Purpose:
This script runs the VAR and BigVar models on our simulated dataset.
I show all combinations for \(n = \{4, 10, 20\}\) and \(t = \{100, 200, 500\}\)
Takeaways:
None of the BigVAR model coefficients look like we would expect. Most are 0.
When \(n = 200\) in the VAR model, there is some strange behavior. The coefficients become quite large, and some become NA. Still, the nonmissing diagonals are very close to what we would expect. Still wanted to flag this as strange behavior.
library(igraph)
library(tidyverse)
library(BigVAR)
library(vars)
library(knitr)
library(kableExtra)
library(Matrix)
options(scipen=20)models <- function(n, t, rho_1_mod, rho_2_mod, p_num, s_alpha_input, s_epsilon_input){
set.seed(4)
N = n
s_epsilon = s_epsilon_input
s_alpha = s_alpha_input
s_beta = 0
p = p_num/N
rho_1 = rho_1_mod
rho_2 = rho_2_mod
alpha = rnorm(N, mean = 0, sd = s_alpha)
# beta is the same as time dimension, for each time stamp there is a time value, when we eventually turn it on
beta = rnorm(N, mean = 0, sd = s_beta)
epsilon = rnorm(N, mean = 0, sd = s_epsilon)
G <- erdos.renyi.game(N, p, type=c("gnp"), directed = FALSE, loops = F) %>%
as_adjacency_matrix(sparse = F)
periods = t
y_0 = rep(0, N)
Y <- matrix(nrow = N, ncol = periods + 1)
colnames(Y) <- 0:periods
Y[, "0"] <- rnorm(N, mean = 0, sd = 1)
for(t1 in 1:periods){
t = t1 - 1
y_t <- Y[, paste(t)]
y_t1 <- alpha + beta + rho_1 * y_t + (rho_2 * G %*% y_t )+ epsilon
Y[, paste(t1)] <- y_t1
}
identity = diag(N)
comparison_matrix = ((rho_1 * identity) +( rho_2 *G))
# VAR
model <- VAR(t(Y), p = 1)
model_matrix <- t(as.data.frame(lapply(model$varresult, `[[`, 1)))
rownames(model_matrix) <- paste("y", 1:N, sep = "")
return(list(
list("Rho_1:", rho_1),
list("Alpha: ", alpha),
list("Epsilon:", epsilon),
list("VAR Matrix:", format(round(model_matrix, 10), scientific = F)),
list("Adjaceny Matrix:", G),
list("Determinant", det(Y[1:n, 1:n])),
list("Rank", rankMatrix(Y)),
list("comparison matrix:", comparison_matrix),
list("frobenius norm", norm(model_matrix[, 1:nrow(model_matrix)] - comparison_matrix, type = "F")),
list("rank_of_square", rankMatrix(Y[1:n, 1:n]))))
}N= 4
models(n = N, t = 100, rho_1_mod = runif(N, min = 0.7, max = 1.3), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1.0514802 0.7053675 0.8762438 0.8664250
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1 const
## y1 "1.0514802" "0.0000000" "0.0000000" "0.0000000" "0.0000000"
## y2 "0.0000000" "0.7053675" "0.0000000" "0.0000000" "0.0000000"
## y3 "0.0000000" "0.0000000" "0.8762438" "0.0000000" "0.0000000"
## y4 "0.0000000" "0.0000000" "0.0000000" "0.8664250" "0.0000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4]
## [1,] 0 0 1 0
## [2,] 0 0 0 0
## [3,] 1 0 0 1
## [4,] 0 0 1 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] 0.000002791174
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 4
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000002242651
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4]
## [1,] 1.05148 0.0000000 0.0000000 0.000000
## [2,] 0.00000 0.7053675 0.0000000 0.000000
## [3,] 0.00000 0.0000000 0.8762438 0.000000
## [4,] 0.00000 0.0000000 0.0000000 0.866425
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.00000000000372412
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 4
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000000008881784N= 10
models(n = N, t = 100, rho_1_mod = runif(N, min = 0.7, max = 1.3), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1.0514802 0.7053675 0.8762438 0.8664250 1.1881445 0.8562567 1.1346435
## [8] 1.2436553 1.2694241 0.7438867
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1
## y1 " 1.0514801830" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" " 0.7053674774" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.8762437672" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.8664249748"
## y5 " 0.0000000004" " 0.0000001557" "-0.0002585288" "-0.0000161378"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" "-0.0000000022" " 0.0000013682" " 0.0000000902"
## y8 " 0.0000000157" " 0.0000080773" "-0.0095189473" "-0.0006016445"
## y9 " 0.0000011080" " 0.0003354927" "-0.4576413263" "-0.0285199342"
## y10 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5.l1 y6.l1 y7.l1 y8.l1
## y1 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 1.1881445290" " 0.0001248674" " 0.0000000000" " 0.0000000000"
## y6 " 0.0000000000" " 0.8562566628" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" "-0.0000007382" " 1.1346435356" " 0.0000000000"
## y8 " 0.0000000000" " 0.0047198883" " 0.0000000001" " 1.2436552908"
## y9 " 0.0000000002" " 0.2207918553" " 0.0000000086" " 0.0000000000"
## y10 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y9.l1 y10.l1 const
## y1 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 0.0000000000" "-0.0000026281" "-0.0000000039"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" " 0.0000000290" " 0.0000000000"
## y8 " 0.0000000000" "-0.0001233318" "-0.0000001348"
## y9 " 1.2694241326" "-0.0052313877" "-0.0000090709"
## y10 " 0.0000000000" " 0.7438866816" " 0.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 1 0 0 0 0 0 1
## [2,] 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0
## [10,] 1 0 0 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -6.400046e-38
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 8
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000002242651
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1.05148 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [2,] 0.00000 0.7053675 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [3,] 0.00000 0.0000000 0.8762438 0.000000 0.000000 0.0000000 0.000000 0.000000
## [4,] 0.00000 0.0000000 0.0000000 0.866425 0.000000 0.0000000 0.000000 0.000000
## [5,] 0.00000 0.0000000 0.0000000 0.000000 1.188145 0.0000000 0.000000 0.000000
## [6,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.8562567 0.000000 0.000000
## [7,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 1.134644 0.000000
## [8,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 1.243655
## [9,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [10,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [,9] [,10]
## [1,] 0.000000 0.0000000
## [2,] 0.000000 0.0000000
## [3,] 0.000000 0.0000000
## [4,] 0.000000 0.0000000
## [5,] 0.000000 0.0000000
## [6,] 0.000000 0.0000000
## [7,] 0.000000 0.0000000
## [8,] 0.000000 0.0000000
## [9,] 1.269424 0.0000000
## [10,] 0.000000 0.7438867
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.5090568
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 20
models(n = N, t = 100, rho_1_mod = runif(N, min = 0.7, max = 1.3), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1.0514802 0.7053675 0.8762438 0.8664250 1.1881445 0.8562567 1.1346435
## [8] 1.2436553 1.2694241 0.7438867 1.1528050 0.8716004 0.7600321 1.2724413
## [15] 0.9493643 0.9730615 1.2826334 1.0503928 1.2773228 1.1570214
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1
## y1 " 1.0514801843" " -0.0000000003" " 0.0000007984"
## y2 " -0.0000000001" " 0.7053674774" " -0.0000000333"
## y3 " 0.0000000003" " -0.0000000001" " 0.8762439572"
## y4 " -0.0000000001" " 0.0000000000" " -0.0000000360"
## y5 " 0.0006816840" " -0.0000863613" " 0.2997536459"
## y6 " 0.0000000001" " 0.0000000000" " 0.0000000426"
## y7 " -0.0000027201" " 0.0000005714" " -0.0014251467"
## y8 " 0.0363165269" " -0.0066755673" " 20.1809408994"
## y9 " -0.1446211477" " 0.0375221905" " -100.2786917858"
## y10 " 0.0000000000" " 0.0000000000" " -0.0000000244"
## y11 " -0.0000032643" " -0.0000052043" " 0.0046818631"
## y12 " 0.0000000000" " 0.0000000000" " 0.0000000084"
## y13 " 0.0000000000" " 0.0000000000" " 0.0000000017"
## y14 " -0.0813292364" " -0.1391233945" " 162.7366082921"
## y15 " 0.0000000000" " 0.0000000000" " 0.0000000055"
## y16 " 0.0000000000" " 0.0000000000" " -0.0000000235"
## y17 " 37182048.2084711865" " -1515356.0565026111" " 8322268450.5631217957"
## y18 " -0.0000000001" " 0.0000000000" " -0.0000000444"
## y19 " 39621891.8529098853" " -1596550.9705988991" " 8790875857.5399055481"
## y20 " -8449.3099089160" " 215.7414998721" " -1295465.5072228485"
## y4.l1 y5.l1 y6.l1
## y1 " 0.0000007240" " 0.0000000000" " -0.0000004701"
## y2 " -0.0000000301" " 0.0000000000" " 0.0000000195"
## y3 " 0.0000001723" " 0.0000000000" " -0.0000001118"
## y4 " 0.8664249427" " 0.0000000000" " 0.0000000205"
## y5 " 0.2665407267" " 1.1881445286" " -0.1696028539"
## y6 " 0.0000000385" " 0.0000000000" " 0.8562566379"
## y7 " -0.0012886736" " 0.0000000000" " 0.0008348067"
## y8 " 18.1427182521" " -0.0000000187" " -11.6715693512"
## y9 " -91.0794391443" " 0.0000000620" " 59.1985355076"
## y10 " -0.0000000220" " 0.0000000000" " 0.0000000143"
## y11 " 0.0046837457" " 0.0000000000" " -0.0033384814"
## y12 " 0.0000000076" " 0.0000000000" " -0.0000000049"
## y13 " 0.0000000017" " 0.0000000000" " -0.0000000011"
## y14 " 158.1982121599" " 0.0000001580" " -109.8185084457"
## y15 " 0.0000000048" " 0.0000000000" " -0.0000000031"
## y16 " -0.0000000224" " 0.0000000000" " 0.0000000152"
## y17 " 7180953656.2784423828" " -58.0247292280" "-4431864791.4191923141"
## y18 " -0.0000000400" " 0.0000000000" " 0.0000000258"
## y19 " 7583534663.0702362061" " -63.9640703615" "-4679270968.7550811768"
## y20 " -1108512.7395004444" " -0.0179186451" " 678665.3249589411"
## y7.l1 y8.l1 y9.l1
## y1 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 0.0000001168" " 0.0000000000" " 0.0000000000"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7 " 1.1346435351" " 0.0000000000" " 0.0000000000"
## y8 " 0.0000056906" " 1.2436552910" " 0.0000000002"
## y9 " -0.0000202373" " -0.0000000007" " 1.2694241319"
## y10 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y11 " -0.0000000007" " 0.0000000000" " 0.0000000000"
## y12 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y13 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y14 " -0.0000355561" " -0.0000000024" " -0.0000000026"
## y15 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y16 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y17 " 10518.0575306849" " 1.8414425775" " 5.5742713617"
## y18 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y19 " 11353.0424740780" " 2.2175806309" " 9.6959185436"
## y20 " -7.1234738108" " 0.0000837765" " 0.0000660815"
## y10.l1 y11.l1 y12.l1
## y1 " -0.0000000051" " 0.0000000000" " 0.0000081813"
## y2 " 0.0000000002" " 0.0000000000" " -0.0000003410"
## y3 " -0.0000000012" " 0.0000000000" " 0.0000019475"
## y4 " 0.0000000002" " 0.0000000000" " -0.0000003657"
## y5 " -0.0014799845" " 0.0000000070" " 3.0432500243"
## y6 " -0.0000000003" " 0.0000000000" " 0.0000004359"
## y7 " 0.0000090667" " 0.0000000000" " -0.0145830717"
## y8 " -0.1118958361" " 0.0000003356" " 205.9618857184"
## y9 " 0.6191231309" " -0.0000011647" " -1028.4325871241"
## y10 " 0.7438866818" " 0.0000000000" " -0.0000002496"
## y11 " -0.0000717722" " 1.1528050161" " 0.0503115713"
## y12 " -0.0000000001" " 0.0000000000" " 0.8716004582"
## y13 " 0.0000000000" " 0.0000000000" " 0.0000000182"
## y14 " -1.9841735901" " -0.0000023588" " 1724.4765678709"
## y15 " 0.0000000000" " 0.0000000000" " 0.0000000552"
## y16 " 0.0000000002" " 0.0000000000" " -0.0000002466"
## y17 " -28522324.9518824853" " 725.3598511915" "83292908557.3597106934"
## y18 " 0.0000000003" " 0.0000000000" " -0.0000004530"
## y19 " -30062130.7156249061" " 786.9731006231" "87973108195.2589263916"
## y20 " 4112.9363133566" " -2.2817270088" " -12913521.7866172437"
## y13.l1 y14.l1 y15.l1
## y1 " -0.0000000031" " 0.0000000000" " -0.0000000023"
## y2 " 0.0000000001" " 0.0000000000" " 0.0000000001"
## y3 " -0.0000000007" " 0.0000000000" " -0.0000000005"
## y4 " 0.0000000001" " 0.0000000000" " 0.0000000001"
## y5 " -0.0009413168" " 0.0000000000" " -0.0010078469"
## y6 " -0.0000000002" " 0.0000000000" " -0.0000000001"
## y7 " 0.0000055820" " 0.0000000000" " 0.0000043155"
## y8 " -0.0704150615" " 0.0000000000" " -0.0618735564"
## y9 " 0.3860977814" " 0.0000000001" " 0.2823220496"
## y10 " 0.0000000001" " 0.0000000000" " 0.0000000001"
## y11 " -0.0000412336" " 0.0000000000" " -0.0000038364"
## y12 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y13 " 0.7600321129" " 0.0000000000" " 0.0000000000"
## y14 " -1.1591366015" " 1.2724412655" " -0.2143758436"
## y15 " 0.0000000000" " 0.0000000000" " 0.9493642711"
## y16 " 0.0000000001" " 0.0000000000" " 0.0000000000"
## y17 " -18893066.8948347420" " -1.2925892981" " -35736797.0918585733"
## y18 " 0.0000000002" " 0.0000000000" " 0.0000000001"
## y19 " -19916732.5677172244" " -2.8069973014" " -37836846.8636485040"
## y20 " 2741.4702600782" " -0.0000115111" " 6071.1063552711"
## y16.l1 y17.l1 y18.l1
## y1 " 0.0000000013" " NA" " 0.0000000006"
## y2 " -0.0000000001" " NA" " 0.0000000000"
## y3 " 0.0000000003" " NA" " 0.0000000001"
## y4 " -0.0000000001" " NA" " 0.0000000000"
## y5 " 0.0005702487" " NA" " 0.0003015168"
## y6 " 0.0000000001" " NA" " 0.0000000000"
## y7 " -0.0000023822" " NA" " -0.0000012035"
## y8 " 0.0338759195" " NA" " 0.0160861100"
## y9 " -0.1499400468" " NA" " -0.0641540236"
## y10 " 0.0000000000" " NA" " 0.0000000000"
## y11 " 0.0000005830" " NA" " -0.0000014293"
## y12 " 0.0000000000" " NA" " 0.0000000000"
## y13 " 0.0000000000" " NA" " 0.0000000000"
## y14 " 0.0701631609" " NA" " -0.0351140224"
## y15 " 0.0000000000" " NA" " 0.0000000000"
## y16 " 0.9730614506" " NA" " 0.0000000000"
## y17 " 22096753.1381563656" " NA" " 16357603.3665776439"
## y18 " -0.0000000001" " NA" " 1.0503927878"
## y19 " 23420044.4122249782" " NA" " 17429171.6042399667"
## y20 " -3916.6602245101" " NA" " -3697.2373175433"
## y19.l1 y20.l1 const
## y1 " NA" " NA" " 0.0000000002"
## y2 " NA" " NA" " 0.0000000000"
## y3 " NA" " NA" " 0.0000000001"
## y4 " NA" " NA" " 0.0000000000"
## y5 " NA" " NA" " 0.0001128671"
## y6 " NA" " NA" " 0.0000000000"
## y7 " NA" " NA" " -0.0000004613"
## y8 " NA" " NA" " 0.0064544257"
## y9 " NA" " NA" " -0.0275662006"
## y10 " NA" " NA" " 0.0000000000"
## y11 " NA" " NA" " -0.0000001738"
## y12 " NA" " NA" " 0.0000000000"
## y13 " NA" " NA" " 0.0000000000"
## y14 " NA" " NA" " 0.0034765271"
## y15 " NA" " NA" " 0.0000000000"
## y16 " NA" " NA" " 0.0000000000"
## y17 " NA" " NA" " 4872646.7774426313"
## y18 " NA" " NA" " 0.0000000000"
## y19 " NA" " NA" " 5172034.8522359543"
## y20 " NA" " NA" " -918.7923292056"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 1 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 1 0 0 0 1 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 1 1 0 0 0 1 0 0 0 0 0
## [8,] 0 0 0 0 0 0 1 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [10,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [11,] 0 0 0 1 0 0 0 0 0 0 0 0 0
## [12,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [13,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [14,] 0 0 0 0 0 1 0 0 0 0 0 0 0
## [15,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [16,] 0 0 0 0 1 0 0 1 0 0 0 0 0
## [17,] 0 0 1 0 0 0 0 0 0 0 0 0 0
## [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [19,] 0 0 0 0 0 0 0 0 0 0 0 1 0
## [20,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [,14] [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0
## [3,] 0 0 0 1 0 0 0
## [4,] 0 0 0 0 0 0 0
## [5,] 0 0 1 0 0 0 0
## [6,] 1 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0
## [8,] 0 0 1 0 0 0 0
## [9,] 0 0 0 0 0 0 0
## [10,] 0 0 0 0 0 0 0
## [11,] 0 0 0 0 0 0 0
## [12,] 0 0 0 0 0 1 0
## [13,] 0 0 0 0 0 0 0
## [14,] 0 0 0 0 1 0 0
## [15,] 0 0 0 0 0 0 0
## [16,] 0 0 0 0 0 0 0
## [17,] 0 0 0 0 0 0 0
## [18,] 1 0 0 0 0 0 0
## [19,] 0 0 0 0 0 0 0
## [20,] 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -5.230822e-144
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 15
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000002242651
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1.05148 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [2,] 0.00000 0.7053675 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [3,] 0.00000 0.0000000 0.8762438 0.000000 0.000000 0.0000000 0.000000 0.000000
## [4,] 0.00000 0.0000000 0.0000000 0.866425 0.000000 0.0000000 0.000000 0.000000
## [5,] 0.00000 0.0000000 0.0000000 0.000000 1.188145 0.0000000 0.000000 0.000000
## [6,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.8562567 0.000000 0.000000
## [7,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 1.134644 0.000000
## [8,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 1.243655
## [9,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [10,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [11,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [12,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [13,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [14,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [15,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [16,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [17,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [18,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [19,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [20,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [,9] [,10] [,11] [,12] [,13] [,14] [,15]
## [1,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [2,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [3,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [4,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [5,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [6,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [7,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [8,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [9,] 1.269424 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [10,] 0.000000 0.7438867 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [11,] 0.000000 0.0000000 1.152805 0.0000000 0.0000000 0.000000 0.0000000
## [12,] 0.000000 0.0000000 0.000000 0.8716004 0.0000000 0.000000 0.0000000
## [13,] 0.000000 0.0000000 0.000000 0.0000000 0.7600321 0.000000 0.0000000
## [14,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 1.272441 0.0000000
## [15,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.9493643
## [16,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [17,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [18,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [19,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [20,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [2,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [3,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [4,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [5,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [6,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [7,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [8,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [9,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [10,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [11,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [12,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [13,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [14,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [15,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [16,] 0.9730615 0.000000 0.000000 0.000000 0.000000
## [17,] 0.0000000 1.282633 0.000000 0.000000 0.000000
## [18,] 0.0000000 0.000000 1.050393 0.000000 0.000000
## [19,] 0.0000000 0.000000 0.000000 1.277323 0.000000
## [20,] 0.0000000 0.000000 0.000000 0.000000 1.157021
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] NA
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 14
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000004440892N= 4
models(n = N, t = 200, rho_1_mod = runif(N, min = 0.7, max = 1.3), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1.0514802 0.7053675 0.8762438 0.8664250
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1 const
## y1 "1.0514801830" "0.0000000001" "0.0000000000" "0.0000000000" "0.0000000000"
## y2 "0.0000000000" "0.7053674774" "0.0000000000" "0.0000000000" "0.0000000000"
## y3 "0.0000000000" "0.0000000000" "0.8762437672" "0.0000000000" "0.0000000000"
## y4 "0.0000000000" "0.0000000000" "0.0000000000" "0.8664249748" "0.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4]
## [1,] 0 0 1 0
## [2,] 0 0 0 0
## [3,] 1 0 0 1
## [4,] 0 0 1 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] 0.000002791174
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 4
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4]
## [1,] 1.05148 0.0000000 0.0000000 0.000000
## [2,] 0.00000 0.7053675 0.0000000 0.000000
## [3,] 0.00000 0.0000000 0.8762438 0.000000
## [4,] 0.00000 0.0000000 0.0000000 0.866425
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.00000000007395807
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 4
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000000008881784N= 10
models(n = N, t = 200, rho_1_mod = runif(N, min = 0.7, max = 1.3), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1.0514802 0.7053675 0.8762438 0.8664250 1.1881445 0.8562567 1.1346435
## [8] 1.2436553 1.2694241 0.7438867
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1
