886 1.393 0.16347
## [11,] -0.03370 0.05707 -0.590 0.55490
## [12,] 0.07988 0.12062 0.662 0.50777
## [13,] 0.14438 0.17402 0.830 0.40670
## [14,] -0.06858 0.14718 -0.466 0.64123
## [15,] 0.63284 0.08496 7.449 9.41e-14 ***
## [16,] -0.12942 0.17956 -0.721 0.47103
## [17,] 0.13402 0.09291 1.442 0.14919
## [18,] 0.03179 0.07858 0.405 0.68582
## [19,] 0.12184 0.04536 2.686 0.00723 **
## [20,] 0.24054 0.09587 2.509 0.01211 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.998136 -1.816159 -0.9912428 -0.3911011
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.251 -0.2016 -0.0517 -0.0836
## [2,] -0.167 0.1378 -0.0337 0.0799
## [3,] 0.144 -0.0686 0.6328 -0.1294
## [4,] 0.134 0.0318 0.1218 0.2405
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 63.36145 48.800901 -11.972341 -14.36581
## [2,] 48.80090 92.880235 -1.609775 -13.75934
## [3,] -11.97234 -1.609775 205.831960 59.93548
## [4,] -14.36581 -13.759342 59.935482 58.67860
## ----
## aic= 17.40035
## bic= 17.80177
## Number of parameters: 20
## initial estimates: -1.6795 -2.6183 -0.7457 -0.3923 0.6948 -0.2913 -0.121 -0.1612 0.0731 0.105 -0.2478 0.0202 0.2196 0.0368 0.8225 -0.1241 -0.0528 0.1788 0.2071 0.4908
## Par. lower-bounds: -3.8226 -4.7941 -2.6753 -2.0458 0.5417 -0.4823 -0.2829 -0.3866 -0.0824 -0.0889 -0.4121 -0.2087 0.0818 -0.1352 0.6767 -0.3271 -0.1709 0.0314 0.0822 0.3169
## Par. upper-bounds: 0.4637 -0.4425 1.1838 1.2613 0.8479 -0.1003 0.041 0.0643 0.2285 0.299 -0.0834 0.2491 0.3574 0.2088 0.9682 0.0789 0.0653 0.3262 0.3321 0.6648
## Final Estimates: -1.59254 -2.501723 -0.6346606 -0.4626868 0.6893081 -0.289409 -0.1200162 -0.1498369 0.06573519 0.107553 -0.2465014 0.03542791 0.2126582 0.03920613 0.8236794 -0.1096869 -0.04835289 0.1773021 0.2063871 0.4816362
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.59254 1.06424 -1.496 0.134545
## [2,] -2.50172 1.08207 -2.312 0.020779 *
## [3,] -0.63466 0.96007 -0.661 0.508574
## [4,] -0.46269 0.82128 -0.563 0.573183
## [5,] 0.68931 0.07611 9.056 < 2e-16 ***
## [6,] -0.28941 0.09536 -3.035 0.002406 **
## [7,] -0.12002 0.08083 -1.485 0.137615
## [8,] -0.14984 0.11163 -1.342 0.179508
## [9,] 0.06574 0.07739 0.849 0.395652
## [10,] 0.10755 0.09696 1.109 0.267311
## [11,] -0.24650 0.08219 -2.999 0.002707 **
## [12,] 0.03543 0.11350 0.312 0.754932
## [13,] 0.21266 0.06866 3.097 0.001954 **
## [14,] 0.03921 0.08602 0.456 0.648558
## [15,] 0.82368 0.07292 11.295 < 2e-16 ***
## [16,] -0.10969 0.10071 -1.089 0.276077
## [17,] -0.04835 0.05874 -0.823 0.410389
## [18,] 0.17730 0.07359 2.409 0.015980 *
## [19,] 0.20639 0.06238 3.308 0.000938 ***
## [20,] 0.48164 0.08615 5.591 2.26e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.59254 -2.501723 -0.6346606 -0.4626868
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.6893 -0.2894 -0.120 -0.1498
## [2,] 0.0657 0.1076 -0.247 0.0354
## [3,] 0.2127 0.0392 0.824 -0.1097
## [4,] -0.0484 0.1773 0.206 0.4816
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 154.66467 96.48699 -22.11742 -14.37168
## [2,] 96.48699 159.89264 -23.25284 -32.84194
## [3,] -22.11742 -23.25284 125.87149 68.83702
## [4,] -14.37168 -32.84194 68.83702 92.11163
## ----
## aic= 18.64217
## bic= 19.04358
## Number of parameters: 20
## initial estimates: -1.9953 -2.5028 -0.5027 0.0182 0.2664 -0.2044 0.0467 -0.3759 -0.1804 0.181 -0.0028 -0.1939 0.4272 -0.307 0.0576 0.2999 0.2257 -0.1514 0.0845 0.0729
## Par. lower-bounds: -4.4102 -4.69 -2.3333 -1.6772 0.0503 -0.4755 -0.1673 -0.6565 -0.3762 -0.0645 -0.1966 -0.448 0.2634 -0.5125 -0.1046 0.0871 0.074 -0.3418 -0.0658 -0.1241
## Par. upper-bounds: 0.4196 -0.3156 1.328 1.7135 0.4826 0.0668 0.2607 -0.0953 0.0153 0.4266 0.191 0.0603 0.591 -0.1014 0.2199 0.5126 0.3775 0.0389 0.2347 0.2699
## Final Estimates: -1.884696 -2.38152 -0.4269138 -0.07284953 0.2511263 -0.1941834 0.05431135 -0.3661298 -0.1972381 0.1922226 0.005553631 -0.1832005 0.4167097 -0.2999847 0.06284703 0.3065233 0.2383319 -0.1598082 0.07818716 0.06484618
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.884696 1.204931 -1.564 0.11778
## [2,] -2.381520 1.093544 -2.178 0.02942 *
## [3,] -0.426914 0.912747 -0.468 0.63998
## [4,] -0.072850 0.847205 -0.086 0.93148
## [5,] 0.251126 0.107359 2.339 0.01933 *
## [6,] -0.194183 0.135427 -1.434 0.15161
## [7,] 0.054311 0.106932 0.508 0.61152
## [8,] -0.366130 0.140203 -2.611 0.00902 **
## [9,] -0.197238 0.097436 -2.024 0.04294 *
## [10,] 0.192223 0.122909 1.564 0.11783
## [11,] 0.005554 0.097039 0.057 0.95436
## [12,] -0.183201 0.127243 -1.440 0.14993
## [13,] 0.416710 0.081317 5.125 2.98e-07 ***
## [14,] -0.299985 0.102577 -2.924 0.00345 **
## [15,] 0.062847 0.080987 0.776 0.43774
## [16,] 0.306523 0.106195 2.886 0.00390 **
## [17,] 0.238332 0.075493 3.157 0.00159 **
## [18,] -0.159808 0.095231 -1.678 0.09333 .
## [19,] 0.078187 0.075183 1.040 0.29836
## [20,] 0.064846 0.098589 0.658 0.51071
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.884696 -2.38152 -0.4269138 -0.07284953
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.251 -0.194 0.05431 -0.3661
## [2,] -0.197 0.192 0.00555 -0.1832
## [3,] 0.417 -0.300 0.06285 0.3065
## [4,] 0.238 -0.160 0.07819 0.0648
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 206.11125 132.51827 -10.40043 -37.33516
## [2,] 132.51827 169.76693 -27.78476 -61.06090
## [3,] -10.40043 -27.78476 118.25114 43.41323
## [4,] -37.33516 -61.06090 43.41323 101.91864
## ----
## aic= 18.9987
## bic= 19.40012
## Number of parameters: 20
## initial estimates: -1.3581 -2.0024 -0.7381 0.109 0.0268 0.0402 0.1894 0.0398 -0.1816 0.0417 0.1038 0.0427 0.3098 0.1734 0.1429 0.0224 0.1994 0.0059 0.0214 -0.2089
## Par. lower-bounds: -3.5748 -4.0511 -4.2256 -2.9383 -0.1711 -0.2197 0.0645 -0.1283 -0.3645 -0.1984 -0.0117 -0.1127 -0.0016 -0.2354 -0.0536 -0.2421 -0.0727 -0.3514 -0.1503 -0.44
## Par. upper-bounds: 0.8586 0.0462 2.7493 3.1564 0.2247 0.3001 0.3143 0.2079 0.0013 0.2819 0.2192 0.1981 0.6211 0.5823 0.3394 0.2869 0.4714 0.3632 0.1931 0.0222
## Final Estimates: -1.254359 -1.879575 -0.6433728 -0.07103082 0.02170315 0.04583789 0.1930996 0.04091495 -0.1876411 0.04838413 0.1081003 0.04399958 0.3051048 0.1785779 0.1462538 0.02341731 0.2082107 -0.003835674 0.01505439 -0.2108488
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.254359 1.105066 -1.135 0.25633
