Vincent A.A _Markov Switching_Proposal

#Load Libraries

# Install necessary packages if you haven't already
# install.packages("readxl")
# install.packages("MSwM")
# install.packages("dplyr")
# install.packages("ggplot2")

# Load the libraries
library(readxl)
library(MSwM)

## Loading required package: parallel

library(dplyr)

## 
## 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

library(ggplot2)
library(tseries)

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

Load Data

library(readxl)
GDP_Growth <- read_excel("/Users/nanaakuaasare/Downloads/GDP Growth for selecterd SSA countries_Working Data.xlsx", 
    sheet = "Quarterly Growth Rate")
#View(GDP_Growth)

head(GDP_Growth)

## # A tibble: 6 × 11
##   Quarterly CAMEROON   DRC GABON GHANA IVOR_COAST  KENYA NIGERIA RWANDA SENEGAL
##   <chr>        <dbl> <dbl> <dbl> <dbl>      <dbl>  <dbl>   <dbl>  <dbl>   <dbl>
## 1 1961Q1       0.191  2.12  4.12 0.829     3.17   -2.98  -0.109  -2.29   0.955 
## 2 1961Q2       0.233  2.10  3.95 0.841     2.89   -2.57  -0.0464 -1.81   0.872 
## 3 1961Q3       0.316  2.08  3.61 0.863     2.35   -1.73   0.0788 -0.831  0.706 
## 4 1961Q4       0.440  2.05  3.09 0.897     1.53   -0.490  0.267   0.632  0.457 
## 5 1962Q1       0.606  2.00  2.40 0.942     0.434   1.17   0.517   2.58   0.126 
## 6 1962Q2       0.734  1.70  1.91 0.994    -0.0539  2.31   0.820   3.46  -0.0711
## # ℹ 1 more variable: TANZANIA <dbl>

colnames(GDP_Growth)

##  [1] "Quarterly"  "CAMEROON"   "DRC"        "GABON"      "GHANA"     
##  [6] "IVOR_COAST" "KENYA"      "NIGERIA"    "RWANDA"     "SENEGAL"   
## [11] "TANZANIA"

# Load necessary libraries
library(readxl)
library(dplyr)
library(tidyr)
library(tseries)
library(lmtest)

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

data <- GDP_Growth

# Display the structure of the dataset
str(data)

## tibble [248 × 11] (S3: tbl_df/tbl/data.frame)
##  $ Quarterly : chr [1:248] "1961Q1" "1961Q2" "1961Q3" "1961Q4" ...
##  $ CAMEROON  : num [1:248] 0.191 0.233 0.316 0.44 0.606 ...
##  $ DRC       : num [1:248] 2.12 2.1 2.08 2.05 2 ...
##  $ GABON     : num [1:248] 4.12 3.95 3.61 3.09 2.4 ...
##  $ GHANA     : num [1:248] 0.829 0.841 0.863 0.897 0.942 ...
##  $ IVOR_COAST: num [1:248] 3.165 2.892 2.346 1.526 0.434 ...
##  $ KENYA     : num [1:248] -2.98 -2.57 -1.73 -0.49 1.17 ...
##  $ NIGERIA   : num [1:248] -0.109 -0.0464 0.0788 0.2667 0.5171 ...
##  $ RWANDA    : num [1:248] -2.295 -1.807 -0.831 0.632 2.584 ...
##  $ SENEGAL   : num [1:248] 0.955 0.872 0.706 0.457 0.126 ...
##  $ TANZANIA  : num [1:248] NA NA NA NA NA NA NA NA NA NA ...

# Reshape the data to long format for easier processing
data_long <- data %>%
  gather(key = "Country", value = "GDP_Growth", -Quarterly)

# Summary statistics for each country
summary_stats <- data_long %>%
  group_by(Country) %>%
  summarize(
    Mean = mean(GDP_Growth, na.rm = TRUE),
    Median = median(GDP_Growth, na.rm = TRUE),
    Std_Dev = sd(GDP_Growth, na.rm = TRUE),
    Min = min(GDP_Growth, na.rm = TRUE),
    Max = max(GDP_Growth, na.rm = TRUE),
    Q1 = quantile(GDP_Growth, 0.25, na.rm = TRUE),
    Q3 = quantile(GDP_Growth, 0.75, na.rm = TRUE),
    N = n()
  )