## y1 " 1.0514801830" " 0.0000000000" " -0.0000000198"
## y2 " 0.0000000000" " 0.7053674774" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.8762437672"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 0.0000151953" " 4.2134533573" " -2327.6850118228"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000009" " 0.0005476199" " -0.2486145344"
## y8 " 0.0332876859" " 4404.0866970078" " -3245594.0082232598"
## y9 " 1.3226735968" " 3557760.2722401517" "-1442087821.2186827660"
## y10 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y4.l1 y5.l1 y6.l1
## y1 " -0.0000000014" " 0.0000000000" " 0.0000000114"
## y2 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y4 " 0.8664249748" " 0.0000000000" " 0.0000000000"
## y5 " -157.5056258565" " 1.1881445290" " 1317.7553498580"
## y6 " 0.0000000000" " 0.0000000000" " 0.8562566628"
## y7 " -0.0170006757" " 0.0000000000" " 0.1439219404"
## y8 " -220904.4396405059" " 0.0000000000" " 1845326.1780071820"
## y9 " -98955024.4346910119" " -0.0000000033" " 842472262.7816085815"
## y10 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7.l1 y8.l1 y9.l1
## y1 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7 " 1.1346435356" " 0.0000000000" " 0.0000000000"
## y8 " 0.0000001558" " 1.2436552908" " 0.0000000000"
## y9 " -0.0000018074" " 0.0000000000" " 1.2694241326"
## y10 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y10.l1 const
## y1 " -0.0000000006" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000"
## y5 " -56.4524790369" " -0.0026421150"
## y6 " 0.0000000000" " 0.0000000000"
## y7 " -0.0070788203" " -0.0000002209"
## y8 " -63984.0204720040" " -5.4263063720"
## y9 " -45215219.7065182179" " -1292.6797517939"
## y10 " 0.7438866816" " 0.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 1 0 0 0 0 0 1
## [2,] 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0
## [10,] 1 0 0 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -6.400046e-38
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 4
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1.05148 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [2,] 0.00000 0.7053675 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [3,] 0.00000 0.0000000 0.8762438 0.000000 0.000000 0.0000000 0.000000 0.000000
## [4,] 0.00000 0.0000000 0.0000000 0.866425 0.000000 0.0000000 0.000000 0.000000
## [5,] 0.00000 0.0000000 0.0000000 0.000000 1.188145 0.0000000 0.000000 0.000000
## [6,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.8562567 0.000000 0.000000
## [7,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 1.134644 0.000000
## [8,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 1.243655
## [9,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [10,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [,9] [,10]
## [1,] 0.000000 0.0000000
## [2,] 0.000000 0.0000000
## [3,] 0.000000 0.0000000
## [4,] 0.000000 0.0000000
## [5,] 0.000000 0.0000000
## [6,] 0.000000 0.0000000
## [7,] 0.000000 0.0000000
## [8,] 0.000000 0.0000000
## [9,] 1.269424 0.0000000
## [10,] 0.000000 0.7438867
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 1673690521
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 20
models(n = N, t = 200, rho_1_mod = runif(N, min = 0.7, max = 1.3), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1.0514802 0.7053675 0.8762438 0.8664250 1.1881445 0.8562567 1.1346435
## [8] 1.2436553 1.2694241 0.7438867 1.1528050 0.8716004 0.7600321 1.2724413
## [15] 0.9493643 0.9730615 1.2826334 1.0503928 1.2773228 1.1570214
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1
## y1 " 1.0514801830" " -0.0000000010"
## y2 " 0.0000000000" " 0.7053674774"
## y3 " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000"
## y5 " 0.0539411273" " 29.9338059580"
## y6 " 0.0000000000" " 0.0000000000"
## y7 " -0.0000072122" " 0.0141926962"
## y8 " 689.9036530900" " -3671561.5319563560"
## y9 " -40038.4323610581" " 63433661.2504457831"
## y10 " 0.0000000000" " 0.0000000000"
## y11 " -0.0012199255" " 1.6481616175"
## y12 " 0.0000000000" " 0.0000000000"
## y13 " 0.0000000000" " 0.0000000000"
## y14 " 187858.0619732596" " -167115167.6761173606"
## y15 " 0.0000000000" " 0.0000000000"
## y16 " 0.0000000000" " 0.0000000000"
## y17 " -140973.6671288183" " 57100455.2706128359"
## y18 " 0.0000000000" " 0.0000000068"
## y19 " 2974229742862.1552734375" " -700703840456902.6250000000"
## y20 " -4030784.0066985041" " 691124352.7919223309"
## y3.l1 y4.l1
## y1 " 0.0000001487" " 0.0000001761"
## y2 " 0.0000000004" " 0.0000000004"
## y3 " 0.8762437673" " 0.0000000002"
## y4 " 0.0000000000" " 0.8664249748"
## y5 " -2999.2865685694" " -4247.4887768048"
## y6 " 0.0000000002" " 0.0000000002"
## y7 " -3.4357998275" " -3.8392410182"
## y8 " 751109168.4132566452" " 854704290.7048753500"
## y9 " -18112741087.9586791992" " -20147440394.8672943115"
## y10 " -0.0000000001" " -0.0000000001"
## y11 " -444.9593079765" " -491.8221435086"
## y12 " -0.0000000002" " -0.0000000003"
## y13 " 0.0000000003" " 0.0000000003"
## y14 " 39006039738.8216781616" " 42465645891.4452133179"
## y15 " 0.0000000009" " 0.0000000010"
## y16 " -0.0000000005" " -0.0000000005"
## y17 " -27265213995.1195259094" " -29011471650.3495903015"
## y18 " -0.0000015302" " -0.0000017193"
## y19 " 393924872427499072.0000000000" " 414608918154778240.0000000000"
## y20 " -402263236714.8742065430" " -421808534105.9307861328"
## y5.l1 y6.l1
## y1 " 0.0000000000" " -0.0000001477"
## y2 " 0.0000000000" " -0.0000000003"
## y3 " 0.0000000000" " -0.0000000001"
## y4 " 0.0000000000" " 0.0000000000"
## y5 " 1.1881445289" " 4040.1532632518"
## y6 " 0.0000000000" " 0.8562566627"
## y7 " 0.0000000000" " 3.0545393173"
## y8 " -0.0000000540" " -691719849.5741842985"
## y9 " 0.0000082481" " 15944061244.4001750946"
## y10 " 0.0000000000" " 0.0000000000"
## y11 " 0.0000000000" " 387.1863700993"
## y12 " 0.0000000000" " 0.0000000002"
## y13 " 0.0000000000" " -0.0000000003"
## y14 " -0.0000368894" " -33038464900.2295989990"
## y15 " 0.0000000000" " -0.0000000008"
## y16 " 0.0000000000" " 0.0000000004"
## y17 " 0.0000280234" " 21972821341.7416877747"
## y18 " 0.0000000000" " 0.0000013751"
## y19 " -1625.5124708593" "-310582667248153152.0000000000"
## y20 " -0.0028489172" " 314877333358.3458251953"
## y7.l1 y8.l1
## y1 " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000"
## y5 " 0.0000000946" " 0.0000000000"
## y6 " 0.0000000000" " 0.0000000000"
## y7 " 1.1346435356" " 0.0000000000"
## y8 " 0.0005053998" " 1.2436552908"
## y9 " -0.0557972040" " -0.0000000059"
## y10 " 0.0000000000" " 0.0000000000"
## y11 " -0.0000000016" " 0.0000000000"
## y12 " 0.0000000000" " 0.0000000000"
## y13 " 0.0000000000" " 0.0000000000"
## y14 " 0.2671533804" " 0.0000000242"
## y15 " 0.0000000000" " 0.0000000000"
## y16 " 0.0000000000" " 0.0000000000"
## y17 " -0.2010186546" " -0.0000000186"
## y18 " 0.0000000000" " 0.0000000000"
## y19 " 6941913.1105783265" " 3.0218975297"
## y20 " -27.3155676377" " 0.0000007139"
## y9.l1 y10.l1
## y1 " 0.0000000000" " -0.0000000108"
## y2 " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000"
## y5 " 0.0000000000" " 366.3923023856"
## y6 " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" " 0.1605605938"
## y8 " 0.0000000000" " -40726249.0706237480"
## y9 " 1.2694241296" " 758028707.6864562035"
## y10 " 0.0000000000" " 0.7438866816"
## y11 " 0.0000000000" " 18.8683484602"
## y12 " 0.0000000000" " 0.0000000000"
## y13 " 0.0000000000" " 0.0000000000"
## y14 " 0.0000000122" " -1748517915.5580444336"
## y15 " 0.0000000000" " 0.0000000000"
## y16 " 0.0000000000" " 0.0000000000"
## y17 " -0.0000000094" " 731989927.5334995985"
## y18 " 0.0000000000" " 0.0000000759"
## y19 " 6.6813996426" " -9290264979934704.0000000000"
## y20 " 0.0000002848" " 9203424319.7239723206"
## y11.l1 y12.l1
## y1 " 0.0000000000" " 0.0000017331"
## y2 " 0.0000000000" " 0.0000000040"
## y3 " 0.0000000000" " 0.0000000016"
## y4 " 0.0000000000" " 0.0000000004"
## y5 " 0.0000000019" " -38395.1522564100"
## y6 " 0.0000000000" " 0.0000000019"
## y7 " 0.0000000000" " -38.9244089288"
## y8 " 0.0000091321" " 8584734830.4675292969"
## y9 " -0.0011366648" " -204773312108.3698120117"
## y10 " 0.0000000000" " -0.0000000006"
## y11 " 1.1528050162" " -5014.6479150344"
## y12 " 0.0000000000" " 0.8716003699"
## y13 " 0.0000000000" " 0.0000000035"
## y14 " 0.0053341665" " 436253267414.2767333984"
## y15 " 0.0000000000" " 0.0000000102"
## y16 " 0.0000000000" " -0.0000000054"
## y17 " -0.0040254445" " -301769892562.2742919922"
## y18 " 0.0000000000" " -0.0000173822"
## y19 " 161743.8365609449" "4337354834763972608.0000000000"
## y20 " -2.9376209475" " -4421144194683.5146484375"
## y13.l1 y14.l1
## y1 " -0.0000000054" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000"
## y5 " 191.4855526019" " 0.0000000000"
## y6 " 0.0000000000" " 0.0000000000"
## y7 " 0.0837530591" " 0.0000000000"
## y8 " -21024597.2606685683" " 0.0000000000"
## y9 " 403181474.7345322967" " 0.0000000006"
## y10 " 0.0000000000" " 0.0000000000"
## y11 " 9.9099422468" " 0.0000000000"
## y12 " 0.0000000000" " 0.0000000000"
## y13 " 0.7600321129" " 0.0000000000"
## y14 " -890615981.4110767841" " 1.2724412627"
## y15 " 0.0000000000" " 0.0000000000"
## y16 " 0.0000000000" " 0.0000000000"
## y17 " 404093951.1801404953" " 0.0000000018"
## y18 " 0.0000000393" " 0.0000000000"
## y19 " -5202763087910703.0000000000" " -2.0403024207"
## y20 " 5165465416.0205535889" " -0.0000000523"
## y15.l1 y16.l1
## y1 " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000"
## y5 " -2.2904053337" " 0.8685549352"
## y6 " 0.0000000000" " 0.0000000000"
## y7 " 0.0012991128" " -0.0002905402"
## y8 " -230174.9659279929" " 46155.5826872014"
## y9 " 6975189.6778228385" " -1562703.3754202358"
## y10 " 0.0000000000" " 0.0000000000"
## y11 " 0.1869094970" " -0.0435838816"
## y12 " 0.0000000000" " 0.0000000000"
## y13 " 0.0000000000" " 0.0000000000"
## y14 " -20296979.2675143071" " 5203506.8317334168"
## y15 " 0.9493642711" " 0.0000000000"
## y16 " 0.0000000000" " 0.9730614506"
## y17 " 15448910.0249528177" " -3966451.6986929476"
## y18 " 0.0000000005" " -0.0000000001"
## y19 " -246057642690275.3125000000" " 65958656129397.3281250000"
## y20 " 263263377.9444451630" " -72562566.7690811604"
## y17.l1 y18.l1
## y1 " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000"
## y5 " 0.0000000000" " 0.0251659025"
## y6 " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" " -0.0000033899"
## y8 " 0.0000000000" " 326.9246817526"
## y9 " 0.0000000003" " -18800.4478220411"
## y10 " 0.0000000000" " 0.0000000000"
## y11 " 0.0000000000" " -0.0005727275"
## y12 " 0.0000000000" " 0.0000000000"
## y13 " 0.0000000000" " 0.0000000000"
## y14 " -0.0000000011" " 88021.6924969080"
## y15 " 0.0000000000" " 0.0000000000"
## y16 " 0.0000000000" " 0.0000000000"
## y17 " 1.2826333944" " -66035.9838893709"
## y18 " 0.0000000000" " 1.0503927878"
## y19 " 0.9291344104" " 1386810342839.1035156250"
## y20 " -0.0000000238" " -1870170.1717281211"
## y19.l1 y20.l1
## y1 " NA" " NA"
## y2 " NA" " NA"
## y3 " NA" " NA"
## y4 " NA" " NA"
## y5 " NA" " NA"
## y6 " NA" " NA"
## y7 " NA" " NA"
## y8 " NA" " NA"
## y9 " NA" " NA"
## y10 " NA" " NA"
## y11 " NA" " NA"
## y12 " NA" " NA"
## y13 " NA" " NA"
## y14 " NA" " NA"
## y15 " NA" " NA"
## y16 " NA" " NA"
## y17 " NA" " NA"
## y18 " NA" " NA"
## y19 " NA" " NA"
## y20 " NA" " NA"
## const
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 0.0787861350"
## y6 " 0.0000000000"
## y7 " -0.0000173182"
## y8 " 2357.9498108204"
## y9 " -93447.8167759453"
## y10 " 0.0000000000"
## y11 " -0.0027245732"
## y12 " 0.0000000000"
## y13 " 0.0000000000"
## y14 " 361476.4628023938"
## y15 " 0.0000000000"
## y16 " 0.0000000000"
## y17 " -274042.1209903131"
## y18 " 0.0000000000"
## y19 " 4848662348981.1250000000"
## y20 " -5585192.4500918044"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 1 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 1 0 0 0 1 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 1 1 0 0 0 1 0 0 0 0 0
## [8,] 0 0 0 0 0 0 1 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [10,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [11,] 0 0 0 1 0 0 0 0 0 0 0 0 0
## [12,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [13,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [14,] 0 0 0 0 0 1 0 0 0 0 0 0 0
## [15,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [16,] 0 0 0 0 1 0 0 1 0 0 0 0 0
## [17,] 0 0 1 0 0 0 0 0 0 0 0 0 0
## [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [19,] 0 0 0 0 0 0 0 0 0 0 0 1 0
## [20,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [,14] [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0
## [3,] 0 0 0 1 0 0 0
## [4,] 0 0 0 0 0 0 0
## [5,] 0 0 1 0 0 0 0
## [6,] 1 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0
## [8,] 0 0 1 0 0 0 0
## [9,] 0 0 0 0 0 0 0
## [10,] 0 0 0 0 0 0 0
## [11,] 0 0 0 0 0 0 0
## [12,] 0 0 0 0 0 1 0
## [13,] 0 0 0 0 0 0 0
## [14,] 0 0 0 0 1 0 0
## [15,] 0 0 0 0 0 0 0
## [16,] 0 0 0 0 0 0 0
## [17,] 0 0 0 0 0 0 0
## [18,] 1 0 0 0 0 0 0
## [19,] 0 0 0 0 0 0 0
## [20,] 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -5.230822e-144
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 7
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1.05148 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [2,] 0.00000 0.7053675 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [3,] 0.00000 0.0000000 0.8762438 0.000000 0.000000 0.0000000 0.000000 0.000000
## [4,] 0.00000 0.0000000 0.0000000 0.866425 0.000000 0.0000000 0.000000 0.000000
## [5,] 0.00000 0.0000000 0.0000000 0.000000 1.188145 0.0000000 0.000000 0.000000
## [6,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.8562567 0.000000 0.000000
## [7,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 1.134644 0.000000
## [8,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 1.243655
## [9,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [10,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [11,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [12,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [13,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [14,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [15,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [16,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [17,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [18,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [19,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [20,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [,9] [,10] [,11] [,12] [,13] [,14] [,15]
## [1,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [2,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [3,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [4,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [5,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [6,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [7,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [8,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [9,] 1.269424 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [10,] 0.000000 0.7438867 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [11,] 0.000000 0.0000000 1.152805 0.0000000 0.0000000 0.000000 0.0000000
## [12,] 0.000000 0.0000000 0.000000 0.8716004 0.0000000 0.000000 0.0000000
## [13,] 0.000000 0.0000000 0.000000 0.0000000 0.7600321 0.000000 0.0000000
## [14,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 1.272441 0.0000000
## [15,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.9493643
## [16,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [17,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [18,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [19,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [20,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [2,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [3,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [4,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [5,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [6,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [7,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [8,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [9,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [10,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [11,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [12,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [13,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [14,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [15,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [16,] 0.9730615 0.000000 0.000000 0.000000 0.000000
## [17,] 0.0000000 1.282633 0.000000 0.000000 0.000000
## [18,] 0.0000000 0.000000 1.050393 0.000000 0.000000
## [19,] 0.0000000 0.000000 0.000000 1.277323 0.000000
## [20,] 0.0000000 0.000000 0.000000 0.000000 1.157021
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] NA
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 14
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000004440892N= 4
models(n = N, t = 500, rho_1_mod = runif(N, min = 0.7, max = 1.3), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1.0514802 0.7053675 0.8762438 0.8664250
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1
## y1 " 1.0514801830" "-0.0004392230" " 0.0001886323" "-0.0002358242"
## y2 " 0.0000000000" " 0.7053674774" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.8762437672" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.8664249748"
## const
## y1 "-0.0000000587"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4]
## [1,] 0 0 1 0
## [2,] 0 0 0 0
## [3,] 1 0 0 1
## [4,] 0 0 1 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] 0.000002791174
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 3
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4]
## [1,] 1.05148 0.0000000 0.0000000 0.000000
## [2,] 0.00000 0.7053675 0.0000000 0.000000
## [3,] 0.00000 0.0000000 0.8762438 0.000000
## [4,] 0.00000 0.0000000 0.0000000 0.866425
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.0005330217
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 4
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000000008881784N= 10
models(n = N, t = 500, rho_1_mod = runif(N, min = 0.7, max = 1.3), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1.0514802 0.7053675 0.8762438 0.8664250 1.1881445 0.8562567 1.1346435
## [8] 1.2436553 1.2694241 0.7438867
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1
## y1 " 1.0514801830"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " -108436586830.1173553467"
## y6 " 0.0000000000"
## y7 " 2.7325772423"
## y8 " 71039063999899721728.0000000000"
## y9 " -8829866681999639537778688.0000000000"
## y10 " 0.0000000000"
## y2.l1
## y1 " 0.0003875307"
## y2 " 0.7053674774"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 15471488322067631177728.0000000000"
## y6 " 0.0000000000"
## y7 " 5810967014419.7792968750"
## y8 " 21930145070286982606182223446016.0000000000"
## y9 " -29738391978175022318941048129997242368.0000000000"
## y10 " 0.0000000000"
## y3.l1
## y1 " -0.1619462745"
## y2 " 0.0000000000"
## y3 " 0.8762437672"
## y4 " 0.0000000000"
## y5 " 5111879270764550515851264.0000000000"
## y6 " 0.0000000000"
## y7 " -4043682859175648.5000000000"
## y8 " -35777703532454121754322972235005952.0000000000"
## y9 "12263599597696199423170387108717402259456.0000000000"
## y10 " 0.0000000000"
## y4.l1
## y1 " -0.0111879205"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.8664249748"
## y5 " 280583840425230500626432.0000000000"
## y6 " 0.0000000000"
## y7 " -269257993058124.8750000000"
## y8 " -2085826345782466872841728530841600.0000000000"
## y9 " 828969131360032715253956827985205002240.0000000000"
## y10 " 0.0000000000"
## y5.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 1.1881445290"
## y6 " 0.0000000000"
## y7 " 0.0000000000"
## y8 " 0.0000047062"
## y9 " -7.4717657366"
## y10 " 0.0000000000"
## y6.l1
## y1 " 0.0956006903"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " -1801821227396129609482240.0000000000"
## y6 " 0.8562566628"
## y7 " 2217184033652228.2500000000"
## y8 " 15048283255302659784148129159315456.0000000000"
## y9 "-6977545075255403194485240168484674994176.0000000000"
## y10 " 0.0000000000"
## y7.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 0.0000112289"
## y6 " 0.0000000000"
## y7 " 1.1346435356"
## y8 " 5377.5361935749"
## y9 " -21520608759.0844345093"
## y10 " 0.0000000000"
## y8.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 0.0000000000"
## y6 " 0.0000000000"
## y7 " 0.0000000000"
## y8 " 1.2436552908"
## y9 " 0.0000000058"
## y10 " 0.0000000000"
## y9.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 0.0000000000"
## y6 " 0.0000000000"
## y7 " 0.0000000000"
## y8 " 0.0000000000"
## y9 " 1.2694241326"
## y10 " 0.0000000000"
## y10.l1
## y1 " -0.0049601641"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " -150074927312740217257984.0000000000"
## y6 " 0.0000000000"
## y7 " -81953469045891.4531250000"
## y8 " -245540596210916276529343259213824.0000000000"
## y9 " 370821435083439850332621483050518183936.0000000000"
## y10 " 0.7438866816"
## const
## y1 " -0.0000000263"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " -48192825616141912.0000000000"
## y6 " 0.0000000000"
## y7 " -476336466.5883103609"
## y8 " -1845781392480999117699416064.0000000000"
## y9 " 3251722623033570392399893294481408.0000000000"
## y10 " 0.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 1 0 0 0 0 0 1
## [2,] 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0
## [10,] 1 0 0 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -6.400046e-38
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 2
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1.05148 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [2,] 0.00000 0.7053675 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [3,] 0.00000 0.0000000 0.8762438 0.000000 0.000000 0.0000000 0.000000 0.000000