## [2,] -1.879575 1.024149 -1.835 0.06647 .
## [3,] -0.643373 1.734561 -0.371 0.71070
## [4,] -0.071031 1.523985 -0.047 0.96283
## [5,] 0.021703 0.098854 0.220 0.82622
## [6,] 0.045838 0.130016 0.353 0.72442
## [7,] 0.193100 0.062386 3.095 0.00197 **
## [8,] 0.040915 0.084132 0.486 0.62674
## [9,] -0.187641 0.091629 -2.048 0.04058 *
## [10,] 0.048384 0.120736 0.401 0.68861
## [11,] 0.108100 0.057804 1.870 0.06147 .
## [12,] 0.044000 0.077998 0.564 0.57268
## [13,] 0.305105 0.155223 1.966 0.04935 *
## [14,] 0.178578 0.204473 0.873 0.38247
## [15,] 0.146254 0.097895 1.494 0.13518
## [16,] 0.023417 0.132109 0.177 0.85931
## [17,] 0.208211 0.136453 1.526 0.12704
## [18,] -0.003836 0.180736 -0.021 0.98307
## [19,] 0.015054 0.085980 0.175 0.86101
## [20,] -0.210849 0.116176 -1.815 0.06954 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.254359 -1.879575 -0.6433728 -0.07103082
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.0217 0.04584 0.1931 0.0409
## [2,] -0.1876 0.04838 0.1081 0.0440
## [3,] 0.3051 0.17858 0.1463 0.0234
## [4,] 0.2082 -0.00384 0.0151 -0.2108
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 172.86368 95.38872 -72.75781 -103.4110
## [2,] 95.38872 148.39561 -116.21165 -143.0497
## [3,] -72.75781 -116.21165 425.62360 214.8358
## [4,] -103.41103 -143.04973 214.83580 328.2216
## ----
## aic= 20.85289
## bic= 21.25431
## Number of parameters: 20
## initial estimates: -0.9423 -1.8424 -0.5063 -0.4136 0.3647 0.1271 0.0788 -0.095 0.0866 0.2855 -0.0339 -0.0583 0.0068 0.0484 0.4214 -0.1851 0.0027 0.0897 0.1779 0.1924
## Par. lower-bounds: -2.4825 -3.4661 -2.4461 -2.4976 0.203 -0.0383 -0.0723 -0.2364 -0.0838 0.1112 -0.1931 -0.2073 -0.1968 -0.1598 0.2312 -0.3632 -0.2161 -0.1341 -0.0265 0.0011
## Par. upper-bounds: 0.5978 -0.2187 1.4335 1.6705 0.5263 0.2924 0.2298 0.0464 0.257 0.4599 0.1253 0.0908 0.2104 0.2567 0.6117 -0.0071 0.2214 0.3135 0.3823 0.3837
## Final Estimates: -0.8996218 -1.779465 -0.4501467 -0.4863747 0.3592135 0.1276549 0.0790947 -0.0891052 0.07856336 0.2864304 -0.03337212 -0.04953898 -0.0003197374 0.04923655 0.4218623 -0.1773623 0.01194902 0.08868403 0.1773011 0.1822893
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.8996218 0.7670847 -1.173 0.24088
## [2,] -1.7794646 0.8111937 -2.194 0.02826 *
## [3,] -0.4501467 0.9834908 -0.458 0.64717
## [4,] -0.4863747 1.0455752 -0.465 0.64181
## [5,] 0.3592135 0.0804531 4.465 8.01e-06 ***
## [6,] 0.1276549 0.0825757 1.546 0.12213
## [7,] 0.0790947 0.0754226 1.049 0.29432
## [8,] -0.0891052 0.0701871 -1.270 0.20425
## [9,] 0.0785634 0.0975439 0.805 0.42058
## [10,] 0.2864304 0.0895199 3.200 0.00138 **
## [11,] -0.0333721 0.0797218 -0.419 0.67550
## [12,] -0.0495390 0.0741583 -0.668 0.50412
## [13,] -0.0003197 0.2339146 -0.001 0.99891
## [14,] 0.0492366 0.1371412 0.359 0.71958
## [15,] 0.4218623 0.0963138 4.380 1.19e-05 ***
## [16,] -0.1773623 0.0887062 -1.999 0.04556 *
## [17,] 0.0119490 0.1733112 0.069 0.94503
## [18,] 0.0886840 0.1259193 0.704 0.48125
## [19,] 0.1773011 0.1026769 1.727 0.08421 .
## [20,] 0.1822893 0.0952035 1.915 0.05553 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.8996218 -1.779465 -0.4501467 -0.4863747
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.35921 0.1277 0.0791 -0.0891
## [2,] 0.07856 0.2864 -0.0334 -0.0495
## [3,] -0.00032 0.0492 0.4219 -0.1774
## [4,] 0.01195 0.0887 0.1773 0.1823
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 80.0555337 27.83268 -1.427742 0.9596891
## [2,] 27.8326792 89.31828 -28.308191 -24.8885789
## [3,] -1.4277419 -28.30819 127.036906 77.8899855
## [4,] 0.9596891 -24.88858 77.889985 146.9309567
## ----
## aic= 18.37893
## bic= 18.78035
## Number of parameters: 20
## initial estimates: -1.0363 -2.1283 -1.0908 -0.2616 0.2392 0.1275 -0.0063 -0.157 -0.1494 0.4883 0.0247 -0.2719 0.0595 -0.2954 0.4528 -0.097 -0.0485 0.0175 0.041 0.1911
## Par. lower-bounds: -2.8638 -4.1343 -4.1211 -2.5503 0.0688 -0.0221 -0.1069 -0.3167 -0.3365 0.3241 -0.0856 -0.4472 -0.2231 -0.5434 0.2861 -0.3619 -0.2619 -0.1698 -0.0849 -0.009
## Par. upper-bounds: 0.7912 -0.1224 1.9395 2.0271 0.4096 0.2771 0.0942 0.0028 0.0376 0.6525 0.135 -0.0965 0.3421 -0.0474 0.6195 0.1678 0.1649 0.2048 0.1669 0.3911
## Final Estimates: -0.9919271 -2.041911 -0.9919051 -0.3368328 0.232647 0.1283509 -0.005383882 -0.1517137 -0.1621877 0.48996 0.0265753 -0.2616125 0.04486959 -0.2935286 0.454938 -0.08529399 -0.03736826 0.01608028 0.03938284 0.1821492
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.991927 0.910413 -1.090 0.27592
## [2,] -2.041911 1.003293 -2.035 0.04183 *
## [3,] -0.991905 1.511914 -0.656 0.51179
## [4,] -0.336833 1.142010 -0.295 0.76803
## [5,] 0.232647 0.084620 2.749 0.00597 **
## [6,] 0.128351 0.074674 1.719 0.08565 .
## [7,] -0.005384 0.050172 -0.107 0.91454
## [8,] -0.151714 0.079438 -1.910 0.05615 .
## [9,] -0.162188 0.093252 -1.739 0.08199 .
## [10,] 0.489960 0.082294 5.954 2.62e-09 ***
## [11,] 0.026575 0.055281 0.481 0.63071
## [12,] -0.261612 0.087538 -2.989 0.00280 **
## [13,] 0.044870 0.140529 0.319 0.74951
## [14,] -0.293529 0.124019 -2.367 0.01794 *
## [15,] 0.454938 0.083305 5.461 4.73e-08 ***
## [16,] -0.085294 0.131919 -0.647 0.51791
## [17,] -0.037368 0.106149 -0.352 0.72481
## [18,] 0.016080 0.093691 0.172 0.86373
## [19,] 0.039383 0.062923 0.626 0.53139
## [20,] 0.182149 0.099643 1.828 0.06755 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.9919271 -2.041911 -0.9919051 -0.3368328
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2326 0.1284 -0.00538 -0.1517
## [2,] -0.1622 0.4900 0.02658 -0.2616
## [3,] 0.0449 -0.2935 0.45494 -0.0853
## [4,] -0.0374 0.0161 0.03938 0.1821
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 115.240026 45.84446 -4.167528 4.996982
## [2,] 45.844464 139.94867 -34.685137 -61.416910
## [3,] -4.167528 -34.68514 317.796166 127.030675
## [4,] 4.996982 -61.41691 127.030675 181.301632
## ----
## aic= 20.23763
## bic= 20.63905
## Number of parameters: 20
## initial estimates: -0.9368 -1.6478 -0.6045 -0.6126 0.3043 -0.0835 -0.0355 -0.1608 0.1295 0.0453 -0.1444 -0.0963 0.5095 -0.1987 0.7165 -0.2493 0.2246 -0.0449 0.2446 0.107
## Par. lower-bounds: -2.4062 -3.0322 -2.7851 -2.3667 0.1367 -0.2684 -0.1579 -0.3369 -0.0284 -0.1288 -0.2598 -0.2623 0.2607 -0.473 0.5348 -0.5106 0.0245 -0.2655 0.0984 -0.1033
## Par. upper-bounds: 0.5327 -0.2635 1.5762 1.1415 0.472 0.1013 0.087 0.0153 0.2874 0.2195 -0.0291 0.0696 0.7583 0.0756 0.8982 0.0121 0.4248 0.1758 0.3908 0.3172
## Final Estimates: -0.8924603 -1.598405 -0.5351216 -0.6585073 0.297697 -0.08589254 -0.03677311 -0.1540203 0.1220907 0.04268371 -0.145884 -0.08875265 0.4990335 -0.2024684 0.7144902 -0.2385563 0.2314837 -0.04239312 0.2459268 0.09992581
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.89246 0.73210 -1.219 0.222830
## [2,] -1.59840 0.69037 -2.315 0.020597 *
## [3,] -0.53512 1.08676 -0.492 0.622435
## [4,] -0.65851 0.87339 -0.754 0.450868
## [5,] 0.29770 0.08337 3.571 0.000356 ***
## [6,] -0.08589 0.09229 -0.931 0.352009
## [7,] -0.03677 0.06114 -0.601 0.547559
## [8,] -0.15402 0.08759 -1.758 0.078692 .
## [9,] 0.12209 0.07861 1.553 0.120414
## [10,] 0.04268 0.08703 0.490 0.623807
## [11,] -0.14588 0.05766 -2.530 0.011401 *
## [12,] -0.08875 0.08260 -1.074 0.282613
## [13,] 0.49903 0.12375 4.033 5.52e-05 ***
## [14,] -0.20247 0.13699 -1.478 0.139426
## [15,] 0.71449 0.09076 7.872 3.55e-15 ***
## [16,] -0.23856 0.13003 -1.835 0.066555 .
## [17,] 0.23148 0.09946 2.328 0.019938 *
## [18,] -0.04239 0.11010 -0.385 0.700200
## [19,] 0.24593 0.07294 3.371 0.000748 ***
## [20,] 0.09993 0.10450 0.956 0.338951
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.8924603 -1.598405 -0.5351216 -0.6585073
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.298 -0.0859 -0.0368 -0.1540
## [2,] 0.122 0.0427 -0.1459 -0.0888
## [3,] 0.499 -0.2025 0.7145 -0.2386
## [4,] 0.231 -0.0424 0.2459 0.0999
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 75.780518 23.57021 -9.709919 -11.30637
## [2,] 23.570208 67.38633 -27.540094 -13.22388
## [3,] -9.709919 -27.54009 166.981707 85.98216
## [4,] -11.306373 -13.22388 85.982164 107.85145
## ----
## aic= 17.87958
## bic= 18.28099
## Number of parameters: 20
## initial estimates: -1.6934 -3.0257 -0.7309 -0.0216 -0.083 0.3138 -0.3256 0.2142 -0.6799 0.7658 -0.39 0.2684 0.5037 -0.2038 0.5744 -0.0317 0.4856 -0.0661 0.3165 0.157
## Par. lower-bounds: -4.2952 -6.0429 -3.6842 -3.059 -0.3066 0.1294 -0.5144 0.0245 -0.9392 0.552 -0.609 0.0484 0.2499 -0.413 0.3601 -0.247 0.2246 -0.2813 0.096 -0.0645
## Par. upper-bounds: 0.9083 -0.0085 2.2224 3.0158 0.1406 0.4981 -0.1368 0.4039 -0.4206 0.9796 -0.1711 0.4883 0.7575 0.0055 0.7887 0.1837 0.7466 0.1491 0.5369 0.3784
## Final Estimates: -1.569484 -2.826238 -0.6556859 -0.1925033 -0.09249735 0.3216353 -0.3219829 0.2207628 -0.6951634 0.7784576 -0.3842012 0.2789593 0.4978953 -0.1989957 0.576615 -0.02767226 0.4987189 -0.07691474 0.3114613 0.1478961
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.56948 1.29414 -1.213 0.225220