summary_stats

## # A tibble: 10 × 9
##    Country     Mean Median Std_Dev     Min   Max      Q1    Q3     N
##    <chr>      <dbl>  <dbl>   <dbl>   <dbl> <dbl>   <dbl> <dbl> <int>
##  1 CAMEROON   0.905  0.971   1.39   -3.29   5.94  0.623   1.27   248
##  2 DRC        0.854  0.749   1.63   -2.92   6.52 -0.0266  1.95   248
##  3 GABON      1.01   0.984   2.36   -7.15  10.8   0.176   1.62   248
##  4 GHANA      0.920  1.07    1.10   -3.78   3.68  0.555   1.43   248
##  5 IVOR_COAST 1.07   1.11    1.39   -3.23   5.49  0.0841  1.98   248
##  6 KENYA      1.15   1.12    1.16   -2.98   6.62  0.482   1.58   248
##  7 NIGERIA    0.919  0.990   1.80   -4.23   7.16  0.0866  1.69   248
##  8 RWANDA     1.20   1.61    2.64  -15.6   12.1   0.387   2.28   248
##  9 SENEGAL    0.787  0.868   0.902  -2.21   2.76  0.355   1.44   248
## 10 TANZANIA   1.28   1.35    0.497   0.123  2.04  1.01    1.68   248

# Function to perform the unit root test (ADF) and homoscedasticity test (Breusch-Pagan)
perform_tests <- function(df) {
  adf_result <- adf.test(df$GDP_Growth, na.action = na.omit)
  bp_test <- bptest(GDP_Growth ~ 1, data = df)
  
  return(data.frame(
    ADF_Test_Statistic = adf_result$statistic,
    ADF_p_value = adf_result$p.value,
    BP_Test_Statistic = bp_test$statistic,
    BP_p_value = bp_test$p.value
  ))
}

# Summary statistics for each country
summary_stats <- data_long %>%
  group_by(Country) %>%
  summarize(
    Mean = mean(GDP_Growth, na.rm = TRUE),
    Median = median(GDP_Growth, na.rm = TRUE),
    Std_Dev = sd(GDP_Growth, na.rm = TRUE),
    Min = min(GDP_Growth, na.rm = TRUE),
    Max = max(GDP_Growth, na.rm = TRUE),
    Q1 = quantile(GDP_Growth, 0.25, na.rm = TRUE),
    Q3 = quantile(GDP_Growth, 0.75, na.rm = TRUE),
    N = n()
  )

# Function to perform the unit root test (ADF) and homoscedasticity test (Breusch-Pagan)
perform_tests <- function(df) {
  # Remove NA values for the tests
  df <- na.omit(df)
  
  adf_result <- adf.test(df$GDP_Growth)
  
  # Convert Quarterly to numeric for the regression
  df$Quarterly <- as.numeric(as.factor(df$Quarterly))
  
  bp_test <- bptest(GDP_Growth ~ Quarterly, data = df)
  
  return(data.frame(
    ADF_Test_Statistic = adf_result$statistic,
    ADF_p_value = adf_result$p.value,
    BP_Test_Statistic = bp_test$statistic,
    BP_p_value = bp_test$p.value
  ))
}

# Perform tests for each country
test_results <- data_long %>%
  group_by(Country) %>%
  do(perform_tests(.))

## Warning in adf.test(df$GDP_Growth): p-value smaller than printed p-value
## Warning in adf.test(df$GDP_Growth): p-value smaller than printed p-value
## Warning in adf.test(df$GDP_Growth): p-value smaller than printed p-value

# Combine summary statistics and test results
combined_results <- summary_stats %>%
  left_join(test_results, by = "Country")

# Print the combined results
print(combined_results)

## # A tibble: 10 × 13
##    Country     Mean Median Std_Dev     Min   Max      Q1    Q3     N
##    <chr>      <dbl>  <dbl>   <dbl>   <dbl> <dbl>   <dbl> <dbl> <int>
##  1 CAMEROON   0.905  0.971   1.39   -3.29   5.94  0.623   1.27   248
##  2 DRC        0.854  0.749   1.63   -2.92   6.52 -0.0266  1.95   248
##  3 GABON      1.01   0.984   2.36   -7.15  10.8   0.176   1.62   248
##  4 GHANA      0.920  1.07    1.10   -3.78   3.68  0.555   1.43   248
##  5 IVOR_COAST 1.07   1.11    1.39   -3.23   5.49  0.0841  1.98   248
##  6 KENYA      1.15   1.12    1.16   -2.98   6.62  0.482   1.58   248
##  7 NIGERIA    0.919  0.990   1.80   -4.23   7.16  0.0866  1.69   248
##  8 RWANDA     1.20   1.61    2.64  -15.6   12.1   0.387   2.28   248
##  9 SENEGAL    0.787  0.868   0.902  -2.21   2.76  0.355   1.44   248
## 10 TANZANIA   1.28   1.35    0.497   0.123  2.04  1.01    1.68   248
## # ℹ 4 more variables: ADF_Test_Statistic <dbl>, ADF_p_value <dbl>,
## #   BP_Test_Statistic <dbl>, BP_p_value <dbl>