## [4,] 0.00000 0.0000000 0.0000000 0.866425 0.000000 0.0000000 0.000000 0.000000
## [5,] 0.00000 0.0000000 0.0000000 0.000000 1.188145 0.0000000 0.000000 0.000000
## [6,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.8562567 0.000000 0.000000
## [7,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 1.134644 0.000000
## [8,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 1.243655
## [9,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [10,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [,9] [,10]
## [1,] 0.000000 0.0000000
## [2,] 0.000000 0.0000000
## [3,] 0.000000 0.0000000
## [4,] 0.000000 0.0000000
## [5,] 0.000000 0.0000000
## [6,] 0.000000 0.0000000
## [7,] 0.000000 0.0000000
## [8,] 0.000000 0.0000000
## [9,] 1.269424 0.0000000
## [10,] 0.000000 0.7438867
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 1.413887e+40
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 20
models(n = N, t = 500, rho_1_mod = runif(N, min = 0.7, max = 1.3), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1.0514802 0.7053675 0.8762438 0.8664250 1.1881445 0.8562567 1.1346435
## [8] 1.2436553 1.2694241 0.7438867 1.1528050 0.8716004 0.7600321 1.2724413
## [15] 0.9493643 0.9730615 1.2826334 1.0503928 1.2773228 1.1570214
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1
## y1 " 1.0514801830"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 59724700593558.9453125000"
## y6 " 0.0000000000"
## y7 " -698.0429785778"
## y8 " 257526916889581908393984.0000000000"
## y9 " 1255650211512541285909004288.0000000000"
## y10 " 0.0000000000"
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## y13 " 0.0000000000"
## y14 " 28503898540588233649658265600.0000000000"
## y15 " 0.0000000000"
## y16 " 0.0000000000"
## y17 " 28318941056417307031284744192.0000000000"
## y18 " 0.0000000000"
## y19 " 7926154054220671697796336298458349568.0000000000"
## y20 " -2272470689628110848.0000000000"
## y2.l1
## y1 " -0.0052001081"
## y2 " 0.7053674774"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " -11941945142787868610002944.0000000000"
## y6 " 0.0000000000"
## y7 " 164409671835566.7812500000"
## y8 " -30395531536839062581080375227842560.0000000000"
## y9 " -383630893402779910673993632974905540608.0000000000"
## y10 " 0.0000000000"
## y11 " -662144314370602624.0000000000"
## y12 " 0.0000000000"
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## y15 " 0.0000000000"
## y16 " 0.0000000000"
## y17 " -13964944756894564486464208004639398821888.0000000000"
## y18 " -0.0009554549"
## y19 " -7652007928730710660133885113805035459594682368.0000000000"
## y20 " 1834677029421227839024267264.0000000000"
## y3.l1
## y1 " 0.4544648914"
## y2 " -0.0000000001"
## y3 " 0.8762437671"
## y4 " 0.0000000000"
## y5 " 1229523908932586514975555584.0000000000"
## y6 " -0.0000000001"
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## y8 " 3231401394921746213498292216294014976.0000000000"
## y9 " 30770196049554263517213095192823697768448.0000000000"
## y10 " -0.0000000001"
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## y18 " 0.0856398722"
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## y20 " -477884719792664034008631345152.0000000000"
## y4.l1
## y1 " 0.5679357160"
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## y4 " 0.8664249748"
## y5 " 1523486075526976975927246848.0000000000"
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## y8 " 3999621971776444696468386024408481792.0000000000"
## y9 " 38487182207771653032027052504744139423744.0000000000"
## y10 " -0.0000000001"
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## y12 " 0.0000000000"
## y13 " -0.0000000003"
## y14 " -166165149842716238056391265047678495490048.0000000000"
## y15 " -0.0000000008"
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## y17 " 1660570819346211674528046737086821833900032.0000000000"
## y18 " 0.1059834891"
## y19 " 2279188131614848480999090597566813210807755603968.0000000000"
## y20 " -546586833042771870166936453120.0000000000"
## y5.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 1.1881445290"
## y6 " 0.0000000000"
## y7 " 0.0000000000"
## y8 " -0.0299151908"
## y9 " -58.0418021810"
## y10 " 0.0000000000"
## y11 " 0.0000000000"
## y12 " 0.0000000000"
## y13 " 0.0000000000"
## y14 " -3392.6212788664"
## y15 " 0.0000000000"
## y16 " 0.0000000000"
## y17 " -8330.4298437573"
## y18 " 0.0000000000"
## y19 " -3138643755269.7690429688"
## y20 " -0.0000012033"
## y6.l1
## y1 " -0.5009391361"
## y2 " 0.0000000001"
## y3 " 0.0000000001"
## y4 " 0.0000000000"
## y5 " -1332491191976595893270872064.0000000000"
## y6 " 0.8562566629"
## y7 " 17960410696945640.0000000000"
## y8 " -3494147156302641074713264390462767104.0000000000"
## y9 " -34011776950706042509016237176873730179072.0000000000"
## y10 " 0.0000000001"
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## y20 " 442370492815901222586890059776.0000000000"
## y7.l1
## y1 " 0.0000000000"
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## y4 " 0.0000000000"
## y5 " 0.0285029017"
## y6 " 0.0000000000"
## y7 " 1.1346435356"
## y8 " 171917245.0252449512"
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## y10 " 0.0000000000"
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## y19 " 9343556350078345019392.0000000000"
## y20 " -7972.7466982115"
## y8.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
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## y4 " 0.0000000000"
## y5 " 0.0000000000"
## y6 " 0.0000000000"
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## y8 " 1.2436552908"
## y9 " 0.0000000492"
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## y18 " 0.0000000000"
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## y9.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
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## y6 " 0.0000000000"
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## y10.l1
## y1 " -0.0515084277"
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## y3 " 0.0000000000"
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## y7 " 1674436418802222.2500000000"
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## y11.l1
## y1 " 0.0000000000"
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## y12.l1
## y1 " 5.4372796116"
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## y1 " -0.0251834822"
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## y1 " 0.0000000000"
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## y9 " 778185826479244050448777216.0000000000"
## y10 " 0.0000000000"
## y11 " -11634752.5412673503"
## y12 " 0.0000000000"
## y13 " 0.0000000000"
## y14 " 17276853823134635083232706560.0000000000"
## y15 " 0.0000000000"
## y16 " 0.0000000000"
## y17 " 17441987655353764634865696768.0000000000"
## y18 " 1.0503927878"
## y19 " 4864922207514947034389604411407073280.0000000000"
## y20 " -1387274056568784896.0000000000"
## y19.l1
## y1 " NA"
## y2 " NA"
## y3 " NA"
## y4 " NA"
## y5 " NA"
## y6 " NA"
## y7 " NA"
## y8 " NA"
## y9 " NA"
## y10 " NA"
## y11 " NA"
## y12 " NA"
## y13 " NA"
## y14 " NA"
## y15 " NA"
## y16 " NA"
## y17 " NA"
## y18 " NA"
## y19 " NA"
## y20 " NA"
## y20.l1
## y1 " NA"
## y2 " NA"
## y3 " NA"
## y4 " NA"
## y5 " NA"
## y6 " NA"
## y7 " NA"
## y8 " NA"
## y9 " NA"
## y10 " NA"
## y11 " NA"
## y12 " NA"
## y13 " NA"
## y14 " NA"
## y15 " NA"
## y16 " NA"
## y17 " NA"
## y18 " NA"
## y19 " NA"
## y20 " NA"
## const
## y1 " -0.0000000015"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 29556671958035570688.0000000000"
## y6 " 0.0000000000"
## y7 " -370602454.0192456841"
## y8 " 85110933371012531322311671808.0000000000"
## y9 " 687725620926420266763396864540672.0000000000"
## y10 " 0.0000000000"
## y11 " -1704089926392.2729492188"
## y12 " 0.0000000000"
## y13 " 0.0000000000"
## y14 " 1808909813408217445787146360193024.0000000000"
## y15 " 0.0000000000"
## y16 " 0.0000000000"
## y17 " 27204695953271586407467588813586432.0000000000"
## y18 " 0.0000000060"
## y19 " 893497244744640683424119439430413103136768.0000000000"
## y20 " -214737802605376537886720.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 1 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 1 0 0 0 1 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 1 1 0 0 0 1 0 0 0 0 0
## [8,] 0 0 0 0 0 0 1 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [10,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [11,] 0 0 0 1 0 0 0 0 0 0 0 0 0
## [12,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [13,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [14,] 0 0 0 0 0 1 0 0 0 0 0 0 0
## [15,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [16,] 0 0 0 0 1 0 0 1 0 0 0 0 0
## [17,] 0 0 1 0 0 0 0 0 0 0 0 0 0
## [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [19,] 0 0 0 0 0 0 0 0 0 0 0 1 0
## [20,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [,14] [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0
## [3,] 0 0 0 1 0 0 0
## [4,] 0 0 0 0 0 0 0
## [5,] 0 0 1 0 0 0 0
## [6,] 1 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0
## [8,] 0 0 1 0 0 0 0
## [9,] 0 0 0 0 0 0 0
## [10,] 0 0 0 0 0 0 0
## [11,] 0 0 0 0 0 0 0
## [12,] 0 0 0 0 0 1 0
## [13,] 0 0 0 0 0 0 0
## [14,] 0 0 0 0 1 0 0
## [15,] 0 0 0 0 0 0 0
## [16,] 0 0 0 0 0 0 0
## [17,] 0 0 0 0 0 0 0
## [18,] 1 0 0 0 0 0 0
## [19,] 0 0 0 0 0 0 0
## [20,] 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -5.230822e-144
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 5
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1.05148 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [2,] 0.00000 0.7053675 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [3,] 0.00000 0.0000000 0.8762438 0.000000 0.000000 0.0000000 0.000000 0.000000
## [4,] 0.00000 0.0000000 0.0000000 0.866425 0.000000 0.0000000 0.000000 0.000000
## [5,] 0.00000 0.0000000 0.0000000 0.000000 1.188145 0.0000000 0.000000 0.000000
## [6,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.8562567 0.000000 0.000000
## [7,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 1.134644 0.000000
## [8,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 1.243655
## [9,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [10,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [11,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [12,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [13,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [14,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [15,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [16,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [17,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [18,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [19,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [20,] 0.00000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 0.000000
## [,9] [,10] [,11] [,12] [,13] [,14] [,15]
## [1,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [2,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [3,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [4,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [5,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [6,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [7,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [8,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [9,] 1.269424 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [10,] 0.000000 0.7438867 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [11,] 0.000000 0.0000000 1.152805 0.0000000 0.0000000 0.000000 0.0000000
## [12,] 0.000000 0.0000000 0.000000 0.8716004 0.0000000 0.000000 0.0000000
## [13,] 0.000000 0.0000000 0.000000 0.0000000 0.7600321 0.000000 0.0000000
## [14,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 1.272441 0.0000000
## [15,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.9493643
## [16,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [17,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [18,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [19,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [20,] 0.000000 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [2,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [3,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [4,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [5,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [6,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [7,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [8,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [9,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [10,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [11,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [12,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [13,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [14,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [15,] 0.0000000 0.000000 0.000000 0.000000 0.000000
## [16,] 0.9730615 0.000000 0.000000 0.000000 0.000000
## [17,] 0.0000000 1.282633 0.000000 0.000000 0.000000
## [18,] 0.0000000 0.000000 1.050393 0.000000 0.000000
## [19,] 0.0000000 0.000000 0.000000 1.277323 0.000000
## [20,] 0.0000000 0.000000 0.000000 0.000000 1.157021
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] NA
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 14
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000004440892N= 10
models(n = N, t = 200, rho_1_mod = rnorm(N), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.2167549 -0.5424926 0.8911446 0.5959806 1.6356180 0.6892754
## [7] -1.2812466 -0.2131445 1.8965399 1.7768632
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1
## y1 " 0.2167548629"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 52090691184594864232105771008.0000000000"
## y6 " 0.0000000000"
## y7 " -57868829.2439193800"
## y8 " 0.0000000000"
## y9 "-209509289916912990380013572376564493975552.0000000000"
## y10 " 20415928087424940511166856335196160.0000000000"
## y2.l1
## y1 " 0.0000000000"
## y2 " -0.5424925723"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " -2179653135687758990656143360.0000000000"
## y6 " 0.0000000000"
## y7 " 3720202.4423230421"
## y8 " 0.0000000000"
## y9 " 8424930645185007303266506344445964713984.0000000000"
## y10 " -838118338384191354250041451610112.0000000000"
## y3.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.8911446451"
## y4 " 0.0000000000"
## y5 " 1383488116882607837911449600.0000000000"
## y6 " 0.0000000000"
## y7 " -557569.2746317915"
## y8 " 0.0000000000"
## y9 " -5845293226255972834796162134308294754304.0000000000"
## y10 " 624840318603053315983938204729344.0000000000"
## y4.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.5959805772"
## y5 " -28210009948868703434760519680.0000000000"
## y6 " 0.0000000000"
## y7 " 20919791.1795130335"
## y8 " 0.0000000000"
## y9 " 116256587173254309673169580451685162024960.0000000000"
## y10 " -11351635376572205567799151206334464.0000000000"
## y5.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 1.6356180011"
## y6 " 0.0000000000"
## y7 " 0.0000000000"
## y8 " 0.0000000000"
## y9 " -0.0416595677"
## y10 " 0.0000000288"
## y6.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " -124314480066755683026984763392.0000000000"
## y6 " 0.6892754419"
## y7 " 79683203.5296093225"
## y8 " 0.0000000000"
## y9 " 515792222531130894611505307800599282057216.0000000000"
## y10 " -50751274983828468998694978503835648.0000000000"
## y7.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " -14648.7134717767"
## y6 " 0.0000000000"
## y7 " -1.2812466301"
## y8 " 0.0000000000"
## y9 " 163605112991310624.0000000000"
## y10 " -682948637185.5759277344"
## y8.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " -12106033500785033004934234112.0000000000"
## y6 " 0.0000000000"
## y7 " 17774351.9524617493"
## y8 " -0.2131445193"
## y9 " 47550523232801240628745575740395648712704.0000000000"
## y10 " -4684241823794522267923110204276736.0000000000"
## y9.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 0.0000000000"
## y6 " 0.0000000000"
## y7 " 0.0000000000"
## y8 " 0.0000000000"
## y9 " 1.8965398719"
## y10 " 0.0000000000"
## y10.l1
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " 0.0000000000"
## y6 " 0.0000000000"
## y7 " 0.0000000000"
## y8 " 0.0000000000"
## y9 " 0.0000000108"
## y10 " 1.7768632137"
## const
## y1 " 0.0000000000"
## y2 " 0.0000000000"
## y3 " 0.0000000000"
## y4 " 0.0000000000"
## y5 " -5673980495028419559424000.0000000000"
## y6 " 0.0000000000"
## y7 " -991.3485006825"
## y8 " 0.0000000000"
## y9 " 28943444569727973322993985893789859840.0000000000"
## y10 " -15046615060585939698218671538176.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 0 0 1 0 0 1 1
## [2,] 0 0 0 0 0 1 1 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0 1
## [5,] 0 0 0 0 0 0 0 0 0 1
## [6,] 1 1 0 0 0 0 0 0 0 0
## [7,] 0 1 0 0 0 0 0 1 0 1
## [8,] 0 0 0 0 0 0 1 0 0 0
## [9,] 1 0 0 0 0 0 0 0 0 0
## [10,] 1 0 0 1 1 0 1 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] 0.003759909
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 2
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.2167549 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.000000
## [2,] 0.0000000 -0.5424926 0.0000000 0.0000000 0.000000 0.0000000 0.000000
## [3,] 0.0000000 0.0000000 0.8911446 0.0000000 0.000000 0.0000000 0.000000
## [4,] 0.0000000 0.0000000 0.0000000 0.5959806 0.000000 0.0000000 0.000000
## [5,] 0.0000000 0.0000000 0.0000000 0.0000000 1.635618 0.0000000 0.000000
## [6,] 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.6892754 0.000000
## [7,] 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 -1.281247
## [8,] 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.000000
## [9,] 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.000000
## [10,] 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.00000 0.000000
## [2,] 0.0000000 0.00000 0.000000
## [3,] 0.0000000 0.00000 0.000000
## [4,] 0.0000000 0.00000 0.000000
## [5,] 0.0000000 0.00000 0.000000
## [6,] 0.0000000 0.00000 0.000000
## [7,] 0.0000000 0.00000 0.000000
## [8,] -0.2131445 0.00000 0.000000
## [9,] 0.0000000 1.89654 0.000000
## [10,] 0.0000000 0.00000 1.776863
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 5.708043e+41
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(n = N, t = 500, rho_1_mod = rnorm(N), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.2167549 -0.5424926 0.8911446 0.5959806 1.6356180 0.6892754
## [7] -1.2812466 -0.2131445 1.8965399 1.7768632
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1
## y1 " 0.2167549"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " 1359673579837988946952006444804744552623246311164855869819441781964053607235524609773662109696.0000000"
## y6 " 0.0000000"
## y7 " 2287293755225308040464390005344807419904.0000000"
## y8 " 0.0000000"
## y9 " 24899661204460953731228054045537011300779237204473957159088919178007717597604244997087430148578866578621356401404840427651072.0000000"
## y10 " -68846581698326745950136583992944617392269702769958457610563110640032832143702356818014134087192531798058860544.0000000"
## y2.l1
## y1 " 0.0000000"
## y2 " -0.5424926"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " -57014635251296577331815613625884055436098602150119796911409260258597857610208282856745074688.0000000"
## y6 " 0.0000000"
## y7 " -195980316394741602760937334944556908544.0000000"
## y8 " 0.0000000"
## y9 " -1006048433973408637409491061959385811227777453886920913910328863530986577065953291564350716251307135965276492131029965864960.0000000"
## y10 " 2887612514632491047782944194314914430697061372028203267986648017400826868233885258965075889122799903320309760.0000000"
## y3.l1
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.8911446"
## y4 " 0.0000000"
## y5 " 35494781463337797389889483871836294687465904627015939063845569499920502661649113530780090368.0000000"
## y6 " 0.0000000"
## y7 " -14045204016855280431293467751490781184.0000000"
## y8 " 0.0000000"
## y9 " 677190382481190753989500677675459083643652975187829728843478250761804579237698393808996978740297587038101849434999127801856.0000000"
## y10 " -1779579594188694678165518953938107865270905072380414636932143266737696083224714557099714128575367411885146112.0000000"
## y4.l1
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.5959806"
## y5 " -734129775961852609802879931108731576441094095214138147961654027201280639121011811659091542016.0000000"
## y6 " 0.0000000"
## y7 " -436191685452536998529098262028079857664.0000000"
## y8 " 0.0000000"
## y9 "-13745838543078083968050424283347470962121386817758082445965917208269848284111399051487951958569272623416339634159317248114688.0000000"
## y10 " 37126436308831907173525725779564055164592472075924885912983883548129792908790201083743760363982848904208056320.0000000"
## y5.l1
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " 1.6356180"
## y6 " 0.0000000"
## y7 " 0.0000000"
## y8 " 0.0000000"
## y9 " -201665691746624608.0000000"
## y10 " 2947.9900255"
## y6.l1
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " -3229690901006658855414236051350904848252770771783404067639247173301639501169174664040228585472.0000000"
## y6 " 0.6892754"
## y7 " -963382868078139399688683119797094842368.0000000"
## y8 " 0.0000000"
## y9 "-60829004482195041046243927498525396087840416679580115770145417783682117411270981762705003856244513375246118029443290028310528.0000000"
## y10 " 163185637545011521246110096194866772711797352892558962824103843879170328218989163037060956754414931540304723968.0000000"
## y7.l1
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " -1620698188995868127678550043948744704.0000000"
## y6 " 0.0000000"
## y7 " -1.2812466"
## y8 " 0.0000000"
## y9 " -611513551971901607812030713025220250245528948838986967881998030340096.0000000"
## y10 " 1830094969358530194807021363840392518574876956918022144.0000000"
## y8.l1
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " -316445852649642893635190261276698678171738768979253916866293356849373852054141697386826694656.0000000"