## [2,] -2.82624 1.50507 -1.878 0.060407 .
## [3,] -0.65569 1.46543 -0.447 0.654560
## [4,] -0.19250 1.51216 -0.127 0.898700
## [5,] -0.09250 0.11134 -0.831 0.406092
## [6,] 0.32164 0.09180 3.504 0.000459 ***
## [7,] -0.32198 0.09430 -3.414 0.000639 ***
## [8,] 0.22076 0.09458 2.334 0.019590 *
## [9,] -0.69516 0.12949 -5.369 7.94e-08 ***
## [10,] 0.77846 0.10676 7.292 3.06e-13 ***
## [11,] -0.38420 0.10968 -3.503 0.000460 ***
## [12,] 0.27896 0.11000 2.536 0.011213 *
## [13,] 0.49790 0.12610 3.949 7.86e-05 ***
## [14,] -0.19900 0.10396 -1.914 0.055609 .
## [15,] 0.57662 0.10680 5.399 6.70e-08 ***
## [16,] -0.02767 0.10711 -0.258 0.796137
## [17,] 0.49872 0.13014 3.832 0.000127 ***
## [18,] -0.07691 0.10730 -0.717 0.473474
## [19,] 0.31146 0.11023 2.826 0.004718 **
## [20,] 0.14790 0.11055 1.338 0.180956
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.569484 -2.826238 -0.6556859 -0.1925033
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] -0.0925 0.3216 -0.322 0.2208
## [2,] -0.6952 0.7785 -0.384 0.2790
## [3,] 0.4979 -0.1990 0.577 -0.0277
## [4,] 0.4987 -0.0769 0.311 0.1479
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 230.2407 191.4342 -110.4795 -100.4550
## [2,] 191.4342 311.4317 -122.6167 -154.9409
## [3,] -110.4795 -122.6167 295.3350 206.6965
## [4,] -100.4550 -154.9409 206.6965 314.5738
## ----
## aic= 21.20193
## bic= 21.60335
## Number of parameters: 20
## initial estimates: -1.9467 -3.2256 -0.1805 -0.0404 0.0037 0.1282 -0.3463 0.0236 -0.2145 0.5336 -0.2392 0.0975 0.1728 -0.1244 0.32 0.1411 0.191 0.1443 0.2305 0.3978
## Par. lower-bounds: -5.1325 -6.9412 -3.5237 -2.9287 -0.2434 -0.0649 -0.5879 -0.1756 -0.5027 0.3084 -0.521 -0.1348 -0.0865 -0.3271 0.0664 -0.068 -0.033 -0.0308 0.0114 0.2172
## Par. upper-bounds: 1.2391 0.4901 3.1628 2.8479 0.2509 0.3213 -0.1047 0.2228 0.0738 0.7589 0.0426 0.3298 0.4322 0.0782 0.5735 0.3501 0.4151 0.3194 0.4495 0.5783
## Final Estimates: -1.837772 -3.031805 -0.1079548 -0.2141806 -0.002517331 0.1329967 -0.3432775 0.0308054 -0.2256202 0.5421219 -0.2338436 0.1103818 0.1686773 -0.121268 0.3219817 0.1458641 0.201045 0.1367098 0.2256391 0.386237
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.837772 1.581056 -1.162 0.24509
## [2,] -3.031805 1.847692 -1.641 0.10083
## [3,] -0.107955 1.656166 -0.065 0.94803
## [4,] -0.214181 1.437735 -0.149 0.88158
## [5,] -0.002517 0.123113 -0.020 0.98369
## [6,] 0.132997 0.096175 1.383 0.16671
## [7,] -0.343277 0.120507 -2.849 0.00439 **
## [8,] 0.030805 0.098845 0.312 0.75530
## [9,] -0.225620 0.143829 -1.569 0.11673
## [10,] 0.542122 0.112375 4.824 1.41e-06 ***
## [11,] -0.233844 0.140843 -1.660 0.09685 .
## [12,] 0.110382 0.115523 0.955 0.33933
## [13,] 0.168677 0.128996 1.308 0.19100
## [14,] -0.121268 0.100811 -1.203 0.22901
## [15,] 0.321982 0.126337 2.549 0.01082 *
## [16,] 0.145864 0.103633 1.408 0.15928
## [17,] 0.201045 0.111889 1.797 0.07236 .
## [18,] 0.136710 0.087431 1.564 0.11790
## [19,] 0.225639 0.109612 2.059 0.03954 *
## [20,] 0.386237 0.089905 4.296 1.74e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.837772 -3.031805 -0.1079548 -0.2141806
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] -0.00252 0.133 -0.343 0.0308
## [2,] -0.22562 0.542 -0.234 0.1104
## [3,] 0.16868 -0.121 0.322 0.1459
## [4,] 0.20105 0.137 0.226 0.3862
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 335.92139 285.4412 -225.0346 -94.87673
## [2,] 285.44118 458.8536 -263.0272 -168.22718
## [3,] -225.03457 -263.0272 369.2643 185.98844
## [4,] -94.87673 -168.2272 185.9884 277.92487
## ----
## aic= 21.87256
## bic= 22.27398
## Number of parameters: 20
## initial estimates: -1.7921 -2.4197 0.0132 0.0809 0.1888 -0.0217 -0.7711 -0.2033 -0.2243 0.2968 -0.528 -0.1068 0.0024 -0.0163 0.2788 0.0287 0.0491 0.0365 0.1552 0.4603
## Par. lower-bounds: -4.266 -4.7218 -1.1592 -1.48 -0.0265 -0.2798 -1.1814 -0.4757 -0.4246 0.0566 -0.9099 -0.3603 -0.0996 -0.1386 0.0843 -0.1004 -0.0867 -0.1263 -0.1037 0.2885
## Par. upper-bounds: 0.6818 -0.1175 1.1856 1.6418 0.404 0.2364 -0.3607 0.069 -0.024 0.537 -0.1462 0.1466 0.1044 0.106 0.4733 0.1578 0.1849 0.1993 0.4141 0.6321
## Final Estimates: -1.705144 -2.306707 0.04663095 -0.008809735 0.1795696 -0.01341701 -0.7650871 -0.1874232 -0.2362119 0.3075876 -0.5202989 -0.08619787 -0.00109624 -0.01312211 0.2810935 0.0348109 0.05853259 0.02793562 0.1490637 0.4439174
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.705144 1.230655 -1.386 0.165882
## [2,] -2.306707 1.142944 -2.018 0.043569 *
## [3,] 0.046631 0.582468 0.080 0.936191
## [4,] -0.008810 0.756133 -0.012 0.990704
## [5,] 0.179570 0.106699 1.683 0.092385 .
## [6,] -0.013417 0.128405 -0.104 0.916781
## [7,] -0.765087 0.204867 -3.735 0.000188 ***
## [8,] -0.187423 0.134850 -1.390 0.164571
## [9,] -0.236212 0.099547 -2.373 0.017651 *
## [10,] 0.307588 0.119767 2.568 0.010222 *
## [11,] -0.520299 0.191122 -2.722 0.006482 **
## [12,] -0.086198 0.125793 -0.685 0.493194
## [13,] -0.001096 0.049956 -0.022 0.982493
## [14,] -0.013122 0.060466 -0.217 0.828195
## [15,] 0.281094 0.096922 2.900 0.003729 **
## [16,] 0.034811 0.063837 0.545 0.585540
## [17,] 0.058533 0.067703 0.865 0.387289
## [18,] 0.027936 0.081341 0.343 0.731268
## [19,] 0.149064 0.129844 1.148 0.250958
## [20,] 0.443917 0.085440 5.196 2.04e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.705144 -2.306707 0.04663095 -0.008809735
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.1796 -0.0134 -0.765 -0.1874
## [2,] -0.2362 0.3076 -0.520 -0.0862
## [3,] -0.0011 -0.0131 0.281 0.0348
## [4,] 0.0585 0.0279 0.149 0.4439
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 215.07353 146.42061 -48.70964 -33.00968
## [2,] 146.42061 187.15634 -44.75732 -58.71422
## [3,] -48.70964 -44.75732 48.21666 23.22532
## [4,] -33.00968 -58.71422 23.22532 86.36136
## ----
## aic= 17.82453
## bic= 18.22595
## Number of parameters: 20
## initial estimates: -1.2129 -2.0925 -0.1286 0.1717 0.5337 -0.1161 -0.0986 -0.086 0.2423 -0.1582 -0.2159 -0.0116 -0.1696 -0.0052 0.3457 0.0664 -0.3208 0.1928 0.3072 -0.0316
## Par. lower-bounds: -3.0529 -4.0382 -2.3812 -1.7612 0.3675 -0.3259 -0.2522 -0.2929 0.0666 -0.3801 -0.3783 -0.2304 -0.373 -0.2621 0.1576 -0.1869 -0.4954 -0.0277 0.1458 -0.249
## Par. upper-bounds: 0.6271 -0.1468 2.1241 2.1045 0.6999 0.0938 0.055 0.1209 0.4181 0.0638 -0.0534 0.2072 0.0339 0.2517 0.5338 0.3198 -0.1462 0.4132 0.4685 0.1857
## Final Estimates: -1.155706 -2.028119 -0.07460205 0.0935123 0.5275554 -0.1146414 -0.09534241 -0.08179301 0.2354418 -0.1565329 -0.2121778 -0.00684729 -0.1753802 -0.003857344 0.3487988 0.07040521 -0.3123901 0.1908257 0.3026799 -0.03739219
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.155706 0.918444 -1.258 0.208272