# Optionally, save the combined results to an Excel file
#write.xlsx(combined_results, "path/to/save/summary_statistics_unit_root_homoscedasticity.xlsx", row.names = FALSE)

# Set seed for reproducibility
set.seed(123)

#Fit Markov-Switching Models ## Fixed Transition Probabilities (FTP) Model

# Fit a linear model as a base model
model <- lm(CAMEROON ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to CAMEROON data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE))
## 
##        AIC     BIC    logLik
##   540.8543 558.908 -268.4272
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   0.9719     0.0230  42.257 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2339457
## Multiple R-squared: 5.63e-30
## 
## Standardized Residuals:
##           Min            Q1           Med            Q3           Max 
## -5.179522e-01 -6.307453e-02 -7.669691e-37  7.228803e-02  4.945360e-01 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   0.8272     0.1883   4.393 1.118e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.016339
## Multiple R-squared: 4.851e-32
## 
## Standardized Residuals:
##         Min          Q1         Med          Q3         Max 
## -4.11289655 -0.03873180  0.00352952  0.08922131  5.11404760 
## 
## Transition probabilities:
##            Regime 1   Regime 2
## Regime 1 0.96061021 0.03684917
## Regime 2 0.03938979 0.96315083

# Extract smoothed probabilities
smoothed_probs <- data.frame(
  Quarterly = GDP_Growth$Quarterly[1:nrow(msm_ftp@Fit@smoProb)], 
  Regime1 = msm_ftp@Fit@smoProb[,1], 
  Regime2 = msm_ftp@Fit@smoProb[,2]
)

#Caneroon

# Fit a linear model as a base model
model <- lm(CAMEROON ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to CAMEROON data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE))
## 
##        AIC     BIC    logLik
##   540.8543 558.908 -268.4272
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   0.9719     0.0230  42.257 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2339457
## Multiple R-squared: 3.603e-30
## 
## Standardized Residuals:
##           Min            Q1           Med            Q3           Max 
## -5.179522e-01 -6.307453e-02 -7.669682e-37  7.228803e-02  4.945360e-01 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   0.8272     0.1882  4.3953 1.106e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.016339
## Multiple R-squared: 1.213e-32
## 
## Standardized Residuals:
##         Min          Q1         Med          Q3         Max 
## -4.11289655 -0.03873181  0.00352952  0.08922131  5.11404760 
## 
## Transition probabilities:
##            Regime 1   Regime 2
## Regime 1 0.96061021 0.03684916
## Regime 2 0.03938979 0.96315084

# Plot the smoothed probabilities of the regimes
plotProb(msm_ftp, which = 1)

# Fit a linear model as a base model
model <- lm(CAMEROON ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to CAMEROON data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, p = 0, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE), p = 0)
## 
##        AIC     BIC    logLik
##   540.8543 558.908 -268.4272
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   0.8272     0.1882  4.3953 1.106e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.016339
## Multiple R-squared: 1.94e-31
## 
## Standardized Residuals:
##         Min          Q1         Med          Q3         Max 
## -4.11289655 -0.03873181  0.00352952  0.08922131  5.11404760 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   0.9719     0.0230  42.257 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2339457
## Multiple R-squared: 2.027e-30
## 
## Standardized Residuals:
##           Min            Q1           Med            Q3           Max 
## -5.179522e-01 -6.307453e-02 -7.669685e-37  7.228803e-02  4.945360e-01 
## 
## Transition probabilities:
##            Regime 1   Regime 2
## Regime 1 0.96315084 0.03938979
## Regime 2 0.03684916 0.96061021

# Extract smoothed probabilities
smoothed_probs <- data.frame(
  Quarterly = GDP_Growth$Quarterly[1:nrow(msm_ftp@Fit@smoProb)], 
  Regime1 = msm_ftp@Fit@smoProb[,1], 
  Regime2 = msm_ftp@Fit@smoProb[,2]
)