## y6 " 0.0000000"
## y7 " -865444802184890394068065783307927814144.0000000"
## y8 " -0.2131445"
## y9 " -5668455793219649766472890281997571565268337650454359451579043446104674281404948225825351225726122867519038055160112473964544.0000000"
## y10 " 16027070996699312042112747903481330501074624883686384181647265752404124438450275602335238133030776357248827392.0000000"
## y9.l1
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " 0.0000000"
## y6 " 0.0000000"
## y7 " 0.0000000"
## y8 " 0.0000000"
## y9 " 1.8965399"
## y10 " 0.0000000"
## y10.l1
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " 0.0000000"
## y6 " 0.0000000"
## y7 " 0.0000000"
## y8 " 0.0000000"
## y9 " 1.3045534"
## y10 " 1.7768632"
## const
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " -52389690658041651374322255620252923227384871154189184605520594755569644235619478997565440.0000000"
## y6 " 0.0000000"
## y7 " 165892387828022124771588509639114752.0000000"
## y8 " 0.0000000"
## y9 " -897659506141117548818337752811018753679329590853559297975953528058355316879866471912441079334713453245477345955275603968.0000000"
## y10 " -453455685117383508482114359209341514198727319566104015518053163718272690443476564234693502339063757144064.0000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 0 0 1 0 0 1 1
## [2,] 0 0 0 0 0 1 1 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0 1
## [5,] 0 0 0 0 0 0 0 0 0 1
## [6,] 1 1 0 0 0 0 0 0 0 0
## [7,] 0 1 0 0 0 0 0 1 0 1
## [8,] 0 0 0 0 0 0 1 0 0 0
## [9,] 1 0 0 0 0 0 0 0 0 0
## [10,] 1 0 0 1 1 0 1 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] 0.003759909
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 1
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.2167549 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.000000
## [2,] 0.0000000 -0.5424926 0.0000000 0.0000000 0.000000 0.0000000 0.000000
## [3,] 0.0000000 0.0000000 0.8911446 0.0000000 0.000000 0.0000000 0.000000
## [4,] 0.0000000 0.0000000 0.0000000 0.5959806 0.000000 0.0000000 0.000000
## [5,] 0.0000000 0.0000000 0.0000000 0.0000000 1.635618 0.0000000 0.000000
## [6,] 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.6892754 0.000000
## [7,] 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 -1.281247
## [8,] 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.000000
## [9,] 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.000000
## [10,] 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.00000 0.000000
## [2,] 0.0000000 0.00000 0.000000
## [3,] 0.0000000 0.00000 0.000000
## [4,] 0.0000000 0.00000 0.000000
## [5,] 0.0000000 0.00000 0.000000
## [6,] 0.0000000 0.00000 0.000000
## [7,] 0.0000000 0.00000 0.000000
## [8,] -0.2131445 0.00000 0.000000
## [9,] 0.0000000 1.89654 0.000000
## [10,] 0.0000000 0.00000 1.776863
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 6.739964e+124
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(n = N, t = 200, rho_1_mod = runif(N, min = 0.95, max = 1.05), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1.0085800 0.9508946 0.9793740 0.9777375 1.0313574 0.9760428 1.0224406
## [8] 1.0406092 1.0449040 0.9573144
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1
## y1 " 1.0085800304" "-0.0000000001" " 0.0000005568" " 0.0000000299"
## y2 " 0.0000000000" " 0.9508945796" " 0.0000000176" " 0.0000000009"
## y3 " 0.0000000000" " 0.0000000000" " 0.9793739609" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000027" " 0.9777374959"
## y5 "-0.0000000003" "-0.0000000002" " 0.0000020138" " 0.0000001080"
## y6 " 0.0000000000" " 0.0000000000" "-0.0000000016" "-0.0000000001"
## y7 "-0.0000000001" "-0.0000000001" " 0.0000008336" " 0.0000000447"
## y8 " 0.0000000014" " 0.0000000014" "-0.0000112709" "-0.0000006072"
## y9 " 0.0000000015" " 0.0000000009" "-0.0000098961" "-0.0000005264"
## y10 " 0.0000000000" " 0.0000000000" "-0.0000000056" "-0.0000000003"
## y5.l1 y6.l1 y7.l1 y8.l1
## y1 " 0.0000000000" "-0.0000001993" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" "-0.0000000063" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000001" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" "-0.0000000010" " 0.0000000000" " 0.0000000000"
## y5 " 1.0313574215" "-0.0000007210" " 0.0000000000" " 0.0000000000"
## y6 " 0.0000000000" " 0.9760427777" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" "-0.0000002985" " 1.0224405893" " 0.0000000000"
## y8 " 0.0000000000" " 0.0000040721" " 0.0000000002" " 1.0406092151"
## y9 " 0.0000000000" " 0.0000034830" " 0.0000000002" " 0.0000000000"
## y10 " 0.0000000000" " 0.0000000020" " 0.0000000000" " 0.0000000000"
## y9.l1 y10.l1 const
## y1 " 0.0000000000" " 0.0000000014" " 0.0000000001"
## y2 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 0.0000000000" " 0.0000000049" " 0.0000000005"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" " 0.0000000020" " 0.0000000002"
## y8 " 0.0000000000" "-0.0000000292" "-0.0000000027"
## y9 " 1.0449040221" "-0.0000000210" "-0.0000000027"
## y10 " 0.0000000000" " 0.9573144469" " 0.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 1 0 0 0 0 0 1
## [2,] 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0
## [10,] 1 0 0 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -3.731872e-72
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1.00858 0.0000000 0.000000 0.0000000 0.000000 0.0000000 0.000000 0.000000
## [2,] 0.00000 0.9508946 0.000000 0.0000000 0.000000 0.0000000 0.000000 0.000000
## [3,] 0.00000 0.0000000 0.979374 0.0000000 0.000000 0.0000000 0.000000 0.000000
## [4,] 0.00000 0.0000000 0.000000 0.9777375 0.000000 0.0000000 0.000000 0.000000
## [5,] 0.00000 0.0000000 0.000000 0.0000000 1.031357 0.0000000 0.000000 0.000000
## [6,] 0.00000 0.0000000 0.000000 0.0000000 0.000000 0.9760428 0.000000 0.000000
## [7,] 0.00000 0.0000000 0.000000 0.0000000 0.000000 0.0000000 1.022441 0.000000
## [8,] 0.00000 0.0000000 0.000000 0.0000000 0.000000 0.0000000 0.000000 1.040609
## [9,] 0.00000 0.0000000 0.000000 0.0000000 0.000000 0.0000000 0.000000 0.000000
## [10,] 0.00000 0.0000000 0.000000 0.0000000 0.000000 0.0000000 0.000000 0.000000
## [,9] [,10]
## [1,] 0.000000 0.0000000
## [2,] 0.000000 0.0000000
## [3,] 0.000000 0.0000000
## [4,] 0.000000 0.0000000
## [5,] 0.000000 0.0000000
## [6,] 0.000000 0.0000000
## [7,] 0.000000 0.0000000
## [8,] 0.000000 0.0000000
## [9,] 1.044904 0.0000000
## [10,] 0.000000 0.9573144
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.00001612608
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 8
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(n = N, t = 500, rho_1_mod = runif(N, min = 0.95, max = 1.05), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1.0085800 0.9508946 0.9793740 0.9777375 1.0313574 0.9760428 1.0224406
## [8] 1.0406092 1.0449040 0.9573144
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1
## y1 " 1.0085800305" " 0.0000000000" " 0.0000000145" " 0.0000000009"
## y2 " 0.0000000000" " 0.9508945796" " 0.0000000002" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.9793739612" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.9777374958"
## y5 " 0.0000000001" " 0.0000000617" "-0.0000595663" "-0.0000037740"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" " 0.0000000002" "-0.0000001879" "-0.0000000122"
## y8 " 0.0000000022" " 0.0000017617" "-0.0015394428" "-0.0000977718"
## y9 "-0.0000001380" "-0.0000268374" " 0.0354632080" " 0.0022146288"
## y10 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5.l1 y6.l1 y7.l1 y8.l1
## y1 " 0.0000000000" "-0.0000000071" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" "-0.0000000001" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 1.0313574215" " 0.0000297543" " 0.0000000000" " 0.0000000000"
## y6 " 0.0000000000" " 0.9760427771" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" " 0.0000000986" " 1.0224405893" " 0.0000000000"
## y8 " 0.0000000000" " 0.0007732993" " 0.0000000000" " 1.0406092151"
## y9 " 0.0000000000" "-0.0171857355" "-0.0000000014" " 0.0000000000"
## y10 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y9.l1 y10.l1 const
## y1 " 0.0000000000" " 0.0000000002" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 0.0000000000" "-0.0000008884" "-0.0000000011"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" "-0.0000000032" " 0.0000000000"
## y8 " 0.0000000000" "-0.0000247060" "-0.0000000237"
## y9 " 1.0449040221" " 0.0004161147" " 0.0000009002"
## y10 " 0.0000000000" " 0.9573144469" " 0.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 1 0 0 0 0 0 1
## [2,] 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0
## [10,] 1 0 0 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -3.731872e-72
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 8
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1.00858 0.0000000 0.000000 0.0000000 0.000000 0.0000000 0.000000 0.000000
## [2,] 0.00000 0.9508946 0.000000 0.0000000 0.000000 0.0000000 0.000000 0.000000
## [3,] 0.00000 0.0000000 0.979374 0.0000000 0.000000 0.0000000 0.000000 0.000000
## [4,] 0.00000 0.0000000 0.000000 0.9777375 0.000000 0.0000000 0.000000 0.000000
## [5,] 0.00000 0.0000000 0.000000 0.0000000 1.031357 0.0000000 0.000000 0.000000
## [6,] 0.00000 0.0000000 0.000000 0.0000000 0.000000 0.9760428 0.000000 0.000000
## [7,] 0.00000 0.0000000 0.000000 0.0000000 0.000000 0.0000000 1.022441 0.000000
## [8,] 0.00000 0.0000000 0.000000 0.0000000 0.000000 0.0000000 0.000000 1.040609
## [9,] 0.00000 0.0000000 0.000000 0.0000000 0.000000 0.0000000 0.000000 0.000000
## [10,] 0.00000 0.0000000 0.000000 0.0000000 0.000000 0.0000000 0.000000 0.000000
## [,9] [,10]
## [1,] 0.000000 0.0000000
## [2,] 0.000000 0.0000000
## [3,] 0.000000 0.0000000
## [4,] 0.000000 0.0000000
## [5,] 0.000000 0.0000000
## [6,] 0.000000 0.0000000
## [7,] 0.000000 0.0000000
## [8,] 0.000000 0.0000000
## [9,] 1.044904 0.0000000
## [10,] 0.000000 0.9573144
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.03951012
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 8
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N = 10
models(n = N, t = 200, rho_1_mod = runif(N, min = 0.7, max = 0.9), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.8171601 0.7017892 0.7587479 0.7554750 0.8627148 0.7520856 0.8448812
## [8] 0.8812184 0.8898080 0.7146289
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1
## y1 " 0.8171600611" " 0.0000000000" " 0.0000001838" " 0.0000000098"
## y2 " 0.0000000005" " 0.7017891590" " 0.0000020307" " 0.0000001086"
## y3 " 0.0000000000" " 0.0000000000" " 0.7587479516" " 0.0000000016"
## y4 " 0.0000000001" " 0.0000000000" " 0.0000002489" " 0.7554750049"
## y5 "-0.0000000001" " 0.0000000000" "-0.0000002448" "-0.0000000130"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000826" " 0.0000000044"
## y7 " 0.0000000003" "-0.0000000001" " 0.0000009783" " 0.0000000524"
## y8 "-0.0000000003" " 0.0000000001" "-0.0000012482" "-0.0000000667"
## y9 " 0.0000000003" "-0.0000000001" " 0.0000011029" " 0.0000000593"
## y10 " 0.0000000001" " 0.0000000000" " 0.0000004388" " 0.0000000235"
## y5.l1 y6.l1 y7.l1 y8.l1
## y1 " 0.0000000000" "-0.0000000650" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000002" "-0.0000007196" " 0.0000000004" "-0.0000000001"
## y3 " 0.0000000000" "-0.0000000104" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" "-0.0000000884" " 0.0000000000" " 0.0000000000"
## y5 " 0.8627148430" " 0.0000000857" "-0.0000000001" " 0.0000000000"
## y6 " 0.0000000000" " 0.7520855250" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000001" "-0.0000003475" " 0.8448811787" "-0.0000000001"
## y8 "-0.0000000001" " 0.0000004419" "-0.0000000002" " 0.8812184303"
## y9 " 0.0000000001" "-0.0000003946" " 0.0000000002" "-0.0000000001"
## y10 " 0.0000000000" "-0.0000001559" " 0.0000000001" " 0.0000000000"
## y9.l1 y10.l1 const
## y1 " 0.0000000000" " 0.0000000003" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000038" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000001" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000005" " 0.0000000000"
## y5 " 0.0000000000" "-0.0000000004" " 0.0000000000"
## y6 " 0.0000000000" " 0.0000000002" " 0.0000000000"
## y7 " 0.0000000000" " 0.0000000019" " 0.0000000000"
## y8 " 0.0000000000" "-0.0000000023" " 0.0000000000"
## y9 " 0.8898080442" " 0.0000000022" " 0.0000000000"
## y10 " 0.0000000000" " 0.7146288947" " 0.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 1 0 0 0 0 0 1
## [2,] 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0
## [10,] 1 0 0 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -2.181369e-59
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8171601 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
## [2,] 0.0000000 0.7017892 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
## [3,] 0.0000000 0.0000000 0.7587479 0.000000 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.0000000 0.755475 0.0000000 0.0000000 0.0000000
## [5,] 0.0000000 0.0000000 0.0000000 0.000000 0.8627148 0.0000000 0.0000000
## [6,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.7520856 0.0000000
## [7,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.8448812
## [8,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
## [9,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
## [10,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.000000 0.0000000
## [2,] 0.0000000 0.000000 0.0000000
## [3,] 0.0000000 0.000000 0.0000000
## [4,] 0.0000000 0.000000 0.0000000
## [5,] 0.0000000 0.000000 0.0000000
## [6,] 0.0000000 0.000000 0.0000000
## [7,] 0.0000000 0.000000 0.0000000
## [8,] 0.8812184 0.000000 0.0000000
## [9,] 0.0000000 0.889808 0.0000000
## [10,] 0.0000000 0.000000 0.7146289
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.00000304448
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 9
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N = 10
models(n = N, t = 500, rho_1_mod = runif(N, min = 0.7, max = 0.9), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.8171601 0.7017892 0.7587479 0.7554750 0.8627148 0.7520856 0.8448812
## [8] 0.8812184 0.8898080 0.7146289
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1
## y1 " 0.8171600610" " 0.0000000000" " 0.0000001790" " 0.0000000096"
## y2 " 0.0000000005" " 0.7017891590" " 0.0000019805" " 0.0000001060"
## y3 " 0.0000000000" " 0.0000000000" " 0.7587479509" " 0.0000000015"
## y4 " 0.0000000001" " 0.0000000000" " 0.0000002430" " 0.7554750046"
## y5 "-0.0000000001" " 0.0000000000" "-0.0000002366" "-0.0000000126"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000806" " 0.0000000043"
## y7 " 0.0000000002" "-0.0000000001" " 0.0000009556" " 0.0000000512"
## y8 "-0.0000000003" " 0.0000000001" "-0.0000012168" "-0.0000000651"
## y9 " 0.0000000003" "-0.0000000001" " 0.0000010827" " 0.0000000582"
## y10 " 0.0000000001" " 0.0000000000" " 0.0000004287" " 0.0000000230"
## y5.l1 y6.l1 y7.l1 y8.l1
## y1 " 0.0000000000" "-0.0000000634" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000002" "-0.0000007024" " 0.0000000004" "-0.0000000001"
## y3 " 0.0000000000" "-0.0000000101" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" "-0.0000000863" " 0.0000000000" " 0.0000000000"
## y5 " 0.8627148430" " 0.0000000829" "-0.0000000001" " 0.0000000000"
## y6 " 0.0000000000" " 0.7520855257" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000001" "-0.0000003397" " 0.8448811787" "-0.0000000001"
## y8 "-0.0000000001" " 0.0000004311" "-0.0000000002" " 0.8812184303"
## y9 " 0.0000000001" "-0.0000003877" " 0.0000000002" "-0.0000000001"
## y10 " 0.0000000000" "-0.0000001525" " 0.0000000001" " 0.0000000000"
## y9.l1 y10.l1 const
## y1 " 0.0000000000" " 0.0000000003" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000037" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000001" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000005" " 0.0000000000"
## y5 " 0.0000000000" "-0.0000000004" " 0.0000000000"
## y6 " 0.0000000000" " 0.0000000002" " 0.0000000000"
## y7 " 0.0000000000" " 0.0000000018" " 0.0000000000"
## y8 " 0.0000000000" "-0.0000000023" " 0.0000000000"
## y9 " 0.8898080442" " 0.0000000022" " 0.0000000000"
## y10 " 0.0000000000" " 0.7146288947" " 0.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 1 0 0 0 0 0 1
## [2,] 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0
## [10,] 1 0 0 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -2.181369e-59
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8171601 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
## [2,] 0.0000000 0.7017892 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
## [3,] 0.0000000 0.0000000 0.7587479 0.000000 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.0000000 0.755475 0.0000000 0.0000000 0.0000000
## [5,] 0.0000000 0.0000000 0.0000000 0.000000 0.8627148 0.0000000 0.0000000
## [6,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.7520856 0.0000000
## [7,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.8448812
## [8,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
## [9,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
## [10,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.000000 0.0000000
## [2,] 0.0000000 0.000000 0.0000000
## [3,] 0.0000000 0.000000 0.0000000
## [4,] 0.0000000 0.000000 0.0000000
## [5,] 0.0000000 0.000000 0.0000000
## [6,] 0.0000000 0.000000 0.0000000
## [7,] 0.0000000 0.000000 0.0000000
## [8,] 0.8812184 0.000000 0.0000000
## [9,] 0.0000000 0.889808 0.0000000
## [10,] 0.0000000 0.000000 0.7146289
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.000002972614
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 9
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(n = N, t = 200, rho_1_mod =runif(N, min = -1, max = 1), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.1716006 -0.9821084 -0.4125208 -0.4452501 0.6271484 -0.4791445
## [7] 0.4488118 0.8121843 0.8980804 -0.8537111
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1 y5.l1
## y1 " 0.1716006" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y2 " 0.0000000" "-0.9821084" " 0.0000000" " 0.0000000" " 0.0000000"
## y3 " 0.0000000" " 0.0000000" "-0.4125208" " 0.0000000" " 0.0000000"
## y4 " 0.0000000" " 0.0000000" " 0.0000000" "-0.4452501" " 0.0000000"
## y5 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.6271484"
## y6 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y7 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y8 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y9 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y10 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y6.l1 y7.l1 y8.l1 y9.l1 y10.l1
## y1 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y2 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y3 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y4 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y5 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y6 "-0.4791445" " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y7 " 0.0000000" " 0.4488118" " 0.0000000" " 0.0000000" " 0.0000000"
## y8 " 0.0000000" " 0.0000000" " 0.8121843" " 0.0000000" " 0.0000000"
## y9 " 0.0000000" " 0.0000000" " 0.0000000" " 0.8980804" " 0.0000000"
## y10 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" "-0.8537111"
## const
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " 0.0000000"
## y6 " 0.0000000"
## y7 " 0.0000000"
## y8 " 0.0000000"
## y9 " 0.0000000"
## y10 " 0.0000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 1 0 0 0 0 0 1
## [2,] 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0
## [10,] 1 0 0 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -0.00000000000002166341
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.1716006 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [2,] 0.0000000 -0.9821084 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [3,] 0.0000000 0.0000000 -0.4125208 0.0000000 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.0000000 -0.4452501 0.0000000 0.0000000 0.0000000
## [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.6271484 0.0000000 0.0000000
## [6,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.4791445 0.0000000
## [7,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4488118
## [8,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [9,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [10,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.0000000 0.0000000
## [2,] 0.0000000 0.0000000 0.0000000
## [3,] 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.0000000
## [5,] 0.0000000 0.0000000 0.0000000
## [6,] 0.0000000 0.0000000 0.0000000
## [7,] 0.0000000 0.0000000 0.0000000
## [8,] 0.8121843 0.0000000 0.0000000
## [9,] 0.0000000 0.8980804 0.0000000
## [10,] 0.0000000 0.0000000 -0.8537111
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.00000000001896384
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(n = N, t = 500, rho_1_mod =runif(N, min = -1, max = 1), rho_2_mod=0, p_num = 1, s_alpha_input = 0, s_epsilon_input = 0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.1716006 -0.9821084 -0.4125208 -0.4452501 0.6271484 -0.4791445
## [7] 0.4488118 0.8121843 0.8980804 -0.8537111
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1