## [2,] -2.028119 0.971825 -2.087 0.036896 *
## [3,] -0.074602 1.123418 -0.066 0.947054
## [4,] 0.093512 0.967496 0.097 0.923001
## [5,] 0.527555 0.082881 6.365 1.95e-10 ***
## [6,] -0.114641 0.104921 -1.093 0.274550
## [7,] -0.095342 0.076757 -1.242 0.214186
## [8,] -0.081793 0.103409 -0.791 0.428963
## [9,] 0.235442 0.087699 2.685 0.007260 **
## [10,] -0.156533 0.110935 -1.411 0.158236
## [11,] -0.212178 0.081227 -2.612 0.008998 **
## [12,] -0.006847 0.109450 -0.063 0.950116
## [13,] -0.175380 0.101347 -1.730 0.083541 .
## [14,] -0.003857 0.128073 -0.030 0.975973
## [15,] 0.348799 0.093860 3.716 0.000202 ***
## [16,] 0.070405 0.126330 0.557 0.577313
## [17,] -0.312390 0.087283 -3.579 0.000345 ***
## [18,] 0.190826 0.110428 1.728 0.083978 .
## [19,] 0.302680 0.080841 3.744 0.000181 ***
## [20,] -0.037392 0.108858 -0.343 0.731227
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.155706 -2.028119 -0.07460205 0.0935123
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.528 -0.11464 -0.0953 -0.08179
## [2,] 0.235 -0.15653 -0.2122 -0.00685
## [3,] -0.175 -0.00386 0.3488 0.07041
## [4,] -0.312 0.19083 0.3027 -0.03739
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 118.16278 58.74181 -21.85137 -51.13266
## [2,] 58.74181 132.25559 -75.06037 -77.92124
## [3,] -21.85137 -75.06037 176.60534 78.85205
## [4,] -51.13266 -77.92124 78.85205 131.02294
## ----
## aic= 18.8377
## bic= 19.23911
## Number of parameters: 20
## initial estimates: -1.9996 -3.0396 -0.8385 -0.1974 0.5663 -0.114 -0.158 0.083 0.1259 0.2481 -0.2818 0.2945 -0.0575 -0.066 0.5842 -0.2137 -0.1524 0.0183 0.2 0.3355
## Par. lower-bounds: -4.6778 -5.6044 -4.201 -2.9515 0.3833 -0.3174 -0.31 -0.0942 -0.0493 0.0533 -0.4274 0.1248 -0.2872 -0.3214 0.3934 -0.4363 -0.3406 -0.1909 0.0438 0.1531
## Par. upper-bounds: 0.6785 -0.4748 2.5241 2.5567 0.7493 0.0895 -0.0061 0.2603 0.3011 0.443 -0.1363 0.4643 0.1723 0.1894 0.775 0.0089 0.0358 0.2276 0.3563 0.5178
## Final Estimates: -1.912614 -2.918421 -0.7279866 -0.3027239 0.5609402 -0.1087128 -0.1586526 0.09132909 0.1184414 0.2554783 -0.2826941 0.3060824 -0.06424342 -0.05935666 0.5834129 -0.2032195 -0.1459403 0.01196209 0.2007579 0.3254388
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.91261 1.33369 -1.434 0.151549
## [2,] -2.91842 1.28058 -2.279 0.022668 *
## [3,] -0.72799 1.67456 -0.435 0.663756
## [4,] -0.30272 1.37284 -0.221 0.825475
## [5,] 0.56094 0.09118 6.152 7.63e-10 ***
## [6,] -0.10871 0.10143 -1.072 0.283808
## [7,] -0.15865 0.07590 -2.090 0.036600 *
## [8,] 0.09133 0.08800 1.038 0.299363
## [9,] 0.11844 0.08755 1.353 0.176084
## [10,] 0.25548 0.09739 2.623 0.008713 **
## [11,] -0.28269 0.07288 -3.879 0.000105 ***
## [12,] 0.30608 0.08450 3.622 0.000292 ***
## [13,] -0.06424 0.11449 -0.561 0.574725
## [14,] -0.05936 0.12740 -0.466 0.641280
## [15,] 0.58341 0.09530 6.122 9.26e-10 ***
## [16,] -0.20322 0.11049 -1.839 0.065886 .
## [17,] -0.14594 0.09387 -1.555 0.120007
## [18,] 0.01196 0.10447 0.115 0.908840
## [19,] 0.20076 0.07813 2.570 0.010180 *
## [20,] 0.32544 0.09058 3.593 0.000327 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.912614 -2.918421 -0.7279866 -0.3027239
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.5609 -0.1087 -0.159 0.0913
## [2,] 0.1184 0.2555 -0.283 0.3061
## [3,] -0.0642 -0.0594 0.583 -0.2032
## [4,] -0.1459 0.0120 0.201 0.3254
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 247.35156 149.22884 -78.30757 -52.32370
## [2,] 149.22884 228.04304 -64.96118 -86.72291
## [3,] -78.30757 -64.96118 389.94360 198.70918
## [4,] -52.32370 -86.72291 198.70918 262.05525
## ----
## aic= 21.57209
## bic= 21.9735
## Number of parameters: 20
## initial estimates: -1.1244 -1.9311 -0.1953 -0.1646 -0.023 0.3341 -0.1259 -0.1065 -0.3159 0.4987 -0.1278 -0.0712 0.3144 -0.2397 0.5132 -0.1822 0.2457 -0.1055 0.0039 0.1832
## Par. lower-bounds: -3.0984 -3.6675 -1.8162 -1.3417 -0.2411 0.1131 -0.3595 -0.3946 -0.5078 0.3043 -0.3332 -0.3246 0.1353 -0.4212 0.3214 -0.4188 0.1156 -0.2373 -0.1353 0.0114
## Par. upper-bounds: 0.8495 -0.1948 1.4256 1.0125 0.1952 0.5551 0.1076 0.1817 -0.124 0.6931 0.0776 0.1823 0.4935 -0.0582 0.7049 0.0543 0.3757 0.0263 0.1432 0.355
## Final Estimates: -1.064493 -1.84792 -0.1552417 -0.2173607 -0.0301019 0.338145 -0.126237 -0.09835893 -0.3258106 0.5042762 -0.1282375 -0.05996073 0.3096516 -0.2370138 0.5129749 -0.1768828 0.2519068 -0.1090044 0.004185572 0.176085
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.064493 0.982587 -1.083 0.278650
## [2,] -1.847920 0.866792 -2.132 0.033014 *
## [3,] -0.155242 0.806415 -0.193 0.847344
## [4,] -0.217361 0.587272 -0.370 0.711294
## [5,] -0.030102 0.108530 -0.277 0.781504
## [6,] 0.338145 0.110223 3.068 0.002156 **
## [7,] -0.126237 0.116622 -1.082 0.279055
## [8,] -0.098359 0.143487 -0.685 0.493034
## [9,] -0.325811 0.095741 -3.403 0.000666 ***
## [10,] 0.504276 0.097237 5.186 2.15e-07 ***
## [11,] -0.128238 0.102879 -1.246 0.212587
## [12,] -0.059961 0.126582 -0.474 0.635720
## [13,] 0.309652 0.089059 3.477 0.000507 ***
## [14,] -0.237014 0.090446 -2.620 0.008780 **
## [15,] 0.512975 0.095729 5.359 8.39e-08 ***
## [16,] -0.176883 0.117746 -1.502 0.133036
## [17,] 0.251907 0.064884 3.882 0.000103 ***
## [18,] -0.109004 0.065879 -1.655 0.098000 .
## [19,] 0.004186 0.069830 0.060 0.952204
## [20,] 0.176085 0.085781 2.053 0.040098 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.064493 -1.84792 -0.1552417 -0.2173607
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] -0.0301 0.338 -0.12624 -0.0984
## [2,] -0.3258 0.504 -0.12824 -0.0600
## [3,] 0.3097 -0.237 0.51297 -0.1769
## [4,] 0.2519 -0.109 0.00419 0.1761
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 134.64378 71.42750 -61.04136 -22.84921
## [2,] 71.42750 104.79107 -34.73946 -17.99682
## [3,] -61.04136 -34.73946 90.66616 32.43063
## [4,] -22.84921 -17.99682 32.43063 48.10155
## ----
## aic= 17.10072
## bic= 17.50214
## Number of parameters: 20
## initial estimates: -0.7304 -1.3274 -0.559 -0.2883 0.3952 -0.2938 -0.203 0.1737 -0.2092 0.3508 -0.1497 -0.0318 -0.0902 0.3338 0.367 -0.1419 -0.0904 0.0511 0.1683 -0.1571
## Par. lower-bounds: -2.3648 -2.9165 -3.7733 -2.6751 0.215 -0.4766 -0.3312 0.0149 -0.3845 0.1731 -0.2744 -0.1861 -0.4448 -0.0257 0.1149 -0.454 -0.3537 -0.2159 -0.0189 -0.3889
## Par. upper-bounds: 0.9039 0.2617 2.6553 2.0985 0.5755 -0.1111 -0.0748 0.3324 -0.0339 0.5285 -0.0251 0.1225 0.2643 0.6933 0.6191 0.1703 0.1728 0.318 0.3555 0.0747
## Final Estimates: -0.720861 -1.306691 -0.5326285 -0.314246 0.3925237 -0.2959932 -0.2029803 0.1750626 -0.2133549 0.3476234 -0.1495282 -0.02961235 -0.09520342 0.3300903 0.3670417 -0.1392889 -0.08410191 0.05606066 0.1681426 -0.1603753
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.72086 0.81312 -0.887 0.37533
## [2,] -1.30669 0.79200 -1.650 0.09897 .
## [3,] -0.53263 1.59881 -0.333 0.73903
## [4,] -0.31425 1.18974 -0.264 0.79168
## [5,] 0.39252 0.08982 4.370 1.24e-05 ***
## [6,] -0.29599 0.09116 -3.247 0.00117 **
## [7,] -0.20298 0.06396 -3.174 0.00151 **
## [8,] 0.17506 0.07915 2.212 0.02699 *
## [9,] -0.21335 0.08749 -2.439 0.01474 *
## [10,] 0.34762 0.08879 3.915 9.03e-05 ***
## [11,] -0.14953 0.06230 -2.400 0.01639 *
## [12,] -0.02961 0.07710 -0.384 0.70091
## [13,] -0.09520 0.17662 -0.539 0.58986
## [14,] 0.33009 0.17924 1.842 0.06553 .
## [15,] 0.36704 0.12576 2.919 0.00352 **
## [16,] -0.13929 0.15564 -0.895 0.37082
## [17,] -0.08410 0.13143 -0.640 0.52223
## [18,] 0.05606 0.13337 0.420 0.67424
## [19,] 0.16814 0.09358 1.797 0.07237 .
## [20,] -0.16038 0.11581 -1.385 0.16612
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.720861 -1.306691 -0.5326285 -0.314246
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3925 -0.2960 -0.203 0.1751
## [2,] -0.2134 0.3476 -0.150 -0.0296
## [3,] -0.0952 0.3301 0.367 -0.1393
## [4,] -0.0841 0.0561 0.168 -0.1604
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 93.03290 56.40902 -98.01401 -57.23088
## [2,] 56.40902 88.26223 -107.45069 -67.13533
## [3,] -98.01401 -107.45069 359.68213 189.22744
## [4,] -57.23088 -67.13533 189.22744 199.16174
## ----
## aic= 18.73546
## bic= 19.13688
## Number of parameters: 20
## initial estimates: -1.9594 -3.1448 -0.1864 -0.1962 0.2471 -0.2203 0.1537 -0.1916 0.0478 -0.29 -0.3095 1e-04 0.0589 -0.0318 0.1055 -0.0111 0.1934 0.0232 0.1701 0.0571
## Par. lower-bounds: -4.3081 -6.1489 -2.8764 -2.8891 0.0391 -0.4119 -0.0185 -0.3612 -0.2182 -0.5351 -0.5297 -0.2168 -0.1793 -0.2512 -0.0917 -0.2053 -0.0451 -0.1964 -0.0273 -0.1373
## Par. upper-bounds: 0.3893 -0.1407 2.5036 2.4967 0.4551 -0.0287 0.3259 -0.0221 0.3139 -0.0449 -0.0892 0.2169 0.2972 0.1877 0.3027 0.183 0.4319 0.2429 0.3675 0.2515
## Final Estimates: -1.865192 -3.009475 -0.1123491 -0.3368142 0.2377856 -0.2165554 0.1569995 -0.1859059 0.03450023 -0.2845617 -0.3047232 0.008279761 0.05159935 -0.02879989 0.1081099 -0.006659589 0.2073017 0.01754119 0.1651375 0.04854392
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.86519 1.17090 -1.593 0.11117