# Convert Quarterly to Date format
GDP_Growth$Date <- as.Date(paste0(substr(GDP_Growth$Quarterly, 1, 4), "-",
                                  (as.numeric(substr(GDP_Growth$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")
smoothed_probs$Date <- as.Date(paste0(substr(smoothed_probs$Quarterly, 1, 4), "-",
                                      (as.numeric(substr(smoothed_probs$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")

# Ensure both data frames have the correct number of rows
smoothed_probs <- smoothed_probs[1:nrow(GDP_Growth), ]

# Plot the actual GDP growth rate and the inferred regimes for CAMEROON
ggplot(GDP_Growth, aes(x = Date)) +
  geom_line(aes(y = CAMEROON), color = "blue") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime1 * max(GDP_Growth$CAMEROON), color = "Regime 1"), linetype = "dashed") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime2 * max(GDP_Growth$CAMEROON), color = "Regime 2"), linetype = "dotted") +
  labs(title = "GDP Growth Rate and Inferred Regimes for CAMEROON",
       x = "Date",
       y = "GDP Growth Rate / Regime Probability") +
  theme_minimal()

# DRC

# Fit a linear model as a base model
model <- lm(DRC ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to DRC data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE))
## 
##        AIC      BIC    logLik
##   861.0235 879.0772 -428.5118
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value Pr(>|t|)
## (Intercept)(S)   0.1384     0.3534  0.3916   0.6954
## 
## Residual standard error: 2.284103
## Multiple R-squared: 5.906e-34
## 
## Standardized Residuals:
##        Min         Q1        Med         Q3        Max 
## -3.0605708 -0.1122525  0.1075989  0.2782024  6.3862095 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   1.2660     0.1245  10.169 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8343038
## Multiple R-squared: 2.833e-31
## 
## Standardized Residuals:
##         Min          Q1         Med          Q3         Max 
## -1.42889489 -0.59489893 -0.05107403  0.50577280  1.55686979 
## 
## Transition probabilities:
##           Regime 1   Regime 2
## Regime 1 0.8930295 0.05981622
## Regime 2 0.1069705 0.94018378

# Plot the smoothed probabilities of the regimes
plotProb(msm_ftp, which = 1)

# Convert Quarterly to Date format
GDP_Growth$Date <- as.Date(paste0(substr(GDP_Growth$Quarterly, 1, 4), "-",
                                  (as.numeric(substr(GDP_Growth$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")
smoothed_probs$Date <- as.Date(paste0(substr(smoothed_probs$Quarterly, 1, 4), "-",
                                      (as.numeric(substr(smoothed_probs$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")

# Ensure both data frames have the correct number of rows
smoothed_probs <- smoothed_probs[1:nrow(GDP_Growth), ]

# Plot the actual GDP growth rate and the inferred regimes for CAMEROON
ggplot(GDP_Growth, aes(x = Date)) +
  geom_line(aes(y = DRC), color = "blue") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime1 * max(GDP_Growth$DRC), color = "Regime 1"), linetype = "dashed") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime2 * max(GDP_Growth$DRC), color = "Regime 2"), linetype = "dotted") +
  labs(title = "GDP Growth Rate and Inferred Regimes for DRC",
       x = "Date",
       y = "GDP Growth Rate / Regime Probability") +
  theme_minimal()

Gabon

# Fit a linear model as a base model
model <- lm(GABON ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to DRC data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE))
## 
##        AIC      BIC    logLik
##   855.9556 874.0093 -425.9778
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   0.8405     0.0699  12.024 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8564853
## Multiple R-squared: 1.075e-30
## 
## Standardized Residuals:
##         Min          Q1         Med          Q3         Max 
## -2.01024628 -0.36956175  0.01152309  0.51107767  1.57523740 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)(S)   1.6505     0.6626  2.4909  0.01274 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.77331
## Multiple R-squared: 7.79e-32
## 
## Standardized Residuals:
##          Min           Q1          Med           Q3          Max 
## -8.799034181 -0.062172755 -0.016395863 -0.001096506  9.169682263 
## 
## Transition probabilities:
##            Regime 1   Regime 2
## Regime 1 0.97673557 0.06663729
## Regime 2 0.02326443 0.93336271

# Plot the smoothed probabilities of the regimes
plotProb(msm_ftp, which = 1)

# Convert Quarterly to Date format
GDP_Growth$Date <- as.Date(paste0(substr(GDP_Growth$Quarterly, 1, 4), "-",
                                  (as.numeric(substr(GDP_Growth$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")
smoothed_probs$Date <- as.Date(paste0(substr(smoothed_probs$Quarterly, 1, 4), "-",
                                      (as.numeric(substr(smoothed_probs$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")