## y1 " 0.1716006100" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" "-0.9821084086" "-0.0000000001" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" "-0.4125207760" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000" "-0.4452500842"
## y5 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y8 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y9 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y10 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5.l1 y6.l1 y7.l1 y8.l1
## y1 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 0.6271484299" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y6 " 0.0000000000" "-0.4791444573" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" " 0.0000000000" " 0.4488117853" " 0.0000000000"
## y8 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.8121843026"
## y9 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y10 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y9.l1 y10.l1 const
## y1 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y2 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y3 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y6 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y8 " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y9 " 0.8980804421" " 0.0000000000" " 0.0000000000"
## y10 " 0.0000000000" "-0.8537110612" " 0.0000000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 1 0 0 0 0 0 1
## [2,] 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0
## [10,] 1 0 0 0 0 0 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -0.00000000000002166341
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.1716006 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [2,] 0.0000000 -0.9821084 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [3,] 0.0000000 0.0000000 -0.4125208 0.0000000 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.0000000 -0.4452501 0.0000000 0.0000000 0.0000000
## [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.6271484 0.0000000 0.0000000
## [6,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.4791445 0.0000000
## [7,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4488118
## [8,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [9,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [10,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.0000000 0.0000000
## [2,] 0.0000000 0.0000000 0.0000000
## [3,] 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.0000000
## [5,] 0.0000000 0.0000000 0.0000000
## [6,] 0.0000000 0.0000000 0.0000000
## [7,] 0.0000000 0.0000000 0.0000000
## [8,] 0.8121843 0.0000000 0.0000000
## [9,] 0.0000000 0.8980804 0.0000000
## [10,] 0.0000000 0.0000000 -0.8537111
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.0000000001158639
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(N, 200, rho_1_mod = runif(N, min = -1, max = 1), rho_2_mod = 1/N, p_num = 3, s_alpha_input =0, s_epsilon_input=0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.1716006 -0.9821084 -0.4125208 -0.4452501 0.6271484 -0.4791445
## [7] 0.4488118 0.8121843 0.8980804 -0.8537111
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1 y5.l1
## y1 " 0.1716006" " 0.1000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y2 " 0.1000000" "-0.9821084" " 0.0000000" " 0.0000000" " 0.0000000"
## y3 " 0.0000000" " 0.0000000" "-0.4125208" " 0.0000000" " 0.0000000"
## y4 " 0.0000000" " 0.0000000" " 0.0000000" "-0.4452501" " 0.0000000"
## y5 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.6271484"
## y6 " 0.0000000" " 0.0000000" " 0.1000000" " 0.0000000" " 0.0000000"
## y7 " 0.0000000" " 0.1000000" " 0.0000000" " 0.1000000" " 0.0000000"
## y8 " 0.0000000" " 0.1000000" " 0.1000000" " 0.0000000" " 0.0000000"
## y9 " 0.1000000" " 0.1000000" " 0.1000000" " 0.0000000" " 0.1000000"
## y10 " 0.0000000" " 0.0000000" " 0.0000000" " 0.1000000" " 0.0000000"
## y6.l1 y7.l1 y8.l1 y9.l1 y10.l1
## y1 " 0.0000000" " 0.0000000" " 0.0000000" " 0.1000000" " 0.0000000"
## y2 " 0.0000000" " 0.1000000" " 0.1000000" " 0.1000000" " 0.0000000"
## y3 " 0.1000000" " 0.0000000" " 0.1000000" " 0.1000000" " 0.0000000"
## y4 " 0.0000000" " 0.1000000" " 0.0000000" " 0.0000000" " 0.1000000"
## y5 " 0.0000000" " 0.0000000" " 0.0000000" " 0.1000000" " 0.0000000"
## y6 "-0.4791445" " 0.1000000" " 0.0000000" " 0.0000000" " 0.1000000"
## y7 " 0.1000000" " 0.4488118" " 0.0000000" " 0.1000000" " 0.0000000"
## y8 " 0.0000000" " 0.0000000" " 0.8121843" " 0.0000000" " 0.0000000"
## y9 " 0.0000000" " 0.1000000" " 0.0000000" " 0.8980804" " 0.1000000"
## y10 " 0.1000000" " 0.0000000" " 0.0000000" " 0.1000000" "-0.8537111"
## const
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " 0.0000000"
## y6 " 0.0000000"
## y7 " 0.0000000"
## y8 " 0.0000000"
## y9 " 0.0000000"
## y10 " 0.0000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 1 0 0 0 0 0 0 1 0
## [2,] 1 0 0 0 0 0 1 1 1 0
## [3,] 0 0 0 0 0 1 0 1 1 0
## [4,] 0 0 0 0 0 0 1 0 0 1
## [5,] 0 0 0 0 0 0 0 0 1 0
## [6,] 0 0 1 0 0 0 1 0 0 1
## [7,] 0 1 0 1 0 1 0 0 1 0
## [8,] 0 1 1 0 0 0 0 0 0 0
## [9,] 1 1 1 0 1 0 1 0 0 1
## [10,] 0 0 0 1 0 1 0 0 1 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] 0.0000000008231043
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.1716006 0.1000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [2,] 0.1000000 -0.9821084 0.0000000 0.0000000 0.0000000 0.0000000 0.1000000
## [3,] 0.0000000 0.0000000 -0.4125208 0.0000000 0.0000000 0.1000000 0.0000000
## [4,] 0.0000000 0.0000000 0.0000000 -0.4452501 0.0000000 0.0000000 0.1000000
## [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.6271484 0.0000000 0.0000000
## [6,] 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000 -0.4791445 0.1000000
## [7,] 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000 0.1000000 0.4488118
## [8,] 0.0000000 0.1000000 0.1000000 0.0000000 0.0000000 0.0000000 0.0000000
## [9,] 0.1000000 0.1000000 0.1000000 0.0000000 0.1000000 0.0000000 0.1000000
## [10,] 0.0000000 0.0000000 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.1000000 0.0000000
## [2,] 0.1000000 0.1000000 0.0000000
## [3,] 0.1000000 0.1000000 0.0000000
## [4,] 0.0000000 0.0000000 0.1000000
## [5,] 0.0000000 0.1000000 0.0000000
## [6,] 0.0000000 0.0000000 0.1000000
## [7,] 0.0000000 0.1000000 0.0000000
## [8,] 0.8121843 0.0000000 0.0000000
## [9,] 0.0000000 0.8980804 0.1000000
## [10,] 0.0000000 0.1000000 -0.8537111
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.0000000000001434733
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(N, 500, rho_1_mod = runif(N, min = -1, max = 1), rho_2_mod = 1/N, p_num = 3, s_alpha_input =0, s_epsilon_input=0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.1716006 -0.9821084 -0.4125208 -0.4452501 0.6271484 -0.4791445
## [7] 0.4488118 0.8121843 0.8980804 -0.8537111
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1 y5.l1
## y1 " 0.1716006" " 0.1000000" " 0.0000000" " 0.0000000" " 0.0000000"
## y2 " 0.1000000" "-0.9821084" " 0.0000000" " 0.0000000" " 0.0000000"
## y3 " 0.0000000" " 0.0000000" "-0.4125208" " 0.0000000" " 0.0000000"
## y4 " 0.0000000" " 0.0000000" " 0.0000000" "-0.4452501" " 0.0000000"
## y5 " 0.0000000" " 0.0000000" " 0.0000000" " 0.0000000" " 0.6271484"
## y6 " 0.0000000" " 0.0000000" " 0.1000000" " 0.0000000" " 0.0000000"
## y7 " 0.0000000" " 0.1000000" " 0.0000000" " 0.1000000" " 0.0000000"
## y8 " 0.0000000" " 0.1000000" " 0.1000000" " 0.0000000" " 0.0000000"
## y9 " 0.1000000" " 0.1000000" " 0.1000000" " 0.0000000" " 0.1000000"
## y10 " 0.0000000" " 0.0000000" " 0.0000000" " 0.1000000" " 0.0000000"
## y6.l1 y7.l1 y8.l1 y9.l1 y10.l1
## y1 " 0.0000000" " 0.0000000" " 0.0000000" " 0.1000000" " 0.0000000"
## y2 " 0.0000000" " 0.1000000" " 0.1000000" " 0.1000000" " 0.0000000"
## y3 " 0.1000000" " 0.0000000" " 0.1000000" " 0.1000000" " 0.0000000"
## y4 " 0.0000000" " 0.1000000" " 0.0000000" " 0.0000000" " 0.1000000"
## y5 " 0.0000000" " 0.0000000" " 0.0000000" " 0.1000000" " 0.0000000"
## y6 "-0.4791445" " 0.1000000" " 0.0000000" " 0.0000000" " 0.1000000"
## y7 " 0.1000000" " 0.4488118" " 0.0000000" " 0.1000000" " 0.0000000"
## y8 " 0.0000000" " 0.0000000" " 0.8121843" " 0.0000000" " 0.0000000"
## y9 " 0.0000000" " 0.1000000" " 0.0000000" " 0.8980804" " 0.1000000"
## y10 " 0.1000000" " 0.0000000" " 0.0000000" " 0.1000000" "-0.8537111"
## const
## y1 " 0.0000000"
## y2 " 0.0000000"
## y3 " 0.0000000"
## y4 " 0.0000000"
## y5 " 0.0000000"
## y6 " 0.0000000"
## y7 " 0.0000000"
## y8 " 0.0000000"
## y9 " 0.0000000"
## y10 " 0.0000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 1 0 0 0 0 0 0 1 0
## [2,] 1 0 0 0 0 0 1 1 1 0
## [3,] 0 0 0 0 0 1 0 1 1 0
## [4,] 0 0 0 0 0 0 1 0 0 1
## [5,] 0 0 0 0 0 0 0 0 1 0
## [6,] 0 0 1 0 0 0 1 0 0 1
## [7,] 0 1 0 1 0 1 0 0 1 0
## [8,] 0 1 1 0 0 0 0 0 0 0
## [9,] 1 1 1 0 1 0 1 0 0 1
## [10,] 0 0 0 1 0 1 0 0 1 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] 0.0000000008231043
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.1716006 0.1000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [2,] 0.1000000 -0.9821084 0.0000000 0.0000000 0.0000000 0.0000000 0.1000000
## [3,] 0.0000000 0.0000000 -0.4125208 0.0000000 0.0000000 0.1000000 0.0000000
## [4,] 0.0000000 0.0000000 0.0000000 -0.4452501 0.0000000 0.0000000 0.1000000
## [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.6271484 0.0000000 0.0000000
## [6,] 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000 -0.4791445 0.1000000
## [7,] 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000 0.1000000 0.4488118
## [8,] 0.0000000 0.1000000 0.1000000 0.0000000 0.0000000 0.0000000 0.0000000
## [9,] 0.1000000 0.1000000 0.1000000 0.0000000 0.1000000 0.0000000 0.1000000
## [10,] 0.0000000 0.0000000 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.1000000 0.0000000
## [2,] 0.1000000 0.1000000 0.0000000
## [3,] 0.1000000 0.1000000 0.0000000
## [4,] 0.0000000 0.0000000 0.1000000
## [5,] 0.0000000 0.1000000 0.0000000
## [6,] 0.0000000 0.0000000 0.1000000
## [7,] 0.0000000 0.1000000 0.0000000
## [8,] 0.8121843 0.0000000 0.0000000
## [9,] 0.0000000 0.8980804 0.1000000
## [10,] 0.0000000 0.1000000 -0.8537111
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.000000000000368831
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(N, 200, rho_1_mod = runif(N, min = -1, max = 1), rho_2_mod = 1/N, p_num = 3, s_alpha_input = 0.1, s_epsilon_input=0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.1716006 -0.9821084 -0.4125208 -0.4452501 0.6271484 -0.4791445
## [7] 0.4488118 0.8121843 0.8980804 -0.8537111
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0.068927544 -0.128124663 -0.021314452 0.189653987 0.177686321
## [6] 0.056660450 0.001571945 0.038305734 -0.004513712 0.003435191
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1
## y1 " 0.1716006100" " 0.1000000000" " 0.0000000000" " 0.0000000000"
## y2 " 0.1000000000" "-0.9821084086" " 0.0000000000" " 0.1000000000"
## y3 " 0.0000000000" " 0.0000000000" "-0.4125207760" " 0.1000000000"
## y4 " 0.0000000000" " 0.1000000000" " 0.1000000000" "-0.4452500842"
## y5 " 0.1000000000" " 0.0000000000" " 0.1000000000" " 0.0000000000"
## y6 " 0.1000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y7 " 0.1000000000" " 0.0000000000" " 0.1000000000" " 0.0000000000"
## y8 " 0.1000000000" " 0.1000000000" " 0.0000000000" " 0.0000000000"
## y9 " 0.1000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y10 "-0.0000000001" " 0.1000000000" " 0.0000000000" " 0.0000000000"
## y5.l1 y6.l1 y7.l1 y8.l1
## y1 " 0.1000000000" " 0.1000000000" " 0.1000000000" " 0.1000000000"
## y2 " 0.0000000000" " 0.0000000001" " 0.0000000000" " 0.1000000000"
## y3 " 0.1000000000" " 0.0000000000" " 0.1000000000" " 0.0000000000"
## y4 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 0.6271484299" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y6 " 0.0000000000" "-0.4791444573" " 0.1000000000" " 0.0000000000"
## y7 " 0.0000000000" " 0.1000000000" " 0.4488117853" " 0.0000000000"
## y8 " 0.0000000000" " 0.0000000000" " 0.0000000000" " 0.8121843026"
## y9 " 0.0000000000" " 0.1000000000" " 0.0000000000" " 0.0000000000"
## y10 " 0.1000000000" " 0.0000000000" " 0.0000000000" " 0.1000000000"
## y9.l1 y10.l1 const
## y1 " 0.1000000000" " 0.0000000000" " 0.0689275442"
## y2 " 0.0000000000" " 0.1000000000" "-0.1281246630"
## y3 " 0.0000000000" " 0.0000000000" "-0.0213144519"
## y4 " 0.0000000000" " 0.0000000000" " 0.1896539872"
## y5 " 0.0000000000" " 0.1000000000" " 0.1776863214"
## y6 " 0.1000000000" " 0.0000000000" " 0.0566604498"
## y7 " 0.0000000000" " 0.0000000000" " 0.0015719454"
## y8 " 0.0000000000" " 0.1000000000" " 0.0383057339"
## y9 " 0.8980804421" " 0.0000000000" "-0.0045137116"
## y10 " 0.0000000000" "-0.8537110612" " 0.0034351907"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 1 0 0 1 1 1 1 1 0
## [2,] 1 0 0 1 0 0 0 1 0 1
## [3,] 0 0 0 1 1 0 1 0 0 0
## [4,] 0 1 1 0 0 0 0 0 0 0
## [5,] 1 0 1 0 0 0 0 0 0 1
## [6,] 1 0 0 0 0 0 1 0 1 0
## [7,] 1 0 1 0 0 1 0 0 0 0
## [8,] 1 1 0 0 0 0 0 0 0 1
## [9,] 1 0 0 0 0 1 0 0 0 0
## [10,] 0 1 0 0 1 0 0 1 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] 0.00000000002680179
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.1716006 0.1000000 0.0000000 0.0000000 0.1000000 0.1000000 0.1000000
## [2,] 0.1000000 -0.9821084 0.0000000 0.1000000 0.0000000 0.0000000 0.0000000
## [3,] 0.0000000 0.0000000 -0.4125208 0.1000000 0.1000000 0.0000000 0.1000000
## [4,] 0.0000000 0.1000000 0.1000000 -0.4452501 0.0000000 0.0000000 0.0000000
## [5,] 0.1000000 0.0000000 0.1000000 0.0000000 0.6271484 0.0000000 0.0000000
## [6,] 0.1000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.4791445 0.1000000
## [7,] 0.1000000 0.0000000 0.1000000 0.0000000 0.0000000 0.1000000 0.4488118
## [8,] 0.1000000 0.1000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [9,] 0.1000000 0.0000000 0.0000000 0.0000000 0.0000000 0.1000000 0.0000000
## [10,] 0.0000000 0.1000000 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.1000000 0.1000000 0.0000000
## [2,] 0.1000000 0.0000000 0.1000000
## [3,] 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.0000000
## [5,] 0.0000000 0.0000000 0.1000000
## [6,] 0.0000000 0.1000000 0.0000000
## [7,] 0.0000000 0.0000000 0.0000000
## [8,] 0.8121843 0.0000000 0.1000000
## [9,] 0.0000000 0.8980804 0.0000000
## [10,] 0.1000000 0.0000000 -0.8537111
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.0000000001166871
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(N, 500, rho_1_mod = runif(N, min = -1, max = 1), rho_2_mod = 1/N, p_num = 3, s_alpha_input = 0.1, s_epsilon_input=0)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.1716006 -0.9821084 -0.4125208 -0.4452501 0.6271484 -0.4791445
## [7] 0.4488118 0.8121843 0.8980804 -0.8537111
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0.068927544 -0.128124663 -0.021314452 0.189653987 0.177686321
## [6] 0.056660450 0.001571945 0.038305734 -0.004513712 0.003435191
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0 0 0 0 0 0 0 0 0 0
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1 y5.l1
## y1 "-1.05867397" " NA" " NA" " NA" " NA"
## y2 "12.63791396" " NA" " NA" " NA" " NA"
## y3 " 0.25413784" " NA" " NA" " NA" " NA"
## y4 "-2.10165466" " NA" " NA" " NA" " NA"
## y5 " 0.41727856" " NA" " NA" " NA" " NA"
## y6 " 0.16752825" " NA" " NA" " NA" " NA"
## y7 " 0.04225631" " NA" " NA" " NA" " NA"
## y8 "-0.28592228" " NA" " NA" " NA" " NA"
## y9 " 0.04554203" " NA" " NA" " NA" " NA"
## y10 "-6.23003940" " NA" " NA" " NA" " NA"
## y6.l1 y7.l1 y8.l1 y9.l1 y10.l1
## y1 " NA" " NA" " NA" " NA" " NA"
## y2 " NA" " NA" " NA" " NA" " NA"
## y3 " NA" " NA" " NA" " NA" " NA"
## y4 " NA" " NA" " NA" " NA" " NA"
## y5 " NA" " NA" " NA" " NA" " NA"
## y6 " NA" " NA" " NA" " NA" " NA"
## y7 " NA" " NA" " NA" " NA" " NA"
## y8 " NA" " NA" " NA" " NA" " NA"
## y9 " NA" " NA" " NA" " NA" " NA"
## y10 " NA" " NA" " NA" " NA" " NA"
## const
## y1 " 0.47579849"
## y2 "-2.93828417"
## y3 "-0.02097898"
## y4 " 0.61530913"
## y5 " 0.45794357"
## y6 " 0.03630595"
## y7 " 0.05350679"
## y8 " 0.40281929"
## y9 " 0.23155739"
## y10 " 1.48222986"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 1 0 0 1 1 1 1 1 0
## [2,] 1 0 0 1 0 0 0 1 0 1
## [3,] 0 0 0 1 1 0 1 0 0 0
## [4,] 0 1 1 0 0 0 0 0 0 0
## [5,] 1 0 1 0 0 0 0 0 0 1
## [6,] 1 0 0 0 0 0 1 0 1 0
## [7,] 1 0 1 0 0 1 0 0 0 0
## [8,] 1 1 0 0 0 0 0 0 0 1
## [9,] 1 0 0 0 0 1 0 0 0 0
## [10,] 0 1 0 0 1 0 0 1 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] 0.00000000002680179
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 6
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.1716006 0.1000000 0.0000000 0.0000000 0.1000000 0.1000000 0.1000000
## [2,] 0.1000000 -0.9821084 0.0000000 0.1000000 0.0000000 0.0000000 0.0000000
## [3,] 0.0000000 0.0000000 -0.4125208 0.1000000 0.1000000 0.0000000 0.1000000
## [4,] 0.0000000 0.1000000 0.1000000 -0.4452501 0.0000000 0.0000000 0.0000000
## [5,] 0.1000000 0.0000000 0.1000000 0.0000000 0.6271484 0.0000000 0.0000000
## [6,] 0.1000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.4791445 0.1000000
## [7,] 0.1000000 0.0000000 0.1000000 0.0000000 0.0000000 0.1000000 0.4488118
## [8,] 0.1000000 0.1000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [9,] 0.1000000 0.0000000 0.0000000 0.0000000 0.0000000 0.1000000 0.0000000
## [10,] 0.0000000 0.1000000 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.1000000 0.1000000 0.0000000
## [2,] 0.1000000 0.0000000 0.1000000
## [3,] 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.0000000
## [5,] 0.0000000 0.0000000 0.1000000
## [6,] 0.0000000 0.1000000 0.0000000
## [7,] 0.0000000 0.0000000 0.0000000
## [8,] 0.8121843 0.0000000 0.1000000
## [9,] 0.0000000 0.8980804 0.0000000
## [10,] 0.1000000 0.0000000 -0.8537111
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] NA
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(N, 200, rho_1_mod = runif(N, min = -1, max = 1), rho_2_mod = 1/N, p_num = 3, s_alpha_input = 0.1, s_epsilon_input=0.1)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.1716006 -0.9821084 -0.4125208 -0.4452501 0.6271484 -0.4791445
## [7] 0.4488118 0.8121843 0.8980804 -0.8537111
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0.068927544 -0.128124663 -0.021314452 0.189653987 0.177686321
## [6] 0.056660450 0.001571945 0.038305734 -0.004513712 0.003435191
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0.01690268 0.11650268 -0.00442040 -0.01003684 -0.02834446 0.15408150
## [7] 0.01651690 0.13076224 0.12882569 0.05928969
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1 y5.l1
## y1 " 0.17160061" " 0.00000000" " 0.00000000" " 0.00000000" " 0.10000000"
## y2 " 0.00000000" "-0.98210841" " 0.00000000" " 0.10000000" " 0.00000000"
## y3 " 0.00000000" " 0.00000000" "-0.41252078" " 0.00000000" " 0.00000000"
## y4 " 0.00000000" " 0.10000000" " 0.00000000" "-0.44525008" " 0.10000000"
## y5 " 0.10000000" " 0.00000000" " 0.00000000" " 0.10000000" " 0.62714843"
## y6 " 0.10000000" " 0.10000000" " 0.00000000" " 0.00000000" " 0.00000000"
## y7 " 0.00000000" " 0.00000000" " 0.10000000" " 0.00000000" " 0.00000000"
## y8 " 0.00000000" " 0.10000000" " 0.00000000" " 0.00000000" " 0.00000000"
## y9 " 0.00000000" " 0.10000000" " 0.00000000" " 0.00000000" " 0.10000000"
## y10 " 0.10000000" " 0.00000000" " 0.00000000" " 0.10000000" " 0.00000000"
## y6.l1 y7.l1 y8.l1 y9.l1 y10.l1
## y1 " 0.10000000" " 0.00000000" " 0.00000000" " 0.00000000" " 0.10000000"
## y2 " 0.10000000" " 0.00000000" " 0.10000000" " 0.10000000" " 0.00000000"
## y3 " 0.00000000" " 0.10000000" " 0.00000000" " 0.00000000" " 0.00000000"
## y4 " 0.00000000" " 0.00000000" " 0.00000000" " 0.00000000" " 0.10000000"
## y5 " 0.00000000" " 0.00000000" " 0.00000000" " 0.10000000" " 0.00000000"
## y6 "-0.47914446" " 0.00000000" " 0.10000000" " 0.00000000" " 0.10000000"
## y7 " 0.00000000" " 0.44881179" " 0.00000000" " 0.00000000" " 0.00000000"
## y8 " 0.10000000" " 0.00000000" " 0.81218430" " 0.10000000" " 0.00000000"
## y9 " 0.00000000" " 0.00000000" " 0.10000000" " 0.89808044" " 0.00000000"
## y10 " 0.10000000" " 0.00000000" " 0.00000000" " 0.00000000" "-0.85371106"
## const
## y1 " 0.08583022"
## y2 "-0.01162198"
## y3 "-0.02573485"
## y4 " 0.17961714"
## y5 " 0.14934186"
## y6 " 0.21074195"
## y7 " 0.01808885"
## y8 " 0.16906797"
## y9 " 0.12431198"
## y10 " 0.06272488"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 0 1 1 0 0 0 1
## [2,] 0 0 0 1 0 1 0 1 1 0
## [3,] 0 0 0 0 0 0 1 0 0 0
## [4,] 0 1 0 0 1 0 0 0 0 1
## [5,] 1 0 0 1 0 0 0 0 1 0
## [6,] 1 1 0 0 0 0 0 1 0 1
## [7,] 0 0 1 0 0 0 0 0 0 0
## [8,] 0 1 0 0 0 1 0 0 1 0
## [9,] 0 1 0 0 1 0 0 1 0 0
## [10,] 1 0 0 1 0 1 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -0.0000000003979678
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.1716006 0.0000000 0.0000000 0.0000000 0.1000000 0.1000000 0.0000000
## [2,] 0.0000000 -0.9821084 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000
## [3,] 0.0000000 0.0000000 -0.4125208 0.0000000 0.0000000 0.0000000 0.1000000
## [4,] 0.0000000 0.1000000 0.0000000 -0.4452501 0.1000000 0.0000000 0.0000000
## [5,] 0.1000000 0.0000000 0.0000000 0.1000000 0.6271484 0.0000000 0.0000000
## [6,] 0.1000000 0.1000000 0.0000000 0.0000000 0.0000000 -0.4791445 0.0000000
## [7,] 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000 0.0000000 0.4488118
## [8,] 0.0000000 0.1000000 0.0000000 0.0000000 0.0000000 0.1000000 0.0000000
## [9,] 0.0000000 0.1000000 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000
## [10,] 0.1000000 0.0000000 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.0000000 0.1000000
## [2,] 0.1000000 0.1000000 0.0000000
## [3,] 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.1000000
## [5,] 0.0000000 0.1000000 0.0000000
## [6,] 0.1000000 0.0000000 0.1000000
## [7,] 0.0000000 0.0000000 0.0000000
## [8,] 0.8121843 0.1000000 0.0000000
## [9,] 0.1000000 0.8980804 0.0000000
## [10,] 0.0000000 0.0000000 -0.8537111
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.00000000006126622