## [2,] -3.00948 1.49888 -2.008 0.04466 *
## [3,] -0.11235 1.33788 -0.084 0.93308
## [4,] -0.33681 1.34566 -0.250 0.80236
## [5,] 0.23779 0.10363 2.295 0.02176 *
## [6,] -0.21655 0.09575 -2.262 0.02372 *
## [7,] 0.15700 0.08605 1.824 0.06808 .
## [8,] -0.18591 0.08467 -2.196 0.02811 *
## [9,] 0.03450 0.13267 0.260 0.79482
## [10,] -0.28456 0.12259 -2.321 0.02027 *
## [11,] -0.30472 0.11018 -2.766 0.00568 **
## [12,] 0.00828 0.10851 0.076 0.93918
## [13,] 0.05160 0.11847 0.436 0.66318
## [14,] -0.02880 0.10948 -0.263 0.79251
## [15,] 0.10811 0.09838 1.099 0.27180
## [16,] -0.00666 0.09686 -0.069 0.94519
## [17,] 0.20730 0.11911 1.740 0.08180 .
## [18,] 0.01754 0.11007 0.159 0.87338
## [19,] 0.16514 0.09891 1.670 0.09499 .
## [20,] 0.04854 0.09728 0.499 0.61779
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.865192 -3.009475 -0.1123491 -0.3368142
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2378 -0.2166 0.157 -0.18591
## [2,] 0.0345 -0.2846 -0.305 0.00828
## [3,] 0.0516 -0.0288 0.108 -0.00666
## [4,] 0.2073 0.0175 0.165 0.04854
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 197.77541 180.6220 -70.66106 -74.61178
## [2,] 180.62197 324.1408 -146.66646 -145.79814
## [3,] -70.66106 -146.6665 258.46357 120.99190
## [4,] -74.61178 -145.7981 120.99190 261.26395
## ----
## aic= 21.06714
## bic= 21.46856
## Number of parameters: 20
## initial estimates: -0.9284 -1.7888 -0.4083 -0.2345 0.2347 0.046 -0.1951 0.0788 -0.0073 0.2867 -0.3118 0.093 0.2521 -0.2084 0.5242 0.041 -0.0544 0.0576 0.2537 0.0788
## Par. lower-bounds: -2.3809 -3.4783 -2.6044 -2.3361 0.0418 -0.1212 -0.3285 -0.0702 -0.2316 0.0922 -0.4669 -0.0803 -0.0395 -0.4612 0.3225 -0.1843 -0.3335 -0.1843 0.0607 -0.1368
## Par. upper-bounds: 0.5241 -0.0994 1.7877 1.8671 0.4276 0.2133 -0.0617 0.2279 0.2171 0.4812 -0.1566 0.2664 0.5437 0.0444 0.7258 0.2664 0.2246 0.2996 0.4467 0.2944
## Final Estimates: -0.8832164 -1.713991 -0.3600484 -0.3119902 0.2291246 0.04805803 -0.1934072 0.0830694 -0.01654423 0.29002 -0.3089476 0.1000286 0.2461181 -0.2062612 0.5259931 0.0455666 -0.0448422 0.05413753 0.2507388 0.07154194
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.88322 0.72345 -1.221 0.22214
## [2,] -1.71399 0.84346 -2.032 0.04214 *
## [3,] -0.36005 1.09258 -0.330 0.74175
## [4,] -0.31199 1.04778 -0.298 0.76588
## [5,] 0.22912 0.09610 2.384 0.01712 *
## [6,] 0.04806 0.08349 0.576 0.56486
## [7,] -0.19341 0.06659 -2.904 0.00368 **
## [8,] 0.08307 0.07427 1.118 0.26336
## [9,] -0.01654 0.11205 -0.148 0.88262
## [10,] 0.29002 0.09733 2.980 0.00289 **
## [11,] -0.30895 0.07764 -3.979 6.91e-05 ***
## [12,] 0.10003 0.08659 1.155 0.24801
## [13,] 0.24612 0.14513 1.696 0.08992 .
## [14,] -0.20626 0.12608 -1.636 0.10186
## [15,] 0.52599 0.10057 5.230 1.69e-07 ***
## [16,] 0.04557 0.11217 0.406 0.68457
## [17,] -0.04484 0.13918 -0.322 0.74731
## [18,] 0.05414 0.12092 0.448 0.65435
## [19,] 0.25074 0.09644 2.600 0.00933 **
## [20,] 0.07154 0.10756 0.665 0.50598
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.8832164 -1.713991 -0.3600484 -0.3119902
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.2291 0.0481 -0.193 0.0831
## [2,] -0.0165 0.2900 -0.309 0.1000
## [3,] 0.2461 -0.2063 0.526 0.0456
## [4,] -0.0448 0.0541 0.251 0.0715
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 72.76030 47.00210 -38.50883 -30.73262
## [2,] 47.00210 98.90180 -50.77751 -47.15583
## [3,] -38.50883 -50.77751 165.93997 105.26686
## [4,] -30.73262 -47.15583 105.26686 152.60839
## ----
## aic= 18.11287
## bic= 18.51429
## Number of parameters: 20
## initial estimates: -1.459 -2.3517 -0.12 -0.3565 0.165 -0.1685 0.0039 -0.0566 -0.1974 -0.2592 -0.1706 -0.0446 -0.2399 0.196 -0.1445 0.1677 0.0017 0.2864 0.1778 0.1265
## Par. lower-bounds: -3.8595 -4.7904 -2.8486 -2.8836 -0.0453 -0.3844 -0.1964 -0.2591 -0.411 -0.4785 -0.3742 -0.2503 -0.479 -0.0494 -0.3723 -0.0625 -0.2197 0.0592 -0.0332 -0.0867
## Par. upper-bounds: 0.9414 0.0869 2.6085 2.1707 0.3753 0.0473 0.2043 0.1459 0.0163 -0.0399 0.0329 0.1611 -9e-04 0.4413 0.0832 0.3979 0.2231 0.5137 0.3887 0.3397
## Final Estimates: -1.373757 -2.255672 -0.0728528 -0.4771819 0.1589823 -0.1632456 0.009126784 -0.05219262 -0.2041221 -0.2532953 -0.1647764 -0.03964566 -0.2432458 0.19889 -0.1416575 0.1701195 0.01012731 0.2789461 0.1704161 0.1203015
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.373757 1.194796 -1.150 0.2502
## [2,] -2.255672 1.214535 -1.857 0.0633 .
## [3,] -0.072853 1.355898 -0.054 0.9572
## [4,] -0.477182 1.260428 -0.379 0.7050
## [5,] 0.158982 0.104820 1.517 0.1293
## [6,] -0.163246 0.107655 -1.516 0.1294
## [7,] 0.009127 0.099910 0.091 0.9272
## [8,] -0.052193 0.101024 -0.517 0.6054
## [9,] -0.204122 0.106554 -1.916 0.0554 .
## [10,] -0.253295 0.109428 -2.315 0.0206 *
## [11,] -0.164776 0.101551 -1.623 0.1047
## [12,] -0.039646 0.102691 -0.386 0.6994
## [13,] -0.243246 0.118960 -2.045 0.0409 *
## [14,] 0.198890 0.122147 1.628 0.1035
## [15,] -0.141658 0.113348 -1.250 0.2114
## [16,] 0.170119 0.114626 1.484 0.1378
## [17,] 0.010127 0.110624 0.092 0.9271
## [18,] 0.278946 0.113562 2.456 0.0140 *
## [19,] 0.170416 0.105373 1.617 0.1058
## [20,] 0.120301 0.106560 1.129 0.2589
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.373757 -2.255672 -0.0728528 -0.4771819
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.1590 -0.163 0.00913 -0.0522
## [2,] -0.2041 -0.253 -0.16478 -0.0396
## [3,] -0.2432 0.199 -0.14166 0.1701
## [4,] 0.0101 0.279 0.17042 0.1203
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 206.81722 138.0754 -107.5155 -92.16978
## [2,] 138.07545 213.6917 -150.7875 -107.73743
## [3,] -107.51547 -150.7875 266.2580 164.46131
## [4,] -92.16978 -107.7374 164.4613 230.10889
## ----
## aic= 20.29085
## bic= 20.69227
## Number of parameters: 20
## initial estimates: -1.62 -2.3101 -0.0272 -0.0722 0.8429 -0.2664 0.2361 -0.1764 0.4258 -0.1217 0.0072 0.0543 -0.272 0.1867 -0.066 0.327 -0.3214 0.3078 0.0351 0.1729
## Par. lower-bounds: -4.0235 -4.3934 -3.0995 -2.5324 0.6332 -0.5494 0.0384 -0.4144 0.2441 -0.3669 -0.1641 -0.1519 -0.54 -0.175 -0.3186 0.0228 -0.536 0.0181 -0.1672 -0.0707
## Par. upper-bounds: 0.7836 -0.2269 3.045 2.388 1.0525 0.0166 0.4337 0.0615 0.6075 0.1236 0.1785 0.2606 -0.004 0.5484 0.1867 0.6312 -0.1068 0.5974 0.2375 0.4165
## Final Estimates: -1.609016 -2.286911 0.0131677 -0.1102735 0.8394126 -0.2635722 0.2384274 -0.17228 0.4215419 -0.1177634 0.01014166 0.05963559 -0.2744688 0.1900177 -0.06406556 0.3305701 -0.3162301 0.3027302 0.03147953 0.1663055
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.60902 1.20744 -1.333 0.18267
## [2,] -2.28691 1.04758 -2.183 0.02903 *
## [3,] 0.01317 1.56193 0.008 0.99327
## [4,] -0.11027 1.24446 -0.089 0.92939
## [5,] 0.83941 0.10455 8.028 8.88e-16 ***
## [6,] -0.26357 0.14119 -1.867 0.06193 .
## [7,] 0.23843 0.09857 2.419 0.01557 *
## [8,] -0.17228 0.11866 -1.452 0.14652
## [9,] 0.42154 0.09079 4.643 3.43e-06 ***
## [10,] -0.11776 0.12260 -0.961 0.33678
## [11,] 0.01014 0.08559 0.118 0.90568
## [12,] 0.05964 0.10305 0.579 0.56278
## [13,] -0.27447 0.13347 -2.056 0.03975 *
## [14,] 0.19002 0.18037 1.053 0.29213
## [15,] -0.06407 0.12583 -0.509 0.61065
## [16,] 0.33057 0.15153 2.182 0.02915 *
## [17,] -0.31623 0.10724 -2.949 0.00319 **
## [18,] 0.30273 0.14486 2.090 0.03663 *
## [19,] 0.03148 0.10110 0.311 0.75552
## [20,] 0.16631 0.12171 1.366 0.17183
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.609016 -2.286911 0.0131677 -0.1102735
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.839 -0.264 0.2384 -0.1723
## [2,] 0.422 -0.118 0.0101 0.0596
## [3,] -0.274 0.190 -0.0641 0.3306
## [4,] -0.316 0.303 0.0315 0.1663
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 193.2298 123.24158 -152.7061 -108.64632
## [2,] 123.2416 145.71118 -124.9776 -96.19215
## [3,] -152.7061 -124.97757 314.9363 184.40895
## [4,] -108.6463 -96.19215 184.4090 203.29382
## ----
## aic= 19.44098
## bic= 19.8424
## Number of parameters: 20
## initial estimates: -1.4668 -2.1769 0.0683 0.1178 0.1685 0.3077 -0.0159 0.1495 -0.0914 0.2751 -0.1598 0.0866 0.3414 -0.5064 0.4571 -0.4853 0.2447 -0.343 0.2872 -0.298
## Par. lower-bounds: -3.8769 -4.4204 -3.1158 -2.4718 -0.0649 0.026 -0.2156 -0.0933 -0.3087 0.0129 -0.3457 -0.1394 0.0331 -0.8785 0.1932 -0.8061 -0.006 -0.6456 0.0726 -0.5589
## Par. upper-bounds: 0.9434 0.0666 3.2524 2.7074 0.4019 0.5893 0.1839 0.3923 0.1258 0.5372 0.0262 0.3126 0.6497 -0.1343 0.721 -0.1646 0.4955 -0.0404 0.5019 -0.0372
## Final Estimates: -1.40174 -2.095237 0.09706634 0.03070822 0.16371 0.3069117 -0.01840488 0.153786 -0.09744267 0.2740923 -0.1629845 0.0920273 0.3392322 -0.5067106 0.4560021 -0.4834242 0.2511358 -0.3420044 0.2906446 -0.3037965
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.40174 1.19825 -1.170 0.242072