# Ensure both data frames have the correct number of rows
smoothed_probs <- smoothed_probs[1:nrow(GDP_Growth), ]

# Plot the actual GDP growth rate and the inferred regimes for CAMEROON
ggplot(GDP_Growth, aes(x = Date)) +
  geom_line(aes(y = DRC), color = "blue") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime1 * max(GDP_Growth$GABON), color = "Regime 1"), linetype = "dashed") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime2 * max(GDP_Growth$GABON), color = "Regime 2"), linetype = "dotted") +
  labs(title = "GDP Growth Rate and Inferred Regimes for GABON",
       x = "Date",
       y = "GDP Growth Rate / Regime Probability") +
  theme_minimal()

#GHANA

# Fit a linear model as a base model
model <- lm(GHANA ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to DRC data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE))
## 
##        AIC      BIC    logLik
##   509.8177 527.8714 -252.9088
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   1.1449     0.0225  50.884 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.222911
## Multiple R-squared: 2.481e-29
## 
## Standardized Residuals:
##           Min            Q1           Med            Q3           Max 
## -4.710480e-01 -3.359472e-02 -6.099398e-14  2.821340e-02  5.586324e-01 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   0.7328     0.1259  5.8205 5.867e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.451642
## Multiple R-squared: 2.866e-31
## 
## Standardized Residuals:
##          Min           Q1          Med           Q3          Max 
## -4.509964383 -0.177106570  0.005384045  0.270535283  2.942876520 
## 
## Transition probabilities:
##           Regime 1   Regime 2
## Regime 1 0.9739964 0.02380021
## Regime 2 0.0260036 0.97619979

# Plot the smoothed probabilities of the regimes
plotProb(msm_ftp, which = 1)

# Convert Quarterly to Date format
GDP_Growth$Date <- as.Date(paste0(substr(GDP_Growth$Quarterly, 1, 4), "-",
                                  (as.numeric(substr(GDP_Growth$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")
smoothed_probs$Date <- as.Date(paste0(substr(smoothed_probs$Quarterly, 1, 4), "-",
                                      (as.numeric(substr(smoothed_probs$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")

# Ensure both data frames have the correct number of rows
smoothed_probs <- smoothed_probs[1:nrow(GDP_Growth), ]

# Plot the actual GDP growth rate and the inferred regimes for CAMEROON
ggplot(GDP_Growth, aes(x = Date)) +
  geom_line(aes(y = DRC), color = "blue") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime1 * max(GDP_Growth$GHANA), color = "Regime 1"), linetype = "dashed") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime2 * max(GDP_Growth$GHANA), color = "Regime 2"), linetype = "dotted") +
  labs(title = "GDP Growth Rate and Inferred Regimes for GHANA",
       x = "Date",
       y = "GDP Growth Rate / Regime Probability") +
  theme_minimal()

#IVORY_COAST

# Fit a linear model as a base model
model <- lm(IVOR_COAST ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to DRC data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE))
## 
##        AIC      BIC    logLik
##   748.6868 766.7406 -372.3434
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   2.0512     0.0736   27.87 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6706564
## Multiple R-squared: 1.754e-30
## 
## Standardized Residuals:
##           Min            Q1           Med            Q3           Max 
## -1.2515197463 -0.2235208941 -0.0198549040 -0.0001433616  1.4848285721 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)(S)   0.2994     0.1218  2.4581  0.01397 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.310813
## Multiple R-squared: 1.793e-33
## 
## Standardized Residuals:
##         Min          Q1         Med          Q3         Max 
## -3.52925080 -0.21535050  0.07609383  0.31596388  5.19073598 
## 
## Transition probabilities:
##            Regime 1   Regime 2
## Regime 1 0.95416035 0.03640898
## Regime 2 0.04583965 0.96359102

# Plot the smoothed probabilities of the regimes
plotProb(msm_ftp, which = 1)

# Convert Quarterly to Date format
GDP_Growth$Date <- as.Date(paste0(substr(GDP_Growth$Quarterly, 1, 4), "-",
                                  (as.numeric(substr(GDP_Growth$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")
smoothed_probs$Date <- as.Date(paste0(substr(smoothed_probs$Quarterly, 1, 4), "-",
                                      (as.numeric(substr(smoothed_probs$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")