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(N, 500, rho_1_mod = runif(N, min = -1, max = 1), rho_2_mod = 1/N, p_num = 3, s_alpha_input = 0.1, s_epsilon_input=0.1)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.1716006 -0.9821084 -0.4125208 -0.4452501 0.6271484 -0.4791445
## [7] 0.4488118 0.8121843 0.8980804 -0.8537111
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0.068927544 -0.128124663 -0.021314452 0.189653987 0.177686321
## [6] 0.056660450 0.001571945 0.038305734 -0.004513712 0.003435191
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0.01690268 0.11650268 -0.00442040 -0.01003684 -0.02834446 0.15408150
## [7] 0.01651690 0.13076224 0.12882569 0.05928969
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1
## y1 " 0.1124697105" "-0.0741353854" "-1.3931093995" "-0.3554338965"
## y2 "-0.0965728816" "-0.9755676260" " 0.7030038712" " 0.2356694981"
## y3 " 0.0000000000" " 0.0000000000" "-0.4125207760" " 0.0000000000"
## y4 " 0.0374419751" " 0.0193238325" "-2.0961132623" "-0.9363534761"
## y5 " 0.1000000007" " 0.0000000000" "-0.0000000008" " 0.0999999997"
## y6 " 0.6001655399" "-0.0120159615" "-5.4645172917" "-1.1411562555"
## y7 " 0.0000000000" " 0.0000000000" " 0.1000000000" " 0.0000000000"
## y8 "-0.0965728740" " 0.1065407820" " 0.7030038620" " 0.1356694952"
## y9 " 0.0000000019" " 0.0999999999" "-0.0000000022" "-0.0000000007"
## y10 "-0.3162191520" " 0.6952821471" "18.5977546306" " 4.4282734722"
## y5.l1 y6.l1 y7.l1 y8.l1
## y1 " 0.1517160843" " NA" " 0.2309695829" "-0.0180885660"
## y2 " 0.0126305111" " NA" " 0.0198263894" " 0.0570377379"
## y3 " 0.0000000000" " NA" " 0.1000000000" " 0.0000000000"
## y4 " 0.1390855743" " NA" " 0.2111431951" " 0.0248736957"
## y5 " 0.6271484297" " NA" "-0.0000000002" " 0.0000000000"
## y6 "-0.0214328124" " NA" " 0.1161461588" " 0.3307249915"
## y7 " 0.0000000000" " NA" " 0.4488117853" " 0.0000000000"
## y8 " 0.0126305100" " NA" " 0.0198263880" " 0.7692220404"
## y9 " 0.0999999996" " NA" "-0.0000000006" " 0.1000000004"
## y10 "-0.3210473617" " NA" "-1.7827264233" "-0.2553117557"
## y9.l1 y10.l1 const
## y1 " 0.0200972760" " NA" " 0.1336798223"
## y2 " 0.1277428936" " NA" " 0.0235254986"
## y3 " 0.0000000000" " NA" "-0.0257348517"
## y4 "-0.0076456175" " NA" " 0.1923192664"
## y5 " 0.1000000000" " NA" " 0.1493418644"
## y6 "-0.1405741542" " NA" " 0.0550368833"
## y7 " 0.0000000000" " NA" " 0.0180888474"
## y8 " 0.1277428937" " NA" " 0.2042154471"
## y9 " 0.8980804419" " NA" " 0.1243119760"
## y10 " 0.0930143775" " NA" "-0.0105670706"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 0 1 1 0 0 0 1
## [2,] 0 0 0 1 0 1 0 1 1 0
## [3,] 0 0 0 0 0 0 1 0 0 0
## [4,] 0 1 0 0 1 0 0 0 0 1
## [5,] 1 0 0 1 0 0 0 0 1 0
## [6,] 1 1 0 0 0 0 0 1 0 1
## [7,] 0 0 1 0 0 0 0 0 0 0
## [8,] 0 1 0 0 0 1 0 0 1 0
## [9,] 0 1 0 0 1 0 0 1 0 0
## [10,] 1 0 0 1 0 1 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -0.0000000003979678
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.1716006 0.0000000 0.0000000 0.0000000 0.1000000 0.1000000 0.0000000
## [2,] 0.0000000 -0.9821084 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000
## [3,] 0.0000000 0.0000000 -0.4125208 0.0000000 0.0000000 0.0000000 0.1000000
## [4,] 0.0000000 0.1000000 0.0000000 -0.4452501 0.1000000 0.0000000 0.0000000
## [5,] 0.1000000 0.0000000 0.0000000 0.1000000 0.6271484 0.0000000 0.0000000
## [6,] 0.1000000 0.1000000 0.0000000 0.0000000 0.0000000 -0.4791445 0.0000000
## [7,] 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000 0.0000000 0.4488118
## [8,] 0.0000000 0.1000000 0.0000000 0.0000000 0.0000000 0.1000000 0.0000000
## [9,] 0.0000000 0.1000000 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000
## [10,] 0.1000000 0.0000000 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.0000000 0.1000000
## [2,] 0.1000000 0.1000000 0.0000000
## [3,] 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.1000000
## [5,] 0.0000000 0.1000000 0.0000000
## [6,] 0.1000000 0.0000000 0.1000000
## [7,] 0.0000000 0.0000000 0.0000000
## [8,] 0.8121843 0.1000000 0.0000000
## [9,] 0.1000000 0.8980804 0.0000000
## [10,] 0.0000000 0.0000000 -0.8537111
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] NA
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(N, 200, rho_1_mod = runif(N, min = -1, max = 1), rho_2_mod = 1/N, p_num = 3, s_alpha_input = 1, s_epsilon_input=0.1)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.1716006 -0.9821084 -0.4125208 -0.4452501 0.6271484 -0.4791445
## [7] 0.4488118 0.8121843 0.8980804 -0.8537111
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0.68927544 -1.28124663 -0.21314452 1.89653987 1.77686321 0.56660450
## [7] 0.01571945 0.38305734 -0.04513712 0.03435191
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0.01690268 0.11650268 -0.00442040 -0.01003684 -0.02834446 0.15408150
## [7] 0.01651690 0.13076224 0.12882569 0.05928969
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1
## y1 " 0.1716006100" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y2 "-0.0000000001" "-0.9821084083" " 0.0000000005" " 0.1000000011"
## y3 " 0.0000000000" " 0.0000000000" "-0.4125207760" " 0.0000000000"
## y4 " 0.0000000000" " 0.1000000000" " 0.0000000000" "-0.4452500842"
## y5 " 0.1000000000" " 0.0000000000" " 0.0000000000" " 0.1000000000"
## y6 " 0.1000000000" " 0.1000000000" " 0.0000000000" "-0.0000000001"
## y7 " 0.0000000000" " 0.0000000000" " 0.1000000000" " 0.0000000000"
## y8 " 0.0000000000" " 0.1000000000" " 0.0000000000" "-0.0000000001"
## y9 " 0.0000000000" " 0.0999999999" "-0.0000000002" "-0.0000000003"
## y10 " 0.1000000000" " 0.0000000000" " 0.0000000000" " 0.1000000000"
## y5.l1 y6.l1 y7.l1 y8.l1
## y1 " 0.1000000000" " 0.1000000000" " 0.0000000000" " 0.0000000000"
## y2 "-0.0000000001" " 0.1000000005" "-0.0000000001" " 0.0999999999"
## y3 " 0.0000000000" " 0.0000000000" " 0.1000000000" " 0.0000000000"
## y4 " 0.1000000000" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y5 " 0.6271484299" " 0.0000000000" " 0.0000000000" " 0.0000000000"
## y6 " 0.0000000000" "-0.4791444573" " 0.0000000000" " 0.1000000000"
## y7 " 0.0000000000" " 0.0000000000" " 0.4488117853" " 0.0000000000"
## y8 " 0.0000000000" " 0.1000000000" " 0.0000000000" " 0.8121843026"
## y9 " 0.1000000000" "-0.0000000001" " 0.0000000000" " 0.1000000000"
## y10 " 0.0000000000" " 0.1000000000" " 0.0000000000" " 0.0000000000"
## y9.l1 y10.l1 const
## y1 " 0.0000000000" " 0.1000000000" " 0.7061781194"
## y2 " 0.1000000000" " 0.0000000003" "-1.1647439474"
## y3 " 0.0000000000" " 0.0000000000" "-0.2175649190"
## y4 " 0.0000000000" " 0.1000000000" " 1.8865030277"
## y5 " 0.1000000000" " 0.0000000000" " 1.7485187568"
## y6 " 0.0000000000" " 0.1000000000" " 0.7206859964"
## y7 " 0.0000000000" " 0.0000000000" " 0.0322363560"
## y8 " 0.1000000000" " 0.0000000000" " 0.5138195746"
## y9 " 0.8980804421" "-0.0000000001" " 0.0836885723"
## y10 " 0.0000000000" "-0.8537110612" " 0.0936416015"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 0 1 1 0 0 0 1
## [2,] 0 0 0 1 0 1 0 1 1 0
## [3,] 0 0 0 0 0 0 1 0 0 0
## [4,] 0 1 0 0 1 0 0 0 0 1
## [5,] 1 0 0 1 0 0 0 0 1 0
## [6,] 1 1 0 0 0 0 0 1 0 1
## [7,] 0 0 1 0 0 0 0 0 0 0
## [8,] 0 1 0 0 0 1 0 0 1 0
## [9,] 0 1 0 0 1 0 0 1 0 0
## [10,] 1 0 0 1 0 1 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -0.0000002307261
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.1716006 0.0000000 0.0000000 0.0000000 0.1000000 0.1000000 0.0000000
## [2,] 0.0000000 -0.9821084 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000
## [3,] 0.0000000 0.0000000 -0.4125208 0.0000000 0.0000000 0.0000000 0.1000000
## [4,] 0.0000000 0.1000000 0.0000000 -0.4452501 0.1000000 0.0000000 0.0000000
## [5,] 0.1000000 0.0000000 0.0000000 0.1000000 0.6271484 0.0000000 0.0000000
## [6,] 0.1000000 0.1000000 0.0000000 0.0000000 0.0000000 -0.4791445 0.0000000
## [7,] 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000 0.0000000 0.4488118
## [8,] 0.0000000 0.1000000 0.0000000 0.0000000 0.0000000 0.1000000 0.0000000
## [9,] 0.0000000 0.1000000 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000
## [10,] 0.1000000 0.0000000 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.0000000 0.1000000
## [2,] 0.1000000 0.1000000 0.0000000
## [3,] 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.1000000
## [5,] 0.0000000 0.1000000 0.0000000
## [6,] 0.1000000 0.0000000 0.1000000
## [7,] 0.0000000 0.0000000 0.0000000
## [8,] 0.8121843 0.1000000 0.0000000
## [9,] 0.1000000 0.8980804 0.0000000
## [10,] 0.0000000 0.0000000 -0.8537111
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] 0.000000001451927
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(N, 500, rho_1_mod = runif(N, min = -1, max = 1), rho_2_mod = 1/N, p_num = 3, s_alpha_input = 1, s_epsilon_input=0.1)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 0.1716006 -0.9821084 -0.4125208 -0.4452501 0.6271484 -0.4791445
## [7] 0.4488118 0.8121843 0.8980804 -0.8537111
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0.68927544 -1.28124663 -0.21314452 1.89653987 1.77686321 0.56660450
## [7] 0.01571945 0.38305734 -0.04513712 0.03435191
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0.01690268 0.11650268 -0.00442040 -0.01003684 -0.02834446 0.15408150
## [7] 0.01651690 0.13076224 0.12882569 0.05928969
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1 y4.l1
## y1 " 0.2234606591" "-0.0820660856" "-0.4323957906" "-0.3979586964"
## y2 "-0.0327984111" "-0.9792935561" " 0.5413826801" " 0.2133092653"
## y3 " 0.0000000000" " 0.0000000000" "-0.4125207760" " 0.0000000000"
## y4 " 0.0846584585" " 0.0151190620" "-0.9737784698" "-0.9565180452"
## y5 " 0.0999999993" " 0.0000000001" "-0.0000000002" " 0.1000000003"
## y6 " 0.3418101750" " 0.0016318561" "-3.5677835780" "-1.0541830054"
## y7 " 0.0000000000" " 0.0000000000" " 0.1000000000" " 0.0000000000"
## y8 "-0.0327984003" " 0.1028148517" " 0.5413826807" " 0.1133092612"
## y9 " 0.0000000035" " 0.0999999997" " 0.0000000003" "-0.0000000013"
## y10 "-0.6555369522" " 0.7274528030" " 8.8546372025" " 4.5780603691"
## y5.l1 y6.l1 y7.l1 y8.l1
## y1 " 0.1317134260" " NA" " 0.0171304483" " 0.0164973539"
## y2 "-0.0039668952" " NA" " 0.0119789846" " 0.1043701167"
## y3 " 0.0000000000" " NA" " 0.1000000000" " 0.0000000000"
## y4 " 0.1356803213" " NA" " 0.0051514678" " 0.0121272367"
## y5 " 0.6271484300" " NA" " 0.0000000005" " 0.0000000000"
## y6 " 0.0546874876" " NA" "-0.0522451200" " 0.0911880621"
## y7 " 0.0000000000" " NA" " 0.4488117853" " 0.0000000000"
## y8 "-0.0039668968" " NA" " 0.0119789732" " 0.8165544199"
## y9 " 0.0999999995" " NA" "-0.0000000034" " 0.1000000002"
## y10 "-0.3085737584" " NA" "-0.0319997306" "-0.0991614434"
## y9.l1 y10.l1 const
## y1 " 0.0017602708" " NA" " 1.0836104422"
## y2 " 0.1016733285" " NA" "-1.1383845190"
## y3 " 0.0000000000" " NA" "-0.2175649190"
## y4 " 0.0000869426" " NA" " 2.2375759248"
## y5 " 0.1000000000" " NA" " 1.7485187568"
## y6 "-0.0079307173" " NA" " 0.9454591694"
## y7 " 0.0000000000" " NA" " 0.0322363560"
## y8 " 0.1016733283" " NA" " 0.5401789994"
## y9 " 0.8980804421" " NA" " 0.0836885712"
## y10 " 0.0009310908" " NA" "-2.8771471347"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 0 1 1 0 0 0 1
## [2,] 0 0 0 1 0 1 0 1 1 0
## [3,] 0 0 0 0 0 0 1 0 0 0
## [4,] 0 1 0 0 1 0 0 0 0 1
## [5,] 1 0 0 1 0 0 0 0 1 0
## [6,] 1 1 0 0 0 0 0 1 0 1
## [7,] 0 0 1 0 0 0 0 0 0 0
## [8,] 0 1 0 0 0 1 0 0 1 0
## [9,] 0 1 0 0 1 0 0 1 0 0
## [10,] 1 0 0 1 0 1 0 0 0 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -0.0000002307261
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.1716006 0.0000000 0.0000000 0.0000000 0.1000000 0.1000000 0.0000000
## [2,] 0.0000000 -0.9821084 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000
## [3,] 0.0000000 0.0000000 -0.4125208 0.0000000 0.0000000 0.0000000 0.1000000
## [4,] 0.0000000 0.1000000 0.0000000 -0.4452501 0.1000000 0.0000000 0.0000000
## [5,] 0.1000000 0.0000000 0.0000000 0.1000000 0.6271484 0.0000000 0.0000000
## [6,] 0.1000000 0.1000000 0.0000000 0.0000000 0.0000000 -0.4791445 0.0000000
## [7,] 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000 0.0000000 0.4488118
## [8,] 0.0000000 0.1000000 0.0000000 0.0000000 0.0000000 0.1000000 0.0000000
## [9,] 0.0000000 0.1000000 0.0000000 0.0000000 0.1000000 0.0000000 0.0000000
## [10,] 0.1000000 0.0000000 0.0000000 0.1000000 0.0000000 0.1000000 0.0000000
## [,8] [,9] [,10]
## [1,] 0.0000000 0.0000000 0.1000000
## [2,] 0.1000000 0.1000000 0.0000000
## [3,] 0.0000000 0.0000000 0.0000000
## [4,] 0.0000000 0.0000000 0.1000000
## [5,] 0.0000000 0.1000000 0.0000000
## [6,] 0.1000000 0.0000000 0.1000000
## [7,] 0.0000000 0.0000000 0.0000000
## [8,] 0.8121843 0.1000000 0.0000000
## [9,] 0.1000000 0.8980804 0.0000000
## [10,] 0.0000000 0.0000000 -0.8537111
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] NA
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(N, 200, rho_1_mod = rep(1, N), rho_2_mod = 1/N, p_num = 3, s_alpha_input = 1, s_epsilon_input=0.1)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1 1 1 1 1 1 1 1 1 1
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0.2167549 -0.5424926 0.8911446 0.5959806 1.6356180 0.6892754
## [7] -1.2812466 -0.2131445 1.8965399 1.7768632
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0.056660450 0.001571945 0.038305734 -0.004513712 0.003435191
## [6] 0.016902677 0.116502684 -0.004420400 -0.010036844 -0.028344457
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1 y2.l1 y3.l1
## y1 " 1.3687531" " NA" " NA"
## y2 " 3.0484745" " NA" " NA"
## y3 " 0.8266981" " NA" " NA"
## y4 " 1.6740627" " NA" " NA"
## y5 " 1.5398637" " NA" " NA"
## y6 " 1.8330696" " NA" " NA"
## y7 " 1.9988444" " NA" " NA"
## y8 " 1.3687531" " NA" " NA"
## y9 " 1.5848192" " NA" " NA"
## y10 " 2.1711621" " NA" " NA"
## y4.l1 y5.l1 y6.l1
## y1 " NA" " NA" " NA"
## y2 " NA" " NA" " NA"
## y3 " NA" " NA" " NA"
## y4 " NA" " NA" " NA"
## y5 " NA" " NA" " NA"
## y6 " NA" " NA" " NA"
## y7 " NA" " NA" " NA"
## y8 " NA" " NA" " NA"
## y9 " NA" " NA" " NA"
## y10 " NA" " NA" " NA"
## y7.l1 y8.l1 y9.l1
## y1 " NA" " NA" " NA"
## y2 " NA" " NA" " NA"
## y3 " NA" " NA" " NA"
## y4 " NA" " NA" " NA"
## y5 " NA" " NA" " NA"
## y6 " NA" " NA" " NA"
## y7 " NA" " NA" " NA"
## y8 " NA" " NA" " NA"
## y9 " NA" " NA" " NA"
## y10 " NA" " NA" " NA"
## y10.l1 const
## y1 " NA" " 4675516737131.4902344"
## y2 " NA" "61059863052241.2578125"
## y3 " NA" "12024843400952.9277344"
## y4 " NA" "58418211190620.7031250"
## y5 " NA" "81205753194282.4687500"
## y6 " NA" "77333750742406.9531250"
## y7 " NA" "11667900086743.1738281"
## y8 " NA" " 4675516737110.0263672"
## y9 " NA" "44807313591500.0546875"
## y10 " NA" "87464936621420.1562500"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 1 0 0 0 0 1 0 0 0
## [2,] 1 0 1 1 0 1 1 1 0 1
## [3,] 0 1 0 0 0 0 0 0 0 0
## [4,] 0 1 0 0 1 0 0 0 1 0
## [5,] 0 0 0 1 0 1 0 0 0 1
## [6,] 0 1 0 0 1 0 0 0 0 1
## [7,] 1 1 0 0 0 0 0 1 1 0
## [8,] 0 1 0 0 0 0 1 0 0 0
## [9,] 0 0 0 1 0 0 1 0 0 1
## [10,] 0 1 0 0 1 1 0 0 1 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -8.856118e-29
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 2
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.00000000000004463097
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 1.0 0.1 0.0 0.0 0.0 0.0 0.1 0.0 0.0 0.0
## [2,] 0.1 1.0 0.1 0.1 0.0 0.1 0.1 0.1 0.0 0.1
## [3,] 0.0 0.1 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
## [4,] 0.0 0.1 0.0 1.0 0.1 0.0 0.0 0.0 0.1 0.0
## [5,] 0.0 0.0 0.0 0.1 1.0 0.1 0.0 0.0 0.0 0.1
## [6,] 0.0 0.1 0.0 0.0 0.1 1.0 0.0 0.0 0.0 0.1
## [7,] 0.1 0.1 0.0 0.0 0.0 0.0 1.0 0.1 0.1 0.0
## [8,] 0.0 0.1 0.0 0.0 0.0 0.0 0.1 1.0 0.0 0.0
## [9,] 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 1.0 0.1
## [10,] 0.0 0.1 0.0 0.0 0.1 0.1 0.0 0.0 0.1 1.0
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] NA
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446N= 10
models(N, 500, rho_1_mod =rep(1, N), rho_2_mod = 1/N, p_num = 3, s_alpha_input = 1, s_epsilon_input=0.1)## [[1]]
## [[1]][[1]]
## [1] "Rho_1:"
##
## [[1]][[2]]
## [1] 1 1 1 1 1 1 1 1 1 1
##
##
## [[2]]
## [[2]][[1]]
## [1] "Alpha: "
##
## [[2]][[2]]
## [1] 0.2167549 -0.5424926 0.8911446 0.5959806 1.6356180 0.6892754
## [7] -1.2812466 -0.2131445 1.8965399 1.7768632
##
##
## [[3]]
## [[3]][[1]]
## [1] "Epsilon:"
##
## [[3]][[2]]
## [1] 0.056660450 0.001571945 0.038305734 -0.004513712 0.003435191
## [6] 0.016902677 0.116502684 -0.004420400 -0.010036844 -0.028344457
##
##
## [[4]]
## [[4]][[1]]
## [1] "VAR Matrix:"
##
## [[4]][[2]]
## y1.l1
## y1 " 1.3687531"
## y2 " 3.0484745"
## y3 " 0.8266981"
## y4 " 1.6740627"
## y5 " 1.5398637"
## y6 " 1.8330696"
## y7 " 1.9988444"
## y8 " 1.3687531"
## y9 " 1.5848192"
## y10 " 2.1711621"
## y2.l1
## y1 " NA"
## y2 " NA"
## y3 " NA"
## y4 " NA"
## y5 " NA"
## y6 " NA"
## y7 " NA"
## y8 " NA"
## y9 " NA"
## y10 " NA"
## y3.l1
## y1 " NA"
## y2 " NA"
## y3 " NA"
## y4 " NA"
## y5 " NA"
## y6 " NA"
## y7 " NA"
## y8 " NA"
## y9 " NA"
## y10 " NA"
## y4.l1
## y1 " NA"
## y2 " NA"
## y3 " NA"
## y4 " NA"
## y5 " NA"
## y6 " NA"
## y7 " NA"
## y8 " NA"
## y9 " NA"
## y10 " NA"
## y5.l1
## y1 " NA"
## y2 " NA"
## y3 " NA"
## y4 " NA"
## y5 " NA"
## y6 " NA"
## y7 " NA"
## y8 " NA"
## y9 " NA"
## y10 " NA"
## y6.l1
## y1 " NA"
## y2 " NA"
## y3 " NA"
## y4 " NA"
## y5 " NA"
## y6 " NA"
## y7 " NA"
## y8 " NA"
## y9 " NA"
## y10 " NA"
## y7.l1
## y1 " NA"
## y2 " NA"
## y3 " NA"
## y4 " NA"
## y5 " NA"
## y6 " NA"
## y7 " NA"
## y8 " NA"
## y9 " NA"
## y10 " NA"
## y8.l1
## y1 " NA"
## y2 " NA"
## y3 " NA"
## y4 " NA"
## y5 " NA"
## y6 " NA"
## y7 " NA"
## y8 " NA"
## y9 " NA"
## y10 " NA"
## y9.l1
## y1 " NA"
## y2 " NA"
## y3 " NA"
## y4 " NA"
## y5 " NA"
## y6 " NA"
## y7 " NA"
## y8 " NA"
## y9 " NA"
## y10 " NA"
## y10.l1
## y1 " NA"
## y2 " NA"
## y3 " NA"
## y4 " NA"
## y5 " NA"
## y6 " NA"
## y7 " NA"
## y8 " NA"
## y9 " NA"
## y10 " NA"
## const
## y1 "71979200148756217182585854128561200977763880665088.0000000"
## y2 "39750702199812680686001836019476623066297402392576.0000000"
## y3 " 3039790496037233654515300213939703105310047600640.0000000"
## y4 "84379171214497239082647412878106854549435933786112.0000000"
## y5 "68210941807897077777231602546047799213764714168320.0000000"
## y6 "66078172473703593090697253791443744261732348985344.0000000"
## y7 "42147611390086016414877544019185169611815202586624.0000000"
## y8 "71979200148756217182585854128561200977763880665088.0000000"
## y9 "60722375897819354414493784817422038802861576421376.0000000"
## y10 "24845928998672682503985577959223052972734749343744.0000000"
##
##
## [[5]]
## [[5]][[1]]
## [1] "Adjaceny Matrix:"
##
## [[5]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 1 0 0 0 0 1 0 0 0
## [2,] 1 0 1 1 0 1 1 1 0 1
## [3,] 0 1 0 0 0 0 0 0 0 0
## [4,] 0 1 0 0 1 0 0 0 1 0
## [5,] 0 0 0 1 0 1 0 0 0 1
## [6,] 0 1 0 0 1 0 0 0 0 1
## [7,] 1 1 0 0 0 0 0 1 1 0
## [8,] 0 1 0 0 0 0 1 0 0 0
## [9,] 0 0 0 1 0 0 1 0 0 1
## [10,] 0 1 0 0 1 1 0 0 1 0
##
##
## [[6]]
## [[6]][[1]]
## [1] "Determinant"
##
## [[6]][[2]]
## [1] -8.856118e-29
##
##
## [[7]]
## [[7]][[1]]
## [1] "Rank"
##
## [[7]][[2]]
## [1] 1
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.0000000000001112443
##
##
## [[8]]
## [[8]][[1]]
## [1] "comparison matrix:"
##
## [[8]][[2]]
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 1.0 0.1 0.0 0.0 0.0 0.0 0.1 0.0 0.0 0.0
## [2,] 0.1 1.0 0.1 0.1 0.0 0.1 0.1 0.1 0.0 0.1
## [3,] 0.0 0.1 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
## [4,] 0.0 0.1 0.0 1.0 0.1 0.0 0.0 0.0 0.1 0.0
## [5,] 0.0 0.0 0.0 0.1 1.0 0.1 0.0 0.0 0.0 0.1
## [6,] 0.0 0.1 0.0 0.0 0.1 1.0 0.0 0.0 0.0 0.1
## [7,] 0.1 0.1 0.0 0.0 0.0 0.0 1.0 0.1 0.1 0.0
## [8,] 0.0 0.1 0.0 0.0 0.0 0.0 0.1 1.0 0.0 0.0
## [9,] 0.0 0.0 0.0 0.1 0.0 0.0 0.1 0.0 1.0 0.1
## [10,] 0.0 0.1 0.0 0.0 0.1 0.1 0.0 0.0 0.1 1.0
##
##
## [[9]]
## [[9]][[1]]
## [1] "frobenius norm"
##
## [[9]][[2]]
## [1] NA
##
##
## [[10]]
## [[10]][[1]]
## [1] "rank_of_square"
##
## [[10]][[2]]
## [1] 10
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 0.000000000000002220446We want to lower T and see if T needs to scale with N or N^2.
In the table, I show different \(\rho_1\), sample size \(N\), and values \(t\) configurations. I count “weird” behavior: (1) number of NA columns outputed and (2) number of large coefficients, where the absolute value of the coefficient must be greater than 10 to be flagged as a large coefficients.
Below, we list all possibilities for \(N\), \(t\), and \(\rho_1\):
\(N \in \{4, 10, 20, 25\}\)
\(t(n) \in \{n + 2, n^2 + n +1\}\)
\(\rho_1 \in \{Unif[0.7, 1.3], Unif[.95, 1.05], Unif[-1, 1], N(0, 1)\}\)
The blue highlighted rows indicate rows without any atypical behavior.
For \(N \geq 30\), I am finding that VAR breaks at \(t(n) = N^2 + N + 1\). This is the specific error: Error in VAR(t(Y), p = 1) : NAs in y.
Color coding:
Blue means that there are no NA columns and no coefficients greater than 10.
Green means that there the only NA column is the intercept, and there are no coefficients greater than 10.
Red means that rank of the full matrix Y is less than N, but rank of the \(Y_{n \times n}\) square is full rank.
N_list <- c(4, 10, 20, 25)
p_num_list <- c(1, 3)
rho_1_list <- c("unif_0.7_1.3", "unif_0.95_1.05", "unif_-1_1", "std_normal")
t_type_list <- c("N", "N-squared")
rho_2_mod=0
s_alpha_input = 0
s_epsilon_input = 0
# df of all configurations!
df <- expand.grid(N = N_list,
p_num = p_num_list,
rho_1 = rho_1_list,
t_type = t_type_list,
rho_2 = rho_2_mod,
s_epsilon_input = s_epsilon_input,
t = NA,
NA_cols = NA,
NA_constant = NA,
large_coefs = NA,
det = NA,
rank = NA,
frobenius_norm = NA,
rank_of_square = NA,
s_alpha_input = s_alpha_input)%>%
mutate(t = case_when(t_type== "N" ~ N + 2,
t_type== "N-squared" ~ N^2 + N+ 1,
t_type == "Larger than N-squared" ~ 2*N^2),
id = 1:nrow(.))