## [2,] -2.09524 1.11674 -1.876 0.060627 .
## [3,] 0.09707 1.57516 0.062 0.950863
## [4,] 0.03071 1.28439 0.024 0.980925
## [5,] 0.16371 0.11642 1.406 0.159675
## [6,] 0.30691 0.14068 2.182 0.029141 *
## [7,] -0.01840 0.09976 -0.184 0.853625
## [8,] 0.15379 0.12117 1.269 0.204382
## [9,] -0.09744 0.10858 -0.897 0.369490
## [10,] 0.27409 0.13120 2.089 0.036703 *
## [11,] -0.16298 0.09303 -1.752 0.079783 .
## [12,] 0.09203 0.11301 0.814 0.415445
## [13,] 0.33923 0.15348 2.210 0.027091 *
## [14,] -0.50671 0.18546 -2.732 0.006291 **
## [15,] 0.45600 0.13150 3.468 0.000525 ***
## [16,] -0.48342 0.15974 -3.026 0.002475 **
## [17,] 0.25114 0.12525 2.005 0.044957 *
## [18,] -0.34200 0.15134 -2.260 0.023831 *
## [19,] 0.29064 0.10731 2.708 0.006760 **
## [20,] -0.30380 0.13036 -2.331 0.019779 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.40174 -2.095237 0.09706634 0.03070822
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.1637 0.307 -0.0184 0.154
## [2,] -0.0974 0.274 -0.1630 0.092
## [3,] 0.3392 -0.507 0.4560 -0.483
## [4,] 0.2511 -0.342 0.2906 -0.304
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 201.9642 138.5962 -164.5039 -122.1310
## [2,] 138.5962 175.6739 -162.9266 -129.7218
## [3,] -164.5039 -162.9266 351.0296 216.4430
## [4,] -122.1310 -129.7218 216.4430 233.7681
## ----
## aic= 19.70764
## bic= 20.10906
## Number of parameters: 20
## initial estimates: -1.1366 -2.0826 -1.1986 -0.1829 0.1742 0.2264 0.0424 0.0135 -0.2822 0.211 -0.0504 -0.1072 0.2739 0.1864 0.5292 -0.1173 0.2378 0.1422 0.1052 0.1389
## Par. lower-bounds: -3.2869 -3.9645 -4.8364 -2.2133 0.0072 0.0206 -0.0567 -0.193 -0.4283 0.0309 -0.1371 -0.2879 -0.0086 -0.1616 0.3616 -0.4666 0.0802 -0.0521 0.0116 -0.0561
## Par. upper-bounds: 1.0137 -0.2007 2.4393 1.8475 0.3411 0.4321 0.1416 0.22 -0.1361 0.391 0.0364 0.0735 0.5563 0.5345 0.6969 0.232 0.3955 0.3364 0.1988 0.3338
## Final Estimates: -1.060423 -1.978896 -1.038307 -0.2768858 0.1681049 0.2281113 0.04425856 0.01945978 -0.2905086 0.2133475 -0.04790589 -0.0990664 0.2610816 0.1901419 0.5330775 -0.1047069 0.2453459 0.1400076 0.1029872 0.1314862
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.06042 1.07032 -0.991 0.32180
## [2,] -1.97890 0.93988 -2.105 0.03525 *
## [3,] -1.03831 1.81307 -0.573 0.56686
## [4,] -0.27689 1.01236 -0.274 0.78447
## [5,] 0.16810 0.08308 2.023 0.04303 *
## [6,] 0.22811 0.10274 2.220 0.02640 *
## [7,] 0.04426 0.04947 0.895 0.37093
## [8,] 0.01946 0.10289 0.189 0.84998
## [9,] -0.29051 0.07296 -3.982 6.83e-05 ***
## [10,] 0.21335 0.09022 2.365 0.01805 *
## [11,] -0.04791 0.04344 -1.103 0.27008
## [12,] -0.09907 0.09036 -1.096 0.27291
## [13,] 0.26108 0.14074 1.855 0.06358 .
## [14,] 0.19014 0.17405 1.092 0.27463
## [15,] 0.53308 0.08379 6.362 1.99e-10 ***
## [16,] -0.10471 0.17430 -0.601 0.54803
## [17,] 0.24535 0.07858 3.122 0.00179 **
## [18,] 0.14001 0.09718 1.441 0.14967
## [19,] 0.10299 0.04679 2.201 0.02772 *
## [20,] 0.13149 0.09732 1.351 0.17669
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.060423 -1.978896 -1.038307 -0.2768858
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.168 0.228 0.0443 0.0195
## [2,] -0.291 0.213 -0.0479 -0.0991
## [3,] 0.261 0.190 0.5331 -0.1047
## [4,] 0.245 0.140 0.1030 0.1315
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 161.00829 53.20099 -11.88893 -15.85691
## [2,] 53.20099 124.15573 -55.18364 -56.23617
## [3,] -11.88893 -55.18364 462.01776 123.43789
## [4,] -15.85691 -56.23617 123.43789 144.03671
## ----
## aic= 20.66204
## bic= 21.06346
## Number of parameters: 20
## initial estimates: -0.7081 -2.7762 -0.4441 -0.1276 0.5751 0.0196 -0.1201 0.1333 -0.3663 0.4631 -0.1546 -0.0783 0.1524 0.0587 0.9915 -0.0714 0.1209 0.0439 0.1661 0.7207
## Par. lower-bounds: -1.7832 -5.2222 -1.7688 -1.2284 0.4418 -0.0467 -0.2227 -0.0099 -0.6697 0.3122 -0.3879 -0.404 -0.0119 -0.023 0.8651 -0.2478 -0.0156 -0.0241 0.0611 0.5741
## Par. upper-bounds: 0.3669 -0.3302 0.8805 0.9732 0.7085 0.086 -0.0175 0.2764 -0.063 0.614 0.0788 0.2474 0.3167 0.1405 1.1178 0.105 0.2574 0.1118 0.2711 0.8673
## Final Estimates: -0.6745966 -2.718427 -0.394102 -0.1702848 0.5714952 0.01920116 -0.1205867 0.1403452 -0.3738598 0.4616441 -0.1559097 -0.06185318 0.1483932 0.05818719 0.9910214 -0.06293577 0.125097 0.0443365 0.166844 0.7119774
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -0.67460 0.53485 -1.261 0.20721
## [2,] -2.71843 1.21705 -2.234 0.02551 *
## [3,] -0.39410 0.65900 -0.598 0.54982
## [4,] -0.17028 0.54814 -0.311 0.75606
## [5,] 0.57150 0.06648 8.596 < 2e-16 ***
## [6,] 0.01920 0.03314 0.579 0.56228
## [7,] -0.12059 0.05124 -2.353 0.01860 *
## [8,] 0.14035 0.07100 1.977 0.04809 *
## [9,] -0.37386 0.15128 -2.471 0.01346 *
## [10,] 0.46164 0.07540 6.123 9.21e-10 ***
## [11,] -0.15591 0.11659 -1.337 0.18115
## [12,] -0.06185 0.16157 -0.383 0.70185
## [13,] 0.14839 0.08191 1.812 0.07005 .
## [14,] 0.05819 0.04083 1.425 0.15409
## [15,] 0.99102 0.06313 15.698 < 2e-16 ***
## [16,] -0.06294 0.08748 -0.719 0.47189
## [17,] 0.12510 0.06813 1.836 0.06634 .
## [18,] 0.04434 0.03396 1.306 0.19167
## [19,] 0.16684 0.05251 3.178 0.00149 **
## [20,] 0.71198 0.07276 9.785 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.6745966 -2.718427 -0.394102 -0.1702848
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.571 0.0192 -0.121 0.1403
## [2,] -0.374 0.4616 -0.156 -0.0619
## [3,] 0.148 0.0582 0.991 -0.0629
## [4,] 0.125 0.0443 0.167 0.7120
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 38.032247 29.14001 -1.857536 -2.082257
## [2,] 29.140011 196.92517 -11.735681 -16.871120
## [3,] -1.857536 -11.73568 57.733141 31.748227
## [4,] -2.082257 -16.87112 31.748227 39.939298
## ----
## aic= 16.19844
## bic= 16.59985
## Number of parameters: 20
## initial estimates: -1.0594 -2.4185 -1.0768 -0.3919 -0.0145 0.0777 -0.1057 -0.0586 -0.3883 0.6163 -0.0825 -0.1772 0.1354 -0.0482 0.7085 -0.2631 0.201 -0.0298 0.0682 0.3856
## Par. lower-bounds: -2.9658 -4.8288 -4.0464 -2.9707 -0.2039 -0.043 -0.215 -0.2052 -0.6278 0.4637 -0.2207 -0.3626 -0.1597 -0.2362 0.5383 -0.4915 -0.0552 -0.193 -0.0796 0.1872
## Par. upper-bounds: 0.847 -0.0082 1.8929 2.1869 0.175 0.1984 0.0035 0.088 -0.1488 0.7689 0.0557 0.0081 0.4305 0.1398 0.8787 -0.0348 0.4573 0.1334 0.216 0.5839
## Final Estimates: -1.037476 -2.3807 -1.016542 -0.4467668 -0.02005504 0.07788916 -0.1062163 -0.05094115 -0.3970901 0.6167246 -0.08332118 -0.1651389 0.1288839 -0.04735901 0.7080258 -0.2539733 0.2078394 -0.03052978 0.06869073 0.376082
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.03748 0.94991 -1.092 0.274751