# Ensure both data frames have the correct number of rows
smoothed_probs <- smoothed_probs[1:nrow(GDP_Growth), ]

# Plot the actual GDP growth rate and the inferred regimes for CAMEROON
ggplot(GDP_Growth, aes(x = Date)) +
  geom_line(aes(y = DRC), color = "blue") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime1 * max(GDP_Growth$IVOR_COAST), color = "Regime 1"), linetype = "dashed") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime2 * max(GDP_Growth$IVOR_COAST), color = "Regime 2"), linetype = "dotted") +
  labs(title = "GDP Growth Rate and Inferred Regimes for IVORY_COAST",
       x = "Date",
       y = "GDP Growth Rate / Regime Probability") +
  theme_minimal()

# KENYA

# Fit a linear model as a base model
model <- lm(KENYA ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to DRC data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE))
## 
##        AIC      BIC   logLik
##   601.9779 620.0316 -298.989
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   0.9798     0.0515  19.025 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6136227
## Multiple R-squared: 1.178e-30
## 
## Standardized Residuals:
##         Min          Q1         Med          Q3         Max 
## -1.32021552 -0.34459544  0.05252642  0.43575291  1.21917801 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   2.0333     0.3816  5.3284 9.908e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.299905
## Multiple R-squared: 9.321e-31
## 
## Standardized Residuals:
##         Min          Q1         Med          Q3         Max 
## -5.01354279 -0.07411568 -0.02421199 -0.01733682  4.58578036 
## 
## Transition probabilities:
##            Regime 1   Regime 2
## Regime 1 0.98372456 0.05829412
## Regime 2 0.01627544 0.94170588

# Plot the smoothed probabilities of the regimes
plotProb(msm_ftp, which = 1)

# Convert Quarterly to Date format
GDP_Growth$Date <- as.Date(paste0(substr(GDP_Growth$Quarterly, 1, 4), "-",
                                  (as.numeric(substr(GDP_Growth$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")
smoothed_probs$Date <- as.Date(paste0(substr(smoothed_probs$Quarterly, 1, 4), "-",
                                      (as.numeric(substr(smoothed_probs$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")

# Ensure both data frames have the correct number of rows
smoothed_probs <- smoothed_probs[1:nrow(GDP_Growth), ]

# Plot the actual GDP growth rate and the inferred regimes for CAMEROON
ggplot(GDP_Growth, aes(x = Date)) +
  geom_line(aes(y = DRC), color = "blue") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime1 * max(GDP_Growth$KENYA), color = "Regime 1"), linetype = "dashed") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime2 * max(GDP_Growth$KENYA), color = "Regime 2"), linetype = "dotted") +
  labs(title = "GDP Growth Rate and Inferred Regimes for KENYA",
       x = "Date",
       y = "GDP Growth Rate / Regime Probability") +
  theme_minimal()

#NIGERIA

# Fit a linear model as a base model
model <- lm(NIGERIA ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to DRC data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE))
## 
##        AIC      BIC    logLik
##   842.5217 860.5754 -419.2608
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   0.9904     0.0972  10.189 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7894524
## Multiple R-squared:     0
## 
## Standardized Residuals:
##           Min            Q1           Med            Q3           Max 
## -1.571624e+00 -3.958431e-01 -9.579633e-06  4.710653e-01  1.428939e+00 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)(S)   0.7558     0.3794  1.9921  0.04636 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.008305
## Multiple R-squared: 1.226e-32
## 
## Standardized Residuals:
##         Min          Q1         Med          Q3         Max 
## -4.98564187 -0.09567266  0.01578043  0.09457793  6.40665464 
## 
## Transition probabilities:
##            Regime 1   Regime 2
## Regime 1 0.96677054 0.07552644
## Regime 2 0.03322946 0.92447356

# Plot the smoothed probabilities of the regimes
plotProb(msm_ftp, which = 1)

# Convert Quarterly to Date format
GDP_Growth$Date <- as.Date(paste0(substr(GDP_Growth$Quarterly, 1, 4), "-",
                                  (as.numeric(substr(GDP_Growth$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")
smoothed_probs$Date <- as.Date(paste0(substr(smoothed_probs$Quarterly, 1, 4), "-",
                                      (as.numeric(substr(smoothed_probs$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")

# Ensure both data frames have the correct number of rows
smoothed_probs <- smoothed_probs[1:nrow(GDP_Growth), ]

# Plot the actual GDP growth rate and the inferred regimes for CAMEROON
ggplot(GDP_Growth, aes(x = Date)) +
  geom_line(aes(y = DRC), color = "blue") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime1 * max(GDP_Growth$NIGERIA), color = "Regime 1"), linetype = "dashed") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime2 * max(GDP_Growth$NIGERIA), color = "Regime 2"), linetype = "dotted") +
  labs(title = "GDP Growth Rate and Inferred Regimes for NIGERIA",
       x = "Date",
       y = "GDP Growth Rate / Regime Probability") +
  theme_minimal()

