fitAutoReg: Vector Autoregressive Model - VAR(p = 1)
Ivan Jacob Agaloos Pesigan
Source:vignettes/var-p1.Rmd
var-p1.RmdGenerate data
set.seed(42)
time <- 1000L
burn_in <- 200L
k <- 3
p <- 1
constant <- c(1, 1, 1)
coef <- matrix(
data = c(
0.4, 0.0, 0.0,
0.0, 0.5, 0.0,
0.0, 0.0, 0.6
),
nrow = k,
byrow = TRUE
)
chol_cov <- chol(diag(3))
dat_p1 <- SimVAR(
time = time,
burn_in = burn_in,
constant = constant,
coef = coef,
chol_cov = chol_cov
)Ordinary Least Squares
Y <- dat_p1_yx$Y
X <- dat_p1_yx$X
FitVAROLS(Y = Y, X = X)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.9084572 0.376670213 0.03481382 0.015427806
#> [2,] 0.9952570 0.002299374 0.51052755 0.002902186
#> [3,] 1.0653119 -0.041211382 0.02013807 0.601902383Lasso Regularization
YStd <- StdMat(dat_p1_yx$Y)
XStd <- StdMat(dat_p1_yx$X[, -1