# loop over df rows for each specification
for(i in 1:nrow(df)){
set.seed(4)
# compute rho1 values
rho_1_value <- if(df[i, "rho_1"] == "unif_-1_1"){
runif(df[i, "N"], -1, 1)
} else if(df[i, "rho_1"] == "unif_0.95_1.05"){
runif(df[i, "N"], 0.95, 1.05)
} else if(df[i, "rho_1"] == "unif_0.7_1.3"){
runif(df[i, "N"], 0.7, 1.3)
} else if(df[i, "rho_1"] == "std_normal"){
rnorm(df[i, "N"])
}
# get model
mod <- models(n = df[i, "N"], t = df[i, "t"],
rho_1_mod = rho_1_value,
rho_2_mod=df[i, "rho_2"],
p_num = df[i, "p_num"],
s_alpha_input = df[i, "s_alpha_input"],
s_epsilon_input = df[i, "s_epsilon_input"])
m <- mod[[4]][[2]]
class(m) <- "numeric"
# number of large coefficients
df[i, "large_coefs"] <- sum(abs(m)> 10, na.rm = T)
# number of NA columns
df[i, "NA_cols"] <- length(colnames(m)[colSums(is.na(m)) > 0])
# is the constant column = NA, if NA_cols = 1
df[i, "NA_constant"] <- sum(is.na(m[, "const"])) == length(m[, "const"])
# det of Y[1:n, 1:n]
df[i, "det"] <- round(mod[[6]][[2]], 20)
# full Y matrix rank
df[i, "rank"] <- mod[[7]][[2]][1]
# frobenius norm
df[i, "frobenius_norm"] <- round(mod[[9]][[2]], 10)
#
df[i, "rank_of_square"] <- mod[[10]][[2]]
}
df <- df %>%
relocate(N, rho_1, rho_2, t_type, t, p_num, s_epsilon_input, s_alpha_input, NA_cols, NA_constant, rank, det_of_square = det, large_coefs, frobenius_norm, rank_of_square
) %>%
arrange(N, rho_1, rho_2, t_type, t, p_num, s_epsilon_input)
kable(df) %>%
kable_styling() %>%
row_spec(which(df$NA_cols == 0 & df$large_coefs == 0), background = "lightblue") %>%
row_spec(which(df$NA_cols == 1 & df$NA_constant == TRUE), background = "lightgreen") %>%
row_spec(which(df$rank < df$N & df$det_of_square != 0), background = "#ff6242") %>%
scroll_box(height = "500px")| N | rho_1 | rho_2 | t_type | t | p_num | s_epsilon_input | s_alpha_input | NA_cols | NA_constant | rank | det_of_square | large_coefs | frobenius_norm | rank_of_square | id |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | unif_0.7_1.3 | 0 | N | 6 | 1 | 0 | 0 | 0 | FALSE | 4 | 0.0000009 | 0 | 0.0000000 | 4 | 1 |
| 4 | unif_0.7_1.3 | 0 | N | 6 | 3 | 0 | 0 | 0 | FALSE | 4 | -0.0000012 | 0 | 0.0000000 | 4 | 5 |
| 4 | unif_0.7_1.3 | 0 | N-squared | 21 | 1 | 0 | 0 | 0 | FALSE | 4 | 0.0000009 | 0 | 0.0000000 | 4 | 33 |
| 4 | unif_0.7_1.3 | 0 | N-squared | 21 | 3 | 0 | 0 | 0 | FALSE | 4 | -0.0000012 | 0 | 0.0000000 | 4 | 37 |
| 4 | unif_0.95_1.05 | 0 | N | 6 | 1 | 0 | 0 | 1 | TRUE | 4 | 0.0000000 | 0 | 0.0000000 | 4 | 9 |
| 4 | unif_0.95_1.05 | 0 | N | 6 | 3 | 0 | 0 | 1 | TRUE | 4 | 0.0000000 | 0 | 0.0000000 | 4 | 13 |
| 4 | unif_0.95_1.05 | 0 | N-squared | 21 | 1 | 0 | 0 | 0 | FALSE | 4 | 0.0000000 | 0 | 0.0000000 | 4 | 41 |
| 4 | unif_0.95_1.05 | 0 | N-squared | 21 | 3 | 0 | 0 | 0 | FALSE | 4 | 0.0000000 | 0 | 0.0000000 | 4 | 45 |
| 4 | unif_-1_1 | 0 | N | 6 | 1 | 0 | 0 | 0 | FALSE | 4 | 0.0012809 | 0 | 0.0000000 | 4 | 17 |
| 4 | unif_-1_1 | 0 | N | 6 | 3 | 0 | 0 | 0 | FALSE | 4 | -0.0016932 | 0 | 0.0000000 | 4 | 21 |
| 4 | unif_-1_1 | 0 | N-squared | 21 | 1 | 0 | 0 | 0 | FALSE | 4 | 0.0012809 | 0 | 0.0000000 | 4 | 49 |
| 4 | unif_-1_1 | 0 | N-squared | 21 | 3 | 0 | 0 | 0 | FALSE | 4 | -0.0016932 | 0 | 0.0000000 | 4 | 53 |
| 4 | std_normal | 0 | N | 6 | 1 | 0 | 0 | 0 | FALSE | 4 | 0.0288004 | 0 | 0.0000000 | 4 | 25 |
| 4 | std_normal | 0 | N | 6 | 3 | 0 | 0 | 0 | FALSE | 4 | -0.0380704 | 0 | 0.0000000 | 4 | 29 |
| 4 | std_normal | 0 | N-squared | 21 | 1 | 0 | 0 | 0 | FALSE | 4 | 0.0288004 | 0 | 0.0000000 | 4 | 57 |
| 4 | std_normal | 0 | N-squared | 21 | 3 | 0 | 0 | 0 | FALSE | 4 | -0.0380704 | 0 | 0.0000000 | 4 | 61 |
| 10 | unif_0.7_1.3 | 0 | N | 12 | 1 | 0 | 0 | 2 | TRUE | 10 | 0.0000000 | 6 | NA | 10 | 2 |
| 10 | unif_0.7_1.3 | 0 | N | 12 | 3 | 0 | 0 | 2 | TRUE | 10 | 0.0000000 | 4 | NA | 10 | 6 |
| 10 | unif_0.7_1.3 | 0 | N-squared | 111 | 1 | 0 | 0 | 0 | FALSE | 8 | 0.0000000 | 0 | 0.0302869 | 10 | 34 |
| 10 | unif_0.7_1.3 | 0 | N-squared | 111 | 3 | 0 | 0 | 0 | FALSE | 8 | 0.0000000 | 0 | 0.0582593 | 10 | 38 |
| 10 | unif_0.95_1.05 | 0 | N | 12 | 1 | 0 | 0 | 5 | TRUE | 8 | 0.0000000 | 3 | NA | 8 | 10 |
| 10 | unif_0.95_1.05 | 0 | N | 12 | 3 | 0 | 0 | 5 | TRUE | 9 | 0.0000000 | 0 | NA | 8 | 14 |
| 10 | unif_0.95_1.05 | 0 | N-squared | 111 | 1 | 0 | 0 | 1 | TRUE | 10 | 0.0000000 | 0 | 0.0000005 | 8 | 42 |
| 10 | unif_0.95_1.05 | 0 | N-squared | 111 | 3 | 0 | 0 | 1 | TRUE | 10 | 0.0000000 | 0 | 0.0000006 | 8 | 46 |
| 10 | unif_-1_1 | 0 | N | 12 | 1 | 0 | 0 | 0 | FALSE | 10 | 0.0000000 | 0 | 0.0000000 | 10 | 18 |
| 10 | unif_-1_1 | 0 | N | 12 | 3 | 0 | 0 | 0 | FALSE | 10 | 0.0000000 | 0 | 0.0000000 | 10 | 22 |
| 10 | unif_-1_1 | 0 | N-squared | 111 | 1 | 0 | 0 | 0 | FALSE | 10 | 0.0000000 | 0 | 0.0000000 | 10 | 50 |
| 10 | unif_-1_1 | 0 | N-squared | 111 | 3 | 0 | 0 | 0 | FALSE | 10 | 0.0000000 | 0 | 0.0000000 | 10 | 54 |
| 10 | std_normal | 0 | N | 12 | 1 | 0 | 0 | 0 | FALSE | 10 | -0.0000015 | 0 | 0.0000000 | 10 | 26 |
| 10 | std_normal | 0 | N | 12 | 3 | 0 | 0 | 0 | FALSE | 10 | 0.0053755 | 0 | 0.0000000 | 10 | 30 |
| 10 | std_normal | 0 | N-squared | 111 | 1 | 0 | 0 | 0 | FALSE | 3 | -0.0000015 | 22 | 79786769798227680.0000000 | 10 | 58 |
| 10 | std_normal | 0 | N-squared | 111 | 3 | 0 | 0 | 0 | FALSE | 3 | 0.0053755 | 22 | 24716453041559136.0000000 | 10 | 62 |
| 20 | unif_0.7_1.3 | 0 | N | 22 | 1 | 0 | 0 | 10 | TRUE | 14 | 0.0000000 | 16 | NA | 14 | 3 |
| 20 | unif_0.7_1.3 | 0 | N | 22 | 3 | 0 | 0 | 10 | TRUE | 14 | 0.0000000 | 20 | NA | 14 | 7 |
| 20 | unif_0.7_1.3 | 0 | N-squared | 421 | 1 | 0 | 0 | 2 | FALSE | 5 | 0.0000000 | 120 | NA | 14 | 35 |
| 20 | unif_0.7_1.3 | 0 | N-squared | 421 | 3 | 0 | 0 | 2 | FALSE | 5 | 0.0000000 | 123 | NA | 14 | 39 |
| 20 | unif_0.95_1.05 | 0 | N | 22 | 1 | 0 | 0 | 14 | TRUE | 10 | 0.0000000 | 7 | NA | 10 | 11 |
| 20 | unif_0.95_1.05 | 0 | N | 22 | 3 | 0 | 0 | 14 | TRUE | 10 | 0.0000000 | 6 | NA | 10 | 15 |
| 20 | unif_0.95_1.05 | 0 | N-squared | 421 | 1 | 0 | 0 | 5 | TRUE | 14 | 0.0000000 | 46 | NA | 10 | 43 |
| 20 | unif_0.95_1.05 | 0 | N-squared | 421 | 3 | 0 | 0 | 5 | TRUE | 14 | 0.0000000 | 43 | NA | 10 | 47 |
| 20 | unif_-1_1 | 0 | N | 22 | 1 | 0 | 0 | 1 | FALSE | 20 | 0.0000000 | 0 | NA | 20 | 19 |
| 20 | unif_-1_1 | 0 | N | 22 | 3 | 0 | 0 | 1 | FALSE | 20 | 0.0000000 | 0 | NA | 20 | 23 |
| 20 | unif_-1_1 | 0 | N-squared | 421 | 1 | 0 | 0 | 0 | FALSE | 20 | 0.0000000 | 0 | 0.0000000 | 20 | 51 |
| 20 | unif_-1_1 | 0 | N-squared | 421 | 3 | 0 | 0 | 0 | FALSE | 20 | 0.0000000 | 0 | 0.0000000 | 20 | 55 |
| 20 | std_normal | 0 | N | 22 | 1 | 0 | 0 | 1 | FALSE | 18 | 0.0000000 | 0 | NA | 18 | 27 |
| 20 | std_normal | 0 | N | 22 | 3 | 0 | 0 | 1 | FALSE | 18 | 0.0000000 | 0 | NA | 19 | 31 |
| 20 | std_normal | 0 | N-squared | 421 | 1 | 0 | 0 | 1 | FALSE | 1 | 0.0000000 | 83 | NA | 18 | 59 |
| 20 | std_normal | 0 | N-squared | 421 | 3 | 0 | 0 | 1 | FALSE | 1 | 0.0000000 | 83 | NA | 19 | 63 |
| 25 | unif_0.7_1.3 | 0 | N | 27 | 1 | 0 | 0 | 14 | TRUE | 15 | 0.0000000 | 52 | NA | 15 | 4 |
| 25 | unif_0.7_1.3 | 0 | N | 27 | 3 | 0 | 0 | 14 | TRUE | 15 | 0.0000000 | 53 | NA | 15 | 8 |
| 25 | unif_0.7_1.3 | 0 | N-squared | 651 | 1 | 0 | 0 | 3 | FALSE | 4 | 0.0000000 | 224 | NA | 15 | 36 |
| 25 | unif_0.7_1.3 | 0 | N-squared | 651 | 3 | 0 | 0 | 3 | FALSE | 4 | 0.0000000 | 224 | NA | 15 | 40 |
| 25 | unif_0.95_1.05 | 0 | N | 27 | 1 | 0 | 0 | 19 | TRUE | 10 | 0.0000000 | 23 | NA | 10 | 12 |
| 25 | unif_0.95_1.05 | 0 | N | 27 | 3 | 0 | 0 | 19 | TRUE | 10 | 0.0000000 | 13 | NA | 10 | 16 |
| 25 | unif_0.95_1.05 | 0 | N-squared | 651 | 1 | 0 | 0 | 7 | TRUE | 10 | 0.0000000 | 111 | NA | 10 | 44 |
| 25 | unif_0.95_1.05 | 0 | N-squared | 651 | 3 | 0 | 0 | 7 | TRUE | 11 | 0.0000000 | 109 | NA | 10 | 48 |
| 25 | unif_-1_1 | 0 | N | 27 | 1 | 0 | 0 | 5 | TRUE | 25 | 0.0000000 | 2 | NA | 25 | 20 |
| 25 | unif_-1_1 | 0 | N | 27 | 3 | 0 | 0 | 5 | TRUE | 25 | 0.0000000 | 0 | NA | 25 | 24 |
| 25 | unif_-1_1 | 0 | N-squared | 651 | 1 | 0 | 0 | 2 | FALSE | 25 | 0.0000000 | 2 | NA | 25 | 52 |
| 25 | unif_-1_1 | 0 | N-squared | 651 | 3 | 0 | 0 | 2 | FALSE | 25 | 0.0000000 | 0 | NA | 25 | 56 |
| 25 | std_normal | 0 | N | 27 | 1 | 0 | 0 | 4 | FALSE | 19 | 0.0000000 | 11 | NA | 20 | 28 |
| 25 | std_normal | 0 | N | 27 | 3 | 0 | 0 | 4 | FALSE | 20 | 0.0000000 | 12 | NA | 21 | 32 |
| 25 | std_normal | 0 | N-squared | 651 | 1 | 0 | 0 | 3 | FALSE | 1 | 0.0000000 | 145 | NA | 20 | 60 |
| 25 | std_normal | 0 | N-squared | 651 | 3 | 0 | 0 | 3 | FALSE | 1 | 0.0000000 | 145 | NA | 21 | 64 |
Fix \(N=20\), and \(\rho_1 \sim Unif(-1, 1)\). Vary \(\rho_2\) and \(s_{epsilon}\). Try larger \(t\), so include \(t(N) = 2N^2\).
N_list <- c(20)
p_num_list <- c(1, 5, 10, 15)
rho_1_list <- c("unif_-1_1")
rho_2_list <- c("1/N", "unif_-1_1", "zero")
t_type_list <- c("N", "N-squared", "Larger than N-squared")
s_epsilon_list <- c(0.05, 0.1, 0.5)
s_alpha_list <- c(0.05, 0.1, 0.5)
# df of all configurations!
df <- expand.grid(N = N_list,
p_num = p_num_list,
rho_1 = rho_1_list,
t_type = t_type_list,
rho_2 = rho_2_list,
s_epsilon_input = s_epsilon_list,
t = NA,
NA_cols = NA,
NA_constant = NA,
large_coefs = NA,
det = NA,
rank = NA,
frobenius_norm = NA,
rank_of_square = NA,
s_alpha_input = s_alpha_list)%>%
mutate(t = case_when(t_type== "N" ~ N + 2,
t_type== "N-squared" ~ N^2 + N+ 1,
t_type == "Larger than N-squared" ~ 2*N^2),
id = 1:nrow(.))
# loop over df rows for each specification
for(i in 1:nrow(df)){
set.seed(4)
# compute rho1 values
rho_1_value <- if(df[i, "rho_1"] == "unif_-1_1"){
runif(df[i, "N"], -1, 1)
}
set.seed(235)
# compute rho2 values
rho_2_value <- if(df[i, "rho_2"] == "1/N"){
1/(df[i, "N"])
} else if(df[i, "rho_2"] == "unif_-1_1"){
runif(df[i, "N"], -1, 1)
} else if(df[i, "rho_2"] == "zero"){
0
}
# get model
mod <- models(n = df[i, "N"], t = df[i, "t"],
rho_1_mod = rho_1_value,
rho_2_mod=rho_2_value,
p_num = df[i, "p_num"],
s_alpha_input = df[i, "s_alpha_input"],
s_epsilon_input = df[i, "s_epsilon_input"])
m <- mod[[4]][[2]]
class(m) <- "numeric"
# number of large coefficients
df[i, "large_coefs"] <- sum(abs(m)> 10, na.rm = T)
# number of NA columns
df[i, "NA_cols"] <- length(colnames(m)[colSums(is.na(m)) > 0])
# is the constant column = NA, if NA_cols = 1
df[i, "NA_constant"] <- sum(is.na(m[, "const"])) == length(m[, "const"])
# det of Y[1:n, 1:n]
df[i, "det"] <- round(mod[[6]][[2]], 20)
# full Y matrix rank
df[i, "rank"] <- mod[[7]][[2]][1]
df[i, "frobenius_norm"] <- round(mod[[9]][[2]], 10)
df[i, "rank_of_square"] <- mod[[10]][[2]]
}
df <- df %>%
relocate(N, rho_1, rho_2, t_type, t, p_num, s_epsilon_input, s_alpha_input, NA_cols, NA_constant, rank, det_of_square = det, large_coefs, frobenius_norm, rank_of_square) %>%
arrange(N, rho_1, rho_2, t_type, t, p_num, s_epsilon_input)
kable(df) %>%
kable_styling() %>%
row_spec(which(df$NA_cols == 0 & df$large_coefs == 0), background = "lightblue") %>%
row_spec(which(df$NA_cols == 1 & df$NA_constant == TRUE), background = "lightgreen") %>%
row_spec(which(df$rank < 20 & df$det_of_square != 0), background = "#ff6242") %>%
scroll_box(height = "500px")| N | rho_1 | rho_2 | t_type | t | p_num | s_epsilon_input | s_alpha_input | NA_cols | NA_constant | rank | det_of_square | large_coefs | frobenius_norm | rank_of_square | id |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 20 | unif_-1_1 | 1/N | N | 22 | 1 | 0.05 | 0.05 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 1 |
| 20 | unif_-1_1 | 1/N | N | 22 | 1 | 0.05 | 0.10 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 109 |
| 20 | unif_-1_1 | 1/N | N | 22 | 1 | 0.05 | 0.50 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 217 |
| 20 | unif_-1_1 | 1/N | N | 22 | 1 | 0.10 | 0.05 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 37 |
| 20 | unif_-1_1 | 1/N | N | 22 | 1 | 0.10 | 0.10 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 145 |
| 20 | unif_-1_1 | 1/N | N | 22 | 1 | 0.10 | 0.50 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 253 |
| 20 | unif_-1_1 | 1/N | N | 22 | 1 | 0.50 | 0.05 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 73 |
| 20 | unif_-1_1 | 1/N | N | 22 | 1 | 0.50 | 0.10 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 181 |
| 20 | unif_-1_1 | 1/N | N | 22 | 1 | 0.50 | 0.50 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 289 |
| 20 | unif_-1_1 | 1/N | N | 22 | 5 | 0.05 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 0.6613146 | 20 | 2 |
| 20 | unif_-1_1 | 1/N | N | 22 | 5 | 0.05 | 0.10 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 110 |
| 20 | unif_-1_1 | 1/N | N | 22 | 5 | 0.05 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 4.8373843 | 20 | 218 |
| 20 | unif_-1_1 | 1/N | N | 22 | 5 | 0.10 | 0.05 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 38 |
| 20 | unif_-1_1 | 1/N | N | 22 | 5 | 0.10 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 1.2383551 | 20 | 146 |
| 20 | unif_-1_1 | 1/N | N | 22 | 5 | 0.10 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 3.7338946 | 20 | 254 |
| 20 | unif_-1_1 | 1/N | N | 22 | 5 | 0.50 | 0.05 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 74 |
| 20 | unif_-1_1 | 1/N | N | 22 | 5 | 0.50 | 0.10 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 182 |
| 20 | unif_-1_1 | 1/N | N | 22 | 5 | 0.50 | 0.50 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 290 |
| 20 | unif_-1_1 | 1/N | N | 22 | 10 | 0.05 | 0.05 | 3 | TRUE | 20 | 0 | 9 | NA | 20 | 3 |
| 20 | unif_-1_1 | 1/N | N | 22 | 10 | 0.05 | 0.10 | 3 | TRUE | 20 | 0 | 3 | NA | 20 | 111 |
| 20 | unif_-1_1 | 1/N | N | 22 | 10 | 0.05 | 0.50 | 2 | FALSE | 20 | 0 | 0 | NA | 20 | 219 |
| 20 | unif_-1_1 | 1/N | N | 22 | 10 | 0.10 | 0.05 | 3 | TRUE | 20 | 0 | 2 | NA | 20 | 39 |
| 20 | unif_-1_1 | 1/N | N | 22 | 10 | 0.10 | 0.10 | 2 | TRUE | 20 | 0 | 3 | NA | 20 | 147 |
| 20 | unif_-1_1 | 1/N | N | 22 | 10 | 0.10 | 0.50 | 2 | FALSE | 20 | 0 | 0 | NA | 20 | 255 |
| 20 | unif_-1_1 | 1/N | N | 22 | 10 | 0.50 | 0.05 | 3 | TRUE | 20 | 0 | 2 | NA | 20 | 75 |
| 20 | unif_-1_1 | 1/N | N | 22 | 10 | 0.50 | 0.10 | 3 | TRUE | 20 | 0 | 2 | NA | 20 | 183 |
| 20 | unif_-1_1 | 1/N | N | 22 | 10 | 0.50 | 0.50 | 3 | TRUE | 20 | 0 | 8 | NA | 20 | 291 |
| 20 | unif_-1_1 | 1/N | N | 22 | 15 | 0.05 | 0.05 | 2 | FALSE | 20 | 0 | 3 | NA | 20 | 4 |
| 20 | unif_-1_1 | 1/N | N | 22 | 15 | 0.05 | 0.10 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 112 |
| 20 | unif_-1_1 | 1/N | N | 22 | 15 | 0.05 | 0.50 | 2 | FALSE | 20 | 0 | 0 | NA | 20 | 220 |
| 20 | unif_-1_1 | 1/N | N | 22 | 15 | 0.10 | 0.05 | 3 | FALSE | 20 | 0 | 0 | NA | 20 | 40 |
| 20 | unif_-1_1 | 1/N | N | 22 | 15 | 0.10 | 0.10 | 2 | FALSE | 20 | 0 | 0 | NA | 20 | 148 |
| 20 | unif_-1_1 | 1/N | N | 22 | 15 | 0.10 | 0.50 | 2 | FALSE | 20 | 0 | 0 | NA | 20 | 256 |
| 20 | unif_-1_1 | 1/N | N | 22 | 15 | 0.50 | 0.05 | 2 | FALSE | 20 | 0 | 0 | NA | 20 | 76 |
| 20 | unif_-1_1 | 1/N | N | 22 | 15 | 0.50 | 0.10 | 2 | FALSE | 20 | 0 | 0 | NA | 20 | 184 |
| 20 | unif_-1_1 | 1/N | N | 22 | 15 | 0.50 | 0.50 | 4 | TRUE | 20 | 0 | 0 | NA | 20 | 292 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 1 | 0.05 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 2.7709588 | 20 | 5 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 1 | 0.05 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 3.9376323 | 20 | 113 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 1 | 0.05 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 8.7618473 | 20 | 221 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 1 | 0.10 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 2.6635118 | 20 | 41 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 1 | 0.10 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 3.4013977 | 20 | 149 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 1 | 0.10 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 9.8172182 | 20 | 257 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 1 | 0.50 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 11.3455462 | 20 | 77 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 1 | 0.50 | 0.10 | 2 | TRUE | 20 | 0 | 10 | NA | 20 | 185 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 1 | 0.50 | 0.50 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 293 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 5 | 0.05 | 0.05 | 3 | FALSE | 20 | 0 | 9 | NA | 20 | 6 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 5 | 0.05 | 0.10 | 5 | FALSE | 20 | 0 | 12 | NA | 20 | 114 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 5 | 0.05 | 0.50 | 5 | FALSE | 20 | 0 | 11 | NA | 20 | 222 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 5 | 0.10 | 0.05 | 2 | TRUE | 20 | 0 | 3 | NA | 20 | 42 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 5 | 0.10 | 0.10 | 3 | FALSE | 20 | 0 | 13 | NA | 20 | 150 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 5 | 0.10 | 0.50 | 5 | FALSE | 20 | 0 | 11 | NA | 20 | 258 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 5 | 0.50 | 0.05 | 5 | FALSE | 20 | 0 | 13 | NA | 20 | 78 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 5 | 0.50 | 0.10 | 5 | FALSE | 20 | 0 | 12 | NA | 20 | 186 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 5 | 0.50 | 0.50 | 6 | FALSE | 20 | 0 | 4 | NA | 20 | 294 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 10 | 0.05 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 7 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 10 | 0.05 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 115 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 10 | 0.05 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 223 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 10 | 0.10 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 43 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 10 | 0.10 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 151 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 10 | 0.10 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 259 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 10 | 0.50 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 79 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 10 | 0.50 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 187 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 10 | 0.50 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 295 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 15 | 0.05 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 8 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 15 | 0.05 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 116 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 15 | 0.05 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 224 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 15 | 0.10 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 44 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 15 | 0.10 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 152 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 15 | 0.10 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 260 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 15 | 0.50 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 80 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 15 | 0.50 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 188 |
| 20 | unif_-1_1 | 1/N | N-squared | 421 | 15 | 0.50 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 296 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 1 | 0.05 | 0.05 | 0 | FALSE | 20 | 0 | 0 | 0.0000000 | 20 | 9 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 1 | 0.05 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 3.9401541 | 20 | 117 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 1 | 0.05 | 0.50 | 0 | FALSE | 20 | 0 | 0 | 0.0000001 | 20 | 225 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 1 | 0.10 | 0.05 | 0 | FALSE | 20 | 0 | 0 | 0.0000000 | 20 | 45 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 1 | 0.10 | 0.10 | 0 | FALSE | 20 | 0 | 0 | 0.0000000 | 20 | 153 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 1 | 0.10 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 9.8478141 | 20 | 261 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 1 | 0.50 | 0.05 | 0 | FALSE | 20 | 0 | 0 | 0.0000004 | 20 | 81 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 1 | 0.50 | 0.10 | 2 | TRUE | 20 | 0 | 10 | NA | 20 | 189 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 1 | 0.50 | 0.50 | 2 | TRUE | 20 | 0 | 3 | NA | 20 | 297 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 5 | 0.05 | 0.05 | 8 | FALSE | 18 | 0 | 15 | NA | 20 | 10 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 5 | 0.05 | 0.10 | 10 | FALSE | 18 | 0 | 19 | NA | 20 | 118 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 5 | 0.05 | 0.50 | 12 | FALSE | 16 | 0 | 12 | NA | 20 | 226 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 5 | 0.10 | 0.05 | 8 | FALSE | 19 | 0 | 21 | NA | 20 | 46 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 5 | 0.10 | 0.10 | 9 | FALSE | 18 | 0 | 32 | NA | 20 | 154 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 5 | 0.10 | 0.50 | 12 | FALSE | 16 | 0 | 9 | NA | 20 | 262 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 5 | 0.50 | 0.05 | 10 | FALSE | 17 | 0 | 26 | NA | 20 | 82 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 5 | 0.50 | 0.10 | 10 | FALSE | 17 | 0 | 24 | NA | 20 | 190 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 5 | 0.50 | 0.50 | 9 | FALSE | 17 | 0 | 48 | NA | 20 | 298 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 10 | 0.05 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 11 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 10 | 0.05 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 119 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 10 | 0.05 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 227 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 10 | 0.10 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 47 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 10 | 0.10 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 155 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 10 | 0.10 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 263 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 10 | 0.50 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 83 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 10 | 0.50 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 191 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 10 | 0.50 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 299 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 15 | 0.05 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 12 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 15 | 0.05 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 120 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 15 | 0.05 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 228 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 15 | 0.10 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 48 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 15 | 0.10 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 156 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 15 | 0.10 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 264 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 15 | 0.50 | 0.05 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 84 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 15 | 0.50 | 0.10 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 192 |
| 20 | unif_-1_1 | 1/N | Larger than N-squared | 800 | 15 | 0.50 | 0.50 | 19 | FALSE | 1 | 0 | 20 | NA | 20 | 300 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 1 | 0.05 | 0.05 | 2 | TRUE | 20 | 0 | 6 | NA | 20 | 13 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 1 | 0.05 | 0.10 | 2 | TRUE | 20 | 0 | 3 | NA | 20 | 121 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 1 | 0.05 | 0.50 | 2 | TRUE | 20 | 0 | 1 | NA | 20 | 229 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 1 | 0.10 | 0.05 | 2 | TRUE | 20 | 0 | 8 | NA | 20 | 49 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 1 | 0.10 | 0.10 | 2 | TRUE | 20 | 0 | 4 | NA | 20 | 157 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 1 | 0.10 | 0.50 | 2 | TRUE | 20 | 0 | 1 | NA | 20 | 265 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 1 | 0.50 | 0.05 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 85 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 1 | 0.50 | 0.10 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 193 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 1 | 0.50 | 0.50 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 301 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 5 | 0.05 | 0.05 | 0 | FALSE | 20 | 174779628826742 | 0 | 0.0000000 | 20 | 14 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 5 | 0.05 | 0.10 | 0 | FALSE | 20 | 912831846617780 | 0 | 0.0000000 | 20 | 122 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 5 | 0.05 | 0.50 | 0 | FALSE | 20 | 26457921743752324 | 0 | 0.0000000 | 20 | 230 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 5 | 0.10 | 0.05 | 0 | FALSE | 20 | 122698807729861 | 0 | 0.0000000 | 20 | 50 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 5 | 0.10 | 0.10 | 0 | FALSE | 20 | 1133654237882196 | 0 | 0.0000000 | 20 | 158 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 5 | 0.10 | 0.50 | 0 | FALSE | 20 | 15597098976440044 | 0 | 0.0000000 | 20 | 266 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 5 | 0.50 | 0.05 | 0 | FALSE | 20 | -236594831432190 | 0 | 0.0000000 | 20 | 86 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 5 | 0.50 | 0.10 | 0 | FALSE | 20 | -3144991356184264 | 0 | 0.0000000 | 20 | 194 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 5 | 0.50 | 0.50 | 0 | FALSE | 20 | -1042653524898574464 | 0 | 0.0000000 | 20 | 302 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 10 | 0.05 | 0.05 | 2 | FALSE | 20 | 1349514698639787052415057920 | 20 | NA | 20 | 15 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 10 | 0.05 | 0.10 | 2 | FALSE | 20 | -34690370183145396139829755904 | 0 | NA | 20 | 123 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 10 | 0.05 | 0.50 | 2 | FALSE | 20 | -13400655776254564412193941487616 | 0 | NA | 20 | 231 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 10 | 0.10 | 0.05 | 2 | FALSE | 20 | 7685928886070001994821533696 | 12 | NA | 20 | 51 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 10 | 0.10 | 0.10 | 2 | FALSE | 20 | 3489520306177820401151770624 | 8 | NA | 20 | 159 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 10 | 0.10 | 0.50 | 2 | FALSE | 20 | -11349159732121145926759265337344 | 0 | NA | 20 | 267 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 10 | 0.50 | 0.05 | 2 | FALSE | 20 | -81319356264860434028868665344 | 9 | NA | 20 | 87 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 10 | 0.50 | 0.10 | 3 | FALSE | 20 | -19837148176085938531486138368 | 3 | NA | 20 | 195 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 10 | 0.50 | 0.50 | 2 | FALSE | 20 | 531239484577949374192419864576 | 0 | NA | 20 | 303 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 15 | 0.05 | 0.05 | 5 | FALSE | 20 | 1315263720274513362944 | 0 | NA | 20 | 16 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 15 | 0.05 | 0.10 | 5 | FALSE | 20 | 7363862739103922520064 | 0 | NA | 20 | 124 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 15 | 0.05 | 0.50 | 5 | FALSE | 20 | -6816307561624475495563264 | 16 | NA | 20 | 232 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 15 | 0.10 | 0.05 | 5 | FALSE | 20 | -4381711556905592160256 | 1 | NA | 20 | 52 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 15 | 0.10 | 0.10 | 5 | FALSE | 20 | -15568572207239234846720 | 3 | NA | 20 | 160 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 15 | 0.10 | 0.50 | 4 | FALSE | 20 | -670988742611470668267520 | 3 | NA | 20 | 268 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 15 | 0.50 | 0.05 | 5 | FALSE | 20 | 314462311050388021706752 | 7 | NA | 20 | 88 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 15 | 0.50 | 0.10 | 5 | FALSE | 20 | 920850423393833250193408 | 8 | NA | 20 | 196 |