#RWANDA

# Fit a linear model as a base model
model <- lm(RWANDA ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to DRC data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE))
## 
##        AIC      BIC    logLik
##   904.2144 922.2681 -450.1072
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   1.6955     0.0738  22.974 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9077772
## Multiple R-squared: 1.496e-30
## 
## Standardized Residuals:
##          Min           Q1          Med           Q3          Max 
## -1.830697420 -0.557912059 -0.001221437  0.442035017  2.095022398 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value Pr(>|t|)
## (Intercept)(S)  -0.5952     0.7026 -0.8471   0.3969
## 
## Residual standard error: 4.982816
## Multiple R-squared: 7.943e-33
## 
## Standardized Residuals:
##          Min           Q1          Med           Q3          Max 
## -15.03436031   0.07495206   0.10478667   0.24374853  12.65182106 
## 
## Transition probabilities:
##            Regime 1 Regime 2
## Regime 1 0.96195984 0.118451
## Regime 2 0.03804016 0.881549

# Plot the smoothed probabilities of the regimes
plotProb(msm_ftp, which = 1)

# Convert Quarterly to Date format
GDP_Growth$Date <- as.Date(paste0(substr(GDP_Growth$Quarterly, 1, 4), "-",
                                  (as.numeric(substr(GDP_Growth$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")
smoothed_probs$Date <- as.Date(paste0(substr(smoothed_probs$Quarterly, 1, 4), "-",
                                      (as.numeric(substr(smoothed_probs$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")

# Ensure both data frames have the correct number of rows
smoothed_probs <- smoothed_probs[1:nrow(GDP_Growth), ]

# Plot the actual GDP growth rate and the inferred regimes for CAMEROON
ggplot(GDP_Growth, aes(x = Date)) +
  geom_line(aes(y = DRC), color = "blue") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime1 * max(GDP_Growth$RWANDA), color = "Regime 1"), linetype = "dashed") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime2 * max(GDP_Growth$RWANDA), color = "Regime 2"), linetype = "dotted") +
  labs(title = "GDP Growth Rate and Inferred Regimes for RWANDA",
       x = "Date",
       y = "GDP Growth Rate / Regime Probability") +
  theme_minimal()

#SENEGAL

# Fit a linear model as a base model
model <- lm(SENEGAL ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to DRC data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE))
## 
##        AIC      BIC    logLik
##   554.4447 572.4985 -275.2224
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   1.1507     0.0643  17.896 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5643157
## Multiple R-squared: 1.548e-31
## 
## Standardized Residuals:
##        Min         Q1        Med         Q3        Max 
## -0.8586419 -0.4069317 -0.1479950  0.2908478  1.6078269 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)(S)  -0.3702     0.2001 -1.8501   0.0643 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7824113
## Multiple R-squared: 2.467e-31
## 
## Standardized Residuals:
##         Min          Q1         Med          Q3         Max 
## -1.84004291  0.05554908  0.10788504  0.26974866  0.68005485 
## 
## Transition probabilities:
##            Regime 1  Regime 2
## Regime 1 0.93267264 0.2142697
## Regime 2 0.06732736 0.7857303

# Plot the smoothed probabilities of the regimes
plotProb(msm_ftp, which = 1)

# Convert Quarterly to Date format
GDP_Growth$Date <- as.Date(paste0(substr(GDP_Growth$Quarterly, 1, 4), "-",
                                  (as.numeric(substr(GDP_Growth$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")
smoothed_probs$Date <- as.Date(paste0(substr(smoothed_probs$Quarterly, 1, 4), "-",
                                      (as.numeric(substr(smoothed_probs$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")

# Ensure both data frames have the correct number of rows
smoothed_probs <- smoothed_probs[1:nrow(GDP_Growth), ]

# Plot the actual GDP growth rate and the inferred regimes for CAMEROON
ggplot(GDP_Growth, aes(x = Date)) +
  geom_line(aes(y = DRC), color = "blue") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime1 * max(GDP_Growth$SENEGAL), color = "Regime 1"), linetype = "dashed") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime2 * max(GDP_Growth$SENEGAL), color = "Regime 2"), linetype = "dotted") +
  labs(title = "GDP Growth Rate and Inferred Regimes for SENEGAL",
       x = "Date",
       y = "GDP Growth Rate / Regime Probability") +
  theme_minimal()