## [2,] -2.38070 1.20315 -1.979 0.047847 *
## [3,] -1.01654 1.47757 -0.688 0.491462
## [4,] -0.44677 1.28414 -0.348 0.727907
## [5,] -0.02006 0.09453 -0.212 0.831985
## [6,] 0.07789 0.06032 1.291 0.196579
## [7,] -0.10622 0.05463 -1.944 0.051862 .
## [8,] -0.05094 0.07285 -0.699 0.484386
## [9,] -0.39709 0.11973 -3.316 0.000912 ***
## [10,] 0.61672 0.07639 8.073 6.66e-16 ***
## [11,] -0.08332 0.06919 -1.204 0.228520
## [12,] -0.16514 0.09227 -1.790 0.073495 .
## [13,] 0.12888 0.14705 0.876 0.380783
## [14,] -0.04736 0.09382 -0.505 0.613719
## [15,] 0.70803 0.08498 8.332 < 2e-16 ***
## [16,] -0.25397 0.11332 -2.241 0.025011 *
## [17,] 0.20784 0.12780 1.626 0.103899
## [18,] -0.03053 0.08154 -0.374 0.708101
## [19,] 0.06869 0.07386 0.930 0.352334
## [20,] 0.37608 0.09849 3.819 0.000134 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.037476 -2.3807 -1.016542 -0.4467668
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] -0.0201 0.0779 -0.1062 -0.0509
## [2,] -0.3971 0.6167 -0.0833 -0.1651
## [3,] 0.1289 -0.0474 0.7080 -0.2540
## [4,] 0.2078 -0.0305 0.0687 0.3761
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 123.71731 77.44472 -48.42643 -56.37123
## [2,] 77.44472 198.46958 -63.47364 -64.90894
## [3,] -48.42643 -63.47364 299.35351 175.60381
## [4,] -56.37123 -64.90894 175.60381 226.11629
## ----
## aic= 20.45386
## bic= 20.85528
## Number of parameters: 20
## initial estimates: -1.3288 -2.039 -0.1296 0.0231 0.1686 -0.0573 0.1934 -0.3682 0.0683 -0.0654 -0.1408 0.0875 0.087 0.0917 0.6896 -0.049 0.118 -0.2819 0.0891 0.4324
## Par. lower-bounds: -3.5441 -3.9837 -2.7854 -1.8902 -0.0165 -0.2926 0.0356 -0.5883 -0.0942 -0.272 -0.2793 -0.1056 -0.1349 -0.1904 0.5003 -0.3128 -0.0419 -0.4852 -0.0472 0.2424
## Par. upper-bounds: 0.8864 -0.0944 2.5262 1.9364 0.3537 0.178 0.3513 -0.1482 0.2308 0.1412 -0.0022 0.2807 0.309 0.3739 0.8788 0.2147 0.2778 -0.0787 0.2254 0.6224
## Final Estimates: -1.261081 -1.970726 -0.07434004 -0.04521504 0.1631704 -0.05368314 0.1956557 -0.360228 0.06281447 -0.06177265 -0.1385315 0.09560206 0.08267296 0.09464993 0.6913612 -0.04251679 0.1234108 -0.2855867 0.08684228 0.4243131
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.26108 1.10442 -1.142 0.25352
## [2,] -1.97073 0.97038 -2.031 0.04227 *
## [3,] -0.07434 1.32308 -0.056 0.95519
## [4,] -0.04522 0.95504 -0.047 0.96224
## [5,] 0.16317 0.09227 1.768 0.07701 .
## [6,] -0.05368 0.11751 -0.457 0.64779
## [7,] 0.19566 0.07882 2.482 0.01305 *
## [8,] -0.36023 0.10954 -3.289 0.00101 **
## [9,] 0.06281 0.08107 0.775 0.43844
## [10,] -0.06177 0.10324 -0.598 0.54962
## [11,] -0.13853 0.06925 -2.001 0.04545 *
## [12,] 0.09560 0.09624 0.993 0.32052
## [13,] 0.08267 0.11047 0.748 0.45424
## [14,] 0.09465 0.14068 0.673 0.50109
## [15,] 0.69136 0.09436 7.326 2.36e-13 ***
## [16,] -0.04252 0.13115 -0.324 0.74579
## [17,] 0.12341 0.07977 1.547 0.12184
## [18,] -0.28559 0.10159 -2.811 0.00493 **
## [19,] 0.08684 0.06814 1.274 0.20249
## [20,] 0.42431 0.09470 4.481 7.44e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.261081 -1.970726 -0.07434004 -0.04521504
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.1632 -0.0537 0.1957 -0.3602
## [2,] 0.0628 -0.0618 -0.1385 0.0956
## [3,] 0.0827 0.0946 0.6914 -0.0425
## [4,] 0.1234 -0.2856 0.0868 0.4243
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 173.13034 81.45661 -90.99676 -70.55791
## [2,] 81.45661 133.63467 -102.18952 -67.57119
## [3,] -90.99676 -102.18952 248.14578 115.88612
## [4,] -70.55791 -67.57119 115.88612 129.38617
## ----
## aic= 19.29415
## bic= 19.69556
## Number of parameters: 20
## initial estimates: -1.4033 -2.68 -0.5025 -0.1172 0.3061 0.1211 -0.1885 0.0358 -0.1554 0.4186 -0.4026 0.2321 0.2736 -0.4026 0.3644 0.0993 0.0828 -0.1918 0.2388 0.0344
## Par. lower-bounds: -4.485 -5.6737 -4.9042 -3.1768 0.1487 -0.0707 -0.3397 -0.1772 -0.3083 0.2323 -0.5495 0.0253 0.0487 -0.6766 0.1484 -0.2048 -0.0735 -0.3822 0.0887 -0.177
## Par. upper-bounds: 1.6783 0.3136 3.8993 2.9425 0.4635 0.3129 -0.0373 0.2487 -0.0024 0.6049 -0.2557 0.4389 0.4985 -0.1286 0.5804 0.4034 0.2391 -0.0013 0.3889 0.2458
## Final Estimates: -1.390455 -2.654966 -0.4691046 -0.1490484 0.301141 0.124729 -0.1870581 0.04120862 -0.1615626 0.423327 -0.4007733 0.2390345 0.2674349 -0.3976502 0.366327 0.1063769 0.09008127 -0.1973298 0.2365717 0.02622953
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.39045 1.53413 -0.906 0.364751
## [2,] -2.65497 1.49223 -1.779 0.075209 .
## [3,] -0.46910 2.19070 -0.214 0.830442
## [4,] -0.14905 1.52676 -0.098 0.922231
## [5,] 0.30114 0.07834 3.844 0.000121 ***
## [6,] 0.12473 0.09555 1.305 0.191752
## [7,] -0.18706 0.07545 -2.479 0.013163 *
## [8,] 0.04121 0.10598 0.389 0.697397
## [9,] -0.16156 0.07619 -2.120 0.033967 *
## [10,] 0.42333 0.09293 4.555 5.23e-06 ***
## [11,] -0.40077 0.07338 -5.461 4.72e-08 ***
## [12,] 0.23903 0.10308 2.319 0.020396 *
## [13,] 0.26743 0.11185 2.391 0.016797 *
## [14,] -0.39765 0.13642 -2.915 0.003558 **
## [15,] 0.36633 0.10772 3.401 0.000672 ***
## [16,] 0.10638 0.15131 0.703 0.482029
## [17,] 0.09008 0.07794 1.156 0.247792
## [18,] -0.19733 0.09507 -2.076 0.037926 *
## [19,] 0.23657 0.07507 3.151 0.001625 **
## [20,] 0.02623 0.10544 0.249 0.803551
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.390455 -2.654966 -0.4691046 -0.1490484
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3011 0.125 -0.187 0.0412
## [2,] -0.1616 0.423 -0.401 0.2390
## [3,] 0.2674 -0.398 0.366 0.1064
## [4,] 0.0901 -0.197 0.237 0.0262
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 330.09533 98.87668 -146.0205 -91.29868
## [2,] 98.87668 312.27325 -261.6894 -163.90248
## [3,] -146.02048 -261.68937 672.8999 277.38655
## [4,] -91.29868 -163.90248 277.3866 326.79424
## ----
## aic= 23.0766
## bic= 23.47802
## Number of parameters: 20
## initial estimates: -1.2489 -2.6701 -0.4353 -0.3754 0.3428 -0.3169 0.2138 -0.0325 0.2132 -0.1084 0.1134 -0.11 0.0522 0.064 -0.2069 0.0629 -0.0607 -0.0948 -0.0051 -0.0222
## Par. lower-bounds: -3.5523 -5.153 -4.1115 -2.8232 0.1293 -0.4986 0.0573 -0.2392 -0.0169 -0.3043 -0.0553 -0.3328 -0.2885 -0.226 -0.4567 -0.267 -0.2876 -0.2879 -0.1714 -0.2419
## Par. upper-bounds: 1.0545 -0.1871 3.2408 2.0724 0.5563 -0.1352 0.3703 0.1742 0.4434 0.0875 0.2821 0.1128 0.3929 0.354 0.0428 0.3929 0.1661 0.0983 0.1612 0.1975
## Final Estimates: -1.216783 -2.566937 -0.3562004 -0.4616779 0.3406443 -0.3173212 0.212945 -0.0298691 0.2063823 -0.1097336 0.1108519 -0.1016023 0.04692256 0.06298686 -0.208898 0.06939619 -0.05500856 -0.09372167 -0.002959577 -0.02922143
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.21678 1.14519 -1.063 0.28800
## [2,] -2.56694 1.23917 -2.071 0.03831 *
## [3,] -0.35620 1.82861 -0.195 0.84556
## [4,] -0.46168 1.21999 -0.378 0.70511
## [5,] 0.34064 0.10624 3.206 0.00134 **
## [6,] -0.31732 0.09059 -3.503 0.00046 ***
## [7,] 0.21294 0.07791 2.733 0.00627 **
## [8,] -0.02987 0.10280 -0.291 0.77140
## [9,] 0.20638 0.11496 1.795 0.07261 .
## [10,] -0.10973 0.09803 -1.119 0.26296
## [11,] 0.11085 0.08431 1.315 0.18856
## [12,] -0.10160 0.11124 -0.913 0.36107
## [13,] 0.04692 0.16956 0.277 0.78198
## [14,] 0.06299 0.14467 0.435 0.66329
## [15,] -0.20890 0.12421 -1.682 0.09262 .
## [16,] 0.06940 0.16411 0.423 0.67240
## [17,] -0.05501 0.11300 -0.487 0.62639
## [18,] -0.09372 0.09652 -0.971 0.33153
## [19,] -0.00296 0.08261 -0.036 0.97142
## [20,] -0.02922 0.10941 -0.267 0.78941
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.216783 -2.566937 -0.3562004 -0.4616779
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.3406 -0.3173 0.21294 -0.0299
## [2,] 0.2064 -0.1097 0.11085 -0.1016
## [3,] 0.0469 0.0630 -0.20890 0.0694
## [4,] -0.0550 -0.0937 -0.00296 -0.0292
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 188.31458 103.25416 -195.5988 -84.76658
## [2,] 103.25416 220.47567 -133.6418 -91.52378
## [3,] -195.59885 -133.64177 480.2889 215.49674
## [4,] -84.76658 -91.52378 215.4967 213.76606
## ----
## aic= 20.91585
## bic= 21.31727
## Number of parameters: 20
## initial estimates: -1.2141 -2.4694 -0.1227 0.2731 0.3811 -0.0301 0.1331 -0.0775 -0.2989 0.3763 -0.0945 -0.0052 0.1652 0.1349 0.1642 -0.0864 0.2379 -0.0651 0.1093 -0.1357
## Par. lower-bounds: -3.2369 -4.9389 -2.9085 -2.1095 0.1993 -0.2027 -0.0205 -0.2732 -0.5208 0.1656 -0.282 -0.2441 -0.0852 -0.1027 -0.0473 -0.356 0.0238 -0.2683 -0.0716 -0.3663
## Par. upper-bounds: 0.8087 2e-04 2.6632 2.6557 0.563 0.1424 0.2867 0.1182 -0.0769 0.5869 0.093 0.2338 0.4156 0.3725 0.3758 0.1831 0.4521 0.1381 0.2903 0.0948
## Final Estimates: -1.162324 -2.371415 -0.07169497 0.1754589 0.3751581 -0.03006921 0.133449 -0.07561561 -0.3101862 0.376406 -0.09379575 -0.001584083 0.159369 0.1349265 0.1646026 -0.08457455 0.2492201 -0.06523977 0.1086188 -0.1392899
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.162324 1.007615 -1.154 0.248689