| 20 | unif_-1_1 | unif_-1_1 | N | 22 | 15 | 0.50 | 0.50 | 4 | FALSE | 20 | 20656379502223239577337856 | 3 | NA | 20 | 304 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 1 | 0.05 | 0.05 | 4 | FALSE | 1 | 0 | 90 | NA | 20 | 17 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 1 | 0.05 | 0.10 | 4 | FALSE | 1 | 0 | 90 | NA | 20 | 125 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 1 | 0.05 | 0.50 | 4 | FALSE | 1 | 0 | 90 | NA | 20 | 233 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 1 | 0.10 | 0.05 | 4 | FALSE | 2 | 0 | 90 | NA | 20 | 53 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 1 | 0.10 | 0.10 | 4 | FALSE | 2 | 0 | 90 | NA | 20 | 161 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 1 | 0.10 | 0.50 | 4 | FALSE | 1 | 0 | 90 | NA | 20 | 269 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 1 | 0.50 | 0.05 | 4 | FALSE | 2 | 0 | 90 | NA | 20 | 89 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 1 | 0.50 | 0.10 | 4 | FALSE | 2 | 0 | 90 | NA | 20 | 197 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 1 | 0.50 | 0.50 | 5 | TRUE | 2 | 0 | 84 | NA | 20 | 305 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 5 | 0.05 | 0.05 | 19 | FALSE | 1 | 174779628826742 | 20 | NA | 20 | 18 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 5 | 0.05 | 0.10 | 19 | FALSE | 1 | 912831846617780 | 20 | NA | 20 | 126 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 5 | 0.05 | 0.50 | 19 | FALSE | 1 | 26457921743752324 | 20 | NA | 20 | 234 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 5 | 0.10 | 0.05 | 19 | FALSE | 1 | 122698807729861 | 20 | NA | 20 | 54 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 5 | 0.10 | 0.10 | 19 | FALSE | 1 | 1133654237882196 | 20 | NA | 20 | 162 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 5 | 0.10 | 0.50 | 19 | FALSE | 1 | 15597098976440044 | 20 | NA | 20 | 270 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 5 | 0.50 | 0.05 | 19 | FALSE | 1 | -236594831432190 | 20 | NA | 20 | 90 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 5 | 0.50 | 0.10 | 19 | FALSE | 1 | -3144991356184264 | 20 | NA | 20 | 198 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 5 | 0.50 | 0.50 | 19 | FALSE | 1 | -1042653524898574464 | 20 | NA | 20 | 306 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 10 | 0.05 | 0.05 | 17 | FALSE | 3 | 1349514698639787052415057920 | 23 | NA | 20 | 19 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 10 | 0.05 | 0.10 | 17 | FALSE | 3 | -34690370183145396139829755904 | 23 | NA | 20 | 127 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 10 | 0.05 | 0.50 | 17 | FALSE | 3 | -13400655776254564412193941487616 | 23 | NA | 20 | 235 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 10 | 0.10 | 0.05 | 17 | FALSE | 3 | 7685928886070001994821533696 | 23 | NA | 20 | 55 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 10 | 0.10 | 0.10 | 17 | FALSE | 3 | 3489520306177820401151770624 | 23 | NA | 20 | 163 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 10 | 0.10 | 0.50 | 17 | FALSE | 3 | -11349159732121145926759265337344 | 23 | NA | 20 | 271 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 10 | 0.50 | 0.05 | 17 | FALSE | 3 | -81319356264860434028868665344 | 23 | NA | 20 | 91 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 10 | 0.50 | 0.10 | 17 | FALSE | 3 | -19837148176085938531486138368 | 23 | NA | 20 | 199 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 10 | 0.50 | 0.50 | 17 | FALSE | 3 | 531239484577949374192419864576 | 23 | NA | 20 | 307 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 15 | 0.05 | 0.05 | 18 | FALSE | 2 | 1315263720274513362944 | 20 | NA | 20 | 20 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 15 | 0.05 | 0.10 | 18 | FALSE | 2 | 7363862739103922520064 | 20 | NA | 20 | 128 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 15 | 0.05 | 0.50 | 18 | FALSE | 2 | -6816307561624475495563264 | 20 | NA | 20 | 236 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 15 | 0.10 | 0.05 | 18 | FALSE | 2 | -4381711556905592160256 | 20 | NA | 20 | 56 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 15 | 0.10 | 0.10 | 18 | FALSE | 2 | -15568572207239234846720 | 20 | NA | 20 | 164 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 15 | 0.10 | 0.50 | 18 | FALSE | 2 | -670988742611470668267520 | 20 | NA | 20 | 272 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 15 | 0.50 | 0.05 | 18 | FALSE | 2 | 314462311050388021706752 | 20 | NA | 20 | 92 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 15 | 0.50 | 0.10 | 18 | FALSE | 2 | 920850423393833250193408 | 20 | NA | 20 | 200 |
| 20 | unif_-1_1 | unif_-1_1 | N-squared | 421 | 15 | 0.50 | 0.50 | 18 | FALSE | 2 | 20656379502223239577337856 | 20 | NA | 20 | 308 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 1 | 0.05 | 0.05 | 4 | FALSE | 1 | 0 | 93 | NA | 20 | 21 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 1 | 0.05 | 0.10 | 4 | FALSE | 1 | 0 | 93 | NA | 20 | 129 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 1 | 0.05 | 0.50 | 4 | FALSE | 1 | 0 | 93 | NA | 20 | 237 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 1 | 0.10 | 0.05 | 4 | FALSE | 1 | 0 | 93 | NA | 20 | 57 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 1 | 0.10 | 0.10 | 4 | FALSE | 1 | 0 | 93 | NA | 20 | 165 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 1 | 0.10 | 0.50 | 4 | FALSE | 1 | 0 | 93 | NA | 20 | 273 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 1 | 0.50 | 0.05 | 4 | FALSE | 1 | 0 | 93 | NA | 20 | 93 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 1 | 0.50 | 0.10 | 5 | TRUE | 1 | 0 | 87 | NA | 20 | 201 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 1 | 0.50 | 0.50 | 5 | TRUE | 1 | 0 | 87 | NA | 20 | 309 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 5 | 0.05 | 0.05 | 19 | FALSE | 1 | 174779628826742 | 20 | NA | 20 | 22 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 5 | 0.05 | 0.10 | 19 | FALSE | 1 | 912831846617780 | 20 | NA | 20 | 130 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 5 | 0.05 | 0.50 | 19 | FALSE | 1 | 26457921743752324 | 20 | NA | 20 | 238 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 5 | 0.10 | 0.05 | 19 | FALSE | 1 | 122698807729861 | 20 | NA | 20 | 58 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 5 | 0.10 | 0.10 | 19 | FALSE | 1 | 1133654237882196 | 20 | NA | 20 | 166 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 5 | 0.10 | 0.50 | 19 | FALSE | 1 | 15597098976440044 | 20 | NA | 20 | 274 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 5 | 0.50 | 0.05 | 19 | FALSE | 1 | -236594831432190 | 20 | NA | 20 | 94 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 5 | 0.50 | 0.10 | 19 | FALSE | 1 | -3144991356184264 | 20 | NA | 20 | 202 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 5 | 0.50 | 0.50 | 19 | FALSE | 1 | -1042653524898574464 | 20 | NA | 20 | 310 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 10 | 0.05 | 0.05 | 17 | FALSE | 3 | 1349514698639787052415057920 | 23 | NA | 20 | 23 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 10 | 0.05 | 0.10 | 17 | FALSE | 3 | -34690370183145396139829755904 | 23 | NA | 20 | 131 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 10 | 0.05 | 0.50 | 17 | FALSE | 3 | -13400655776254564412193941487616 | 23 | NA | 20 | 239 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 10 | 0.10 | 0.05 | 17 | FALSE | 3 | 7685928886070001994821533696 | 23 | NA | 20 | 59 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 10 | 0.10 | 0.10 | 17 | FALSE | 3 | 3489520306177820401151770624 | 23 | NA | 20 | 167 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 10 | 0.10 | 0.50 | 17 | FALSE | 3 | -11349159732121145926759265337344 | 23 | NA | 20 | 275 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 10 | 0.50 | 0.05 | 17 | FALSE | 3 | -81319356264860434028868665344 | 23 | NA | 20 | 95 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 10 | 0.50 | 0.10 | 17 | FALSE | 3 | -19837148176085938531486138368 | 23 | NA | 20 | 203 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 10 | 0.50 | 0.50 | 17 | FALSE | 3 | 531239484577949374192419864576 | 23 | NA | 20 | 311 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 15 | 0.05 | 0.05 | 18 | FALSE | 2 | 1315263720274513362944 | 20 | NA | 20 | 24 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 15 | 0.05 | 0.10 | 18 | FALSE | 2 | 7363862739103922520064 | 20 | NA | 20 | 132 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 15 | 0.05 | 0.50 | 18 | FALSE | 2 | -6816307561624475495563264 | 20 | NA | 20 | 240 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 15 | 0.10 | 0.05 | 18 | FALSE | 2 | -4381711556905592160256 | 20 | NA | 20 | 60 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 15 | 0.10 | 0.10 | 18 | FALSE | 2 | -15568572207239234846720 | 20 | NA | 20 | 168 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 15 | 0.10 | 0.50 | 18 | FALSE | 2 | -670988742611470668267520 | 20 | NA | 20 | 276 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 15 | 0.50 | 0.05 | 18 | FALSE | 2 | 314462311050388021706752 | 20 | NA | 20 | 96 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 15 | 0.50 | 0.10 | 18 | FALSE | 2 | 920850423393833250193408 | 20 | NA | 20 | 204 |
| 20 | unif_-1_1 | unif_-1_1 | Larger than N-squared | 800 | 15 | 0.50 | 0.50 | 18 | FALSE | 2 | 20656379502223239577337856 | 20 | NA | 20 | 312 |
| 20 | unif_-1_1 | zero | N | 22 | 1 | 0.05 | 0.05 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 25 |
| 20 | unif_-1_1 | zero | N | 22 | 1 | 0.05 | 0.10 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 133 |
| 20 | unif_-1_1 | zero | N | 22 | 1 | 0.05 | 0.50 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 241 |
| 20 | unif_-1_1 | zero | N | 22 | 1 | 0.10 | 0.05 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 61 |
| 20 | unif_-1_1 | zero | N | 22 | 1 | 0.10 | 0.10 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 169 |
| 20 | unif_-1_1 | zero | N | 22 | 1 | 0.10 | 0.50 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 277 |
| 20 | unif_-1_1 | zero | N | 22 | 1 | 0.50 | 0.05 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 97 |
| 20 | unif_-1_1 | zero | N | 22 | 1 | 0.50 | 0.10 | 4 | TRUE | 20 | 0 | 0 | NA | 20 | 205 |
| 20 | unif_-1_1 | zero | N | 22 | 1 | 0.50 | 0.50 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 313 |
| 20 | unif_-1_1 | zero | N | 22 | 5 | 0.05 | 0.05 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 26 |
| 20 | unif_-1_1 | zero | N | 22 | 5 | 0.05 | 0.10 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 134 |
| 20 | unif_-1_1 | zero | N | 22 | 5 | 0.05 | 0.50 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 242 |
| 20 | unif_-1_1 | zero | N | 22 | 5 | 0.10 | 0.05 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 62 |
| 20 | unif_-1_1 | zero | N | 22 | 5 | 0.10 | 0.10 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 170 |
| 20 | unif_-1_1 | zero | N | 22 | 5 | 0.10 | 0.50 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 278 |
| 20 | unif_-1_1 | zero | N | 22 | 5 | 0.50 | 0.05 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 98 |
| 20 | unif_-1_1 | zero | N | 22 | 5 | 0.50 | 0.10 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 206 |
| 20 | unif_-1_1 | zero | N | 22 | 5 | 0.50 | 0.50 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 314 |
| 20 | unif_-1_1 | zero | N | 22 | 10 | 0.05 | 0.05 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 27 |
| 20 | unif_-1_1 | zero | N | 22 | 10 | 0.05 | 0.10 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 135 |
| 20 | unif_-1_1 | zero | N | 22 | 10 | 0.05 | 0.50 | 3 | TRUE | 20 | 0 | 3 | NA | 20 | 243 |
| 20 | unif_-1_1 | zero | N | 22 | 10 | 0.10 | 0.05 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 63 |
| 20 | unif_-1_1 | zero | N | 22 | 10 | 0.10 | 0.10 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 171 |
| 20 | unif_-1_1 | zero | N | 22 | 10 | 0.10 | 0.50 | 4 | TRUE | 20 | 0 | 1 | NA | 20 | 279 |
| 20 | unif_-1_1 | zero | N | 22 | 10 | 0.50 | 0.05 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 99 |
| 20 | unif_-1_1 | zero | N | 22 | 10 | 0.50 | 0.10 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 207 |
| 20 | unif_-1_1 | zero | N | 22 | 10 | 0.50 | 0.50 | 3 | FALSE | 20 | 0 | 0 | NA | 20 | 315 |
| 20 | unif_-1_1 | zero | N | 22 | 15 | 0.05 | 0.05 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 28 |
| 20 | unif_-1_1 | zero | N | 22 | 15 | 0.05 | 0.10 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 136 |
| 20 | unif_-1_1 | zero | N | 22 | 15 | 0.05 | 0.50 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 244 |
| 20 | unif_-1_1 | zero | N | 22 | 15 | 0.10 | 0.05 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 64 |
| 20 | unif_-1_1 | zero | N | 22 | 15 | 0.10 | 0.10 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 172 |
| 20 | unif_-1_1 | zero | N | 22 | 15 | 0.10 | 0.50 | 3 | TRUE | 20 | 0 | 1 | NA | 20 | 280 |
| 20 | unif_-1_1 | zero | N | 22 | 15 | 0.50 | 0.05 | 4 | TRUE | 20 | 0 | 1 | NA | 20 | 100 |
| 20 | unif_-1_1 | zero | N | 22 | 15 | 0.50 | 0.10 | 4 | TRUE | 20 | 0 | 1 | NA | 20 | 208 |
| 20 | unif_-1_1 | zero | N | 22 | 15 | 0.50 | 0.50 | 3 | TRUE | 20 | 0 | 0 | NA | 20 | 316 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 1 | 0.05 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 2.7034122 | 20 | 29 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 1 | 0.05 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 3.8897351 | 20 | 137 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 1 | 0.05 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 8.6894981 | 20 | 245 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 1 | 0.10 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 2.3496956 | 20 | 65 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 1 | 0.10 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 2.9371840 | 20 | 173 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 1 | 0.10 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 4.9773423 | 20 | 281 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 1 | 0.50 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 7.2708653 | 20 | 101 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 1 | 0.50 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 8.0109095 | 20 | 209 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 1 | 0.50 | 0.50 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 317 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 5 | 0.05 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 2.7713498 | 20 | 30 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 5 | 0.05 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 4.9973577 | 20 | 138 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 5 | 0.05 | 0.50 | 0 | FALSE | 20 | 0 | 0 | 0.0000001 | 20 | 246 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 5 | 0.10 | 0.05 | 0 | FALSE | 20 | 0 | 0 | 0.0000000 | 20 | 66 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 5 | 0.10 | 0.10 | 0 | FALSE | 20 | 0 | 0 | 0.0000000 | 20 | 174 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 5 | 0.10 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 6.6731773 | 20 | 282 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 5 | 0.50 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 5.1483936 | 20 | 102 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 5 | 0.50 | 0.10 | 0 | FALSE | 20 | 0 | 0 | 0.0000001 | 20 | 210 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 5 | 0.50 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 7.6761736 | 20 | 318 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 10 | 0.05 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 9.8894295 | 20 | 31 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 10 | 0.05 | 0.10 | 1 | TRUE | 20 | 0 | 1 | 22.5546575 | 20 | 139 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 10 | 0.05 | 0.50 | 1 | TRUE | 20 | 0 | 3 | 36.3630860 | 20 | 247 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 10 | 0.10 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 8.2727493 | 20 | 67 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 10 | 0.10 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 12.8995062 | 20 | 175 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 10 | 0.10 | 0.50 | 2 | TRUE | 20 | 0 | 2 | NA | 20 | 283 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 10 | 0.50 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 15.1014500 | 20 | 103 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 10 | 0.50 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 16.8070013 | 20 | 211 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 10 | 0.50 | 0.50 | 1 | FALSE | 20 | 0 | 0 | NA | 20 | 319 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 15 | 0.05 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 3.8275313 | 20 | 32 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 15 | 0.05 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 5.1379478 | 20 | 140 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 15 | 0.05 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 9.0698480 | 20 | 248 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 15 | 0.10 | 0.05 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 68 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 15 | 0.10 | 0.10 | 0 | FALSE | 20 | 0 | 0 | 0.0000000 | 20 | 176 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 15 | 0.10 | 0.50 | 1 | FALSE | 20 | 0 | 0 | NA | 20 | 284 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 15 | 0.50 | 0.05 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 104 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 15 | 0.50 | 0.10 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 212 |
| 20 | unif_-1_1 | zero | N-squared | 421 | 15 | 0.50 | 0.50 | 1 | FALSE | 20 | 0 | 0 | NA | 20 | 320 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 1 | 0.05 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 2.7038777 | 20 | 33 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 1 | 0.05 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 3.8907457 | 20 | 141 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 1 | 0.05 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 8.6765368 | 20 | 249 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 1 | 0.10 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 2.3505341 | 20 | 69 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 1 | 0.10 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 2.9385099 | 20 | 177 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 1 | 0.10 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 4.9673734 | 20 | 285 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 1 | 0.50 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 7.2782434 | 20 | 105 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 1 | 0.50 | 0.10 | 1 | FALSE | 20 | 0 | 0 | NA | 20 | 213 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 1 | 0.50 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 4.2620056 | 20 | 321 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 5 | 0.05 | 0.05 | 0 | FALSE | 20 | 0 | 0 | 0.0000000 | 20 | 34 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 5 | 0.05 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 4.9979504 | 20 | 142 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 5 | 0.05 | 0.50 | 0 | FALSE | 20 | 0 | 0 | 0.0000002 | 20 | 250 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 5 | 0.10 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 2.7945227 | 20 | 70 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 5 | 0.10 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 3.6484038 | 20 | 178 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 5 | 0.10 | 0.50 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 286 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 5 | 0.50 | 0.05 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 106 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 5 | 0.50 | 0.10 | 1 | TRUE | 20 | 0 | 0 | 5.2304935 | 20 | 214 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 5 | 0.50 | 0.50 | 1 | TRUE | 20 | 0 | 0 | 7.6760070 | 20 | 322 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 10 | 0.05 | 0.05 | 0 | FALSE | 20 | 0 | 0 | 0.0000000 | 20 | 35 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 10 | 0.05 | 0.10 | 1 | FALSE | 20 | 0 | 0 | NA | 20 | 143 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 10 | 0.05 | 0.50 | 0 | FALSE | 20 | 0 | 0 | 0.0000002 | 20 | 251 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 10 | 0.10 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 8.2752062 | 20 | 71 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 10 | 0.10 | 0.10 | 0 | FALSE | 20 | 0 | 0 | 0.0000000 | 20 | 179 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 10 | 0.10 | 0.50 | 2 | TRUE | 20 | 0 | 2 | NA | 20 | 287 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 10 | 0.50 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 15.1102809 | 20 | 107 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 10 | 0.50 | 0.10 | 0 | FALSE | 20 | 0 | 0 | 0.0000000 | 20 | 215 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 10 | 0.50 | 0.50 | 1 | FALSE | 20 | 0 | 0 | NA | 20 | 323 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 15 | 0.05 | 0.05 | 1 | TRUE | 20 | 0 | 0 | 3.8269902 | 20 | 36 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 15 | 0.05 | 0.10 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 144 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 15 | 0.05 | 0.50 | 2 | FALSE | 20 | 0 | 0 | NA | 20 | 252 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 15 | 0.10 | 0.05 | 1 | FALSE | 20 | 0 | 0 | NA | 20 | 72 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 15 | 0.10 | 0.10 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 180 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 15 | 0.10 | 0.50 | 2 | TRUE | 20 | 0 | 0 | NA | 20 | 288 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 15 | 0.50 | 0.05 | 2 | FALSE | 20 | 0 | 1 | NA | 20 | 108 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 15 | 0.50 | 0.10 | 1 | FALSE | 20 | 0 | 0 | NA | 20 | 216 |
| 20 | unif_-1_1 | zero | Larger than N-squared | 800 | 15 | 0.50 | 0.50 | 1 | FALSE | 20 | 0 | 0 | NA | 20 | 324 |
Two Cross Validated links: How many endogenous variables in a VAR model with 120 observations?
A curated list of Vector Autoregression resources.
I looked into some of the R packages, but didn’t find any that claimed to speed up run time/fix NA problem etc. Also I am not sure exactly what I am looking for.
Note BigVAR not on this list so it might be a bit outdated (posted in 2021).
I found a package called fastVAR but it’s (1) been removed from CRAN and (2) it has not been updated in 10 years so I am suspicious of it Github link. The author was at some point affiliated with Stanford.
– Search for “Basic” since we tried the Lasso Function
– beta is computed using the .lassoVARFistX function
– Y amd Z are preprocessed useing the pre_process function
– this function return beta
– beta is computed using gamloopFista function
– this function calls ’_BigVAR_gamloopFista’ which is a Rcpp (R C++) function
– It doesn’t look like there is an objective function here.
pre_process function– It looks like this transforms the data given whether or not an intercept is included
– Not sure if this would create an issue