#TANZANIA

# Fit a linear model as a base model
model <- lm(TANZANIA ~ 1, data = GDP_Growth)

# Fit a Markov-Switching model to DRC data with fixed transition probabilities
msm_ftp <- msmFit(model, k = 2, sw = c(TRUE, TRUE))

# Summarize the model
summary(msm_ftp)

## Markov Switching Model
## 
## Call: msmFit(object = model, k = 2, sw = c(TRUE, TRUE))
## 
##        AIC      BIC   logLik
##   56.19241 71.84303 -26.0962
## 
## Coefficients:
## 
## Regime 1 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   0.8292     0.0495  16.752 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3692079
## Multiple R-squared: 1.447e-30
## 
## Standardized Residuals:
##          Min           Q1          Med           Q3          Max 
## -0.706390025  0.007192186  0.011767141  0.147404594  0.419853457 
## 
## Regime 2 
## ---------
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)(S)   1.6448     0.0227  72.458 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1863317
## Multiple R-squared: 2.272e-29
## 
## Standardized Residuals:
##           Min            Q1           Med            Q3           Max 
## -0.3407641425 -0.0450097768 -0.0006673555  0.0339662618  0.3995802719 
## 
## Transition probabilities:
##            Regime 1   Regime 2
## Regime 1 0.94967697 0.04088305
## Regime 2 0.05032303 0.95911695

# Plot the smoothed probabilities of the regimes
plotProb(msm_ftp, which = 1)

# Convert Quarterly to Date format
GDP_Growth$Date <- as.Date(paste0(substr(GDP_Growth$Quarterly, 1, 4), "-",
                                  (as.numeric(substr(GDP_Growth$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")
smoothed_probs$Date <- as.Date(paste0(substr(smoothed_probs$Quarterly, 1, 4), "-",
                                      (as.numeric(substr(smoothed_probs$Quarterly, 6, 6)) - 1) * 3 + 1, "-01"), format="%Y-%m-%d")

# Ensure both data frames have the correct number of rows
smoothed_probs <- smoothed_probs[1:nrow(GDP_Growth), ]

# Plot the actual GDP growth rate and the inferred regimes for CAMEROON
ggplot(GDP_Growth, aes(x = Date)) +
  geom_line(aes(y = DRC), color = "blue") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime1 * max(GDP_Growth$TANZANIA), color = "Regime 1"), linetype = "dashed") +
  geom_line(data = smoothed_probs, aes(x = Date, y = Regime2 * max(GDP_Growth$TANZANIA), color = "Regime 2"), linetype = "dotted") +
  labs(title = "GDP Growth Rate and Inferred Regimes for TANZANIA",
       x = "Date",
       y = "GDP Growth Rate / Regime Probability") +
  theme_minimal()

## Warning: Removed 248 rows containing missing values or values outside the scale range
## (`geom_line()`).
## Removed 248 rows containing missing values or values outside the scale range
## (`geom_line()`).

data <- GDP_Growth

# Define a function to count expansions and recessions
count_phases <- function(df, country) {
  expansion_count <- sum(df[[country]] > 0, na.rm = TRUE)
  recession_count <- sum(df[[country]] <= 0, na.rm = TRUE)
  return(list(expansion_count = expansion_count, recession_count = recession_count))
}

# List of countries
countries <- colnames(data)[-1]

# Create a data frame to store the results
results <- data.frame(
  Country = character(),
  Expansions = numeric(),
  Recessions = numeric(),
  stringsAsFactors = FALSE
)

# Calculate expansions and recessions for each country
for (country in countries) {
  counts <- count_phases(data, country)
  results <- rbind(results, data.frame(
    Country = country,
    Expansions = counts$expansion_count,
    Recessions = counts$recession_count
  ))
}

# Print the results
print(results)

##       Country Expansions Recessions
## 1    CAMEROON        205         43
## 2         DRC        184         64
## 3       GABON        196         52
## 4       GHANA        210         38
## 5  IVOR_COAST        192         56
## 6       KENYA        230         18
## 7     NIGERIA        189         59
## 8      RWANDA        204         44
## 9     SENEGAL        209         39
## 10   TANZANIA        136          0
## 11       Date        211         37

# Save the results to an Excel file
#write.xlsx(results, "path/to/save/expansion_recession_counts.xlsx", row.names = FALSE)