## [2,] -2.371415 1.233671 -1.922 0.054575 .
## [3,] -0.071695 1.385095 -0.052 0.958719
## [4,] 0.175459 1.190813 0.147 0.882861
## [5,] 0.375158 0.090452 4.148 3.36e-05 ***
## [6,] -0.030069 0.085866 -0.350 0.726199
## [7,] 0.133449 0.076435 1.746 0.080824 .
## [8,] -0.075616 0.096255 -0.786 0.432115
## [9,] -0.310186 0.110719 -2.802 0.005086 **
## [10,] 0.376406 0.104623 3.598 0.000321 ***
## [11,] -0.093796 0.093039 -1.008 0.313389
## [12,] -0.001584 0.114916 -0.014 0.989002
## [13,] 0.159369 0.124455 1.281 0.200355
## [14,] 0.134927 0.118273 1.141 0.253950
## [15,] 0.164603 0.105256 1.564 0.117858
## [16,] -0.084575 0.133025 -0.636 0.524919
## [17,] 0.249220 0.106888 2.332 0.019722 *
## [18,] -0.065240 0.101489 -0.643 0.520335
## [19,] 0.108619 0.090310 1.203 0.229081
## [20,] -0.139290 0.113710 -1.225 0.220591
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.162324 -2.371415 -0.07169497 0.1754589
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.375 -0.0301 0.1334 -0.07562
## [2,] -0.310 0.3764 -0.0938 -0.00158
## [3,] 0.159 0.1349 0.1646 -0.08457
## [4,] 0.249 -0.0652 0.1086 -0.13929
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 141.45334 106.9362 -89.57735 -66.32445
## [2,] 106.93621 212.0587 -126.54223 -130.92438
## [3,] -89.57735 -126.5422 267.75649 141.82951
## [4,] -66.32445 -130.9244 141.82951 197.51803
## ----
## aic= 19.86546
## bic= 20.26688
## Number of parameters: 20
## initial estimates: -2.045 -2.9451 -0.1075 -0.0447 0.2233 0.0847 -0.24 0.1817 -0.1921 0.3159 -0.3409 0.1198 0.1737 -0.0363 0.1362 0.1785 0.156 -0.1183 0.0699 0.1044
## Par. lower-bounds: -4.59 -5.6621 -2.4873 -2.5257 -0.0517 -0.1898 -0.5724 -0.1416 -0.4857 0.0228 -0.6956 -0.2253 -0.0835 -0.293 -0.1746 -0.1238 -0.1121 -0.3859 -0.2541 -0.2108
## Par. upper-bounds: 0.5001 -0.2281 2.2724 2.4363 0.4984 0.3592 0.0923 0.505 0.1016 0.6089 0.0139 0.4649 0.4309 0.2204 0.4469 0.4808 0.4241 0.1493 0.3939 0.4195
## Final Estimates: -1.945494 -2.812854 -0.100558 -0.1322487 0.2147415 0.08963622 -0.2325871 0.1850543 -0.2034752 0.3224366 -0.3309743 0.1242295 0.1731 -0.03594318 0.1366747 0.1787343 0.1635579 -0.1226691 0.06335275 0.1014519
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## [1,] -1.94549 1.26932 -1.533 0.1253
## [2,] -2.81285 1.35780 -2.072 0.0383 *
## [3,] -0.10056 1.18287 -0.085 0.9323
## [4,] -0.13225 1.23677 -0.107 0.9148
## [5,] 0.21474 0.13730 1.564 0.1178
## [6,] 0.08964 0.13721 0.653 0.5136
## [7,] -0.23259 0.16606 -1.401 0.1613
## [8,] 0.18505 0.16166 1.145 0.2523
## [9,] -0.20348 0.14687 -1.385 0.1659
## [10,] 0.32244 0.14678 2.197 0.0280 *
## [11,] -0.33097 0.17764 -1.863 0.0624 .
## [12,] 0.12423 0.17293 0.718 0.4725
## [13,] 0.17310 0.12793 1.353 0.1760
## [14,] -0.03594 0.12785 -0.281 0.7786
## [15,] 0.13667 0.15473 0.883 0.3771
## [16,] 0.17873 0.15062 1.187 0.2354
## [17,] 0.16356 0.13376 1.223 0.2214
## [18,] -0.12267 0.13367 -0.918 0.3588
## [19,] 0.06335 0.16178 0.392 0.6954
## [20,] 0.10145 0.15748 0.644 0.5194
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -1.945494 -2.812854 -0.100558 -0.1322487
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2] [,3] [,4]
## [1,] 0.215 0.0896 -0.2326 0.185
## [2,] -0.203 0.3224 -0.3310 0.124
## [3,] 0.173 -0.0359 0.1367 0.179
## [4,] 0.164 -0.1227 0.0634 0.101
##
## Residuals cov-matrix:
## [,1] [,2] [,3] [,4]
## [1,] 226.64573 204.5265 -99.00106 -93.61005
## [2,] 204.52648 259.3395 -114.69575 -116.17787
## [3,] -99.00106 -114.6958 196.75888 176.17487
## [4,] -93.61005 -116.1779 176.17487 215.09950
## ----
## aic= 19.00558
## bic= 19.40699We can compare matrices using Frobinius norm. Closer to 0 is more similar/identical.
# Function to calculate Frobenius norm of the difference between two matrices
frobenius_norm <- function(mat1, mat2) {
if (is.null(mat1) || is.null(mat2) || !all(dim(mat1) == dim(mat2))) {
return(NA) # Handle cases where the matrices are incompatible or NULL
}
return(sqrt(sum((mat1 - mat2)^2)))
}
# Initialize lists to store Frobenius norm results for phi and sigma
phi_frobenius_list <- list()
sigma_frobenius_list <- list()
# Loop through both fit_result_list and fit_result_list1
for (i in 1:length(fit_results_list_AR)) {
# Extract phi and sigma from both result lists
phi_1 <- fit_results_list_AR[[i]]$Phi
sigma_1 <- fit_results_list_AR[[i]]$Sigma
phi_2 <- fit_result_list_ARSIM[[i]]$Phi
sigma_2 <- fit_result_list_ARSIM[[i]]$Sigma
# Compare phi and sigma matrices using Frobenius norm
phi_frobenius_list[[i]] <- frobenius_norm(phi_1, phi_2)
sigma_frobenius_list[[i]] <- frobenius_norm(sigma_1, sigma_2)
}
# Convert to data frame for better visualization
frobenius_comparison <- data.frame(
Individual = 1:length(fit_results_list_AR),
Phi_Frobenius = unlist(phi_frobenius_list),
Sigma_Frobenius = unlist(sigma_frobenius_list)
)
# Display the results
print(frobenius_comparison)## Individual Phi_Frobenius Sigma_Frobenius
## 1 1 0.4409940 40.361500
## 2 2 0.3070987 25.027349
## 3 3 0.3364339 53.262569
## 4 4 0.3092464 38.774388
## 5 5 0.3945059 34.828856
## 6 6 0.3227188 73.350738
## 7 7 0.2613760 12.431548
## 8 8 0.4183870 45.051921
## 9 9 0.3748305 75.786938
## 10 10 0.4071310 23.553755
## 11 11 0.2885868 47.775452
## 12 12 0.4102702 45.611374
## 13 13 0.3259242 34.011421
## 14 14 0.2375469 23.919988
## 15 15 0.2780511 64.233653
## 16 16 0.4688770 24.062143
## 17 17 0.3686353 48.559394
## 18 18 0.2566152 38.449167
## 19 19 0.3078663 12.635663
## 20 20 0.4234440 73.449965
## 21 21 0.2789370 78.834936
## 22 22 0.4351761 34.728553
## 23 23 0.3082703 23.475199
## 24 24 0.3668025 40.141219
## 25 25 0.3105220 17.330057
## 26 26 0.2866016 11.040514
## 27 27 0.2839121 19.968591
## 28 28 0.2588402 34.344579
## 29 29 0.6224626 51.186341
## 30 30 0.5127936 23.941692
## 31 31 0.3227706 71.317298
## 32 32 0.2619554 5.061435
## 33 33 0.4968024 33.062887
## 34 34 0.3001525 17.841267
## 35 35 0.5178016 55.800428
## 36 36 0.5339477 133.658819
## 37 37 0.3421424 10.075108
## 38 38 0.3446234 64.317129
## 39 39 0.3542742 20.485658
## 40 40 0.2791491 22.609947
## 41 41 0.3749959 100.861650
## 42 42 0.3018213 50.825554
## 43 43 0.5912889 66.487966
## 44 44 0.2762885 12.364572
## 45 45 0.3052828 65.323157
## 46 46 0.3122971 36.989521
## 47 47 0.3342967 56.492099
## 48 48 0.5833802 86.382086
## 49 49 0.2970031 59.096464
## 50 50 0.4472076 63.774068
## 51 51 0.5037553 52.489713
## 52 52 0.3531112 32.626311
## 53 53 0.3655809 24.802637
## 54 54 0.2515201 31.413356
## 55 55 0.3412585 23.290553
## 56 56 0.3111960 77.659816
## 57 57 0.3893399 26.251085
## 58 58 0.5681709 32.893105
## 59 59 0.3377378 84.426727
## 60 60 0.3202067 47.857244
## 61 61 0.3882259 33.425155
## 62 62 0.4568790 76.284704
## 63 63 0.5222409 42.858592
## 64 64 0.2941585 78.316231
## 65 65 0.3296728 71.631840
## 66 66 0.3813763 103.961541
## 67 67 0.3483216 145.909815
## 68 68 0.4724758 81.583448
## 69 69 0.3777689 44.616104
## 70 70 0.3610730 37.829157
## 71 71 0.4487197 43.835545
## 72 72 0.2996951 45.748154
## 73 73 0.3552166 55.030410
## 74 74 0.6370325 74.942707
## 75 75 0.4092938 37.960146
## 76 76 0.4124284 35.403902
## 77 77 0.3058308 37.120374
## 78 78 0.3003511 34.661287
## 79 79 0.3379685 69.932417
## 80 80 0.3484494 25.405027
## 81 81 0.3958271 54.285672
## 82 82 0.3650887 29.060158
## 83 83 0.4756769 64.178861
## 84 84 0.4046552 108.933713
## 85 85 0.3314550 34.025749
## 86 86 0.3423249 37.995327
## 87 87 0.3625892 77.913977
## 88 88 0.3074921 30.019814
## 89 89 0.4805754 64.607849
## 90 90 0.4516778 67.340356
## 91 91 0.4030234 30.151514
## 92 92 0.3604653 59.852483
## 93 93 0.3545844 69.667758
## 94 94 0.4335096 68.268597
## 95 95 0.3155259 75.705145
## 96 96 0.4373245 16.224631
## 97 97 0.3650647 49.257256
## 98 98 0.2949102 52.143736
## 99 99 0.3541755 133.250224
## 100 100 0.4150223 102.631841
## 101 101 0.4497485 57.606957
## 102 102 0.5107225 41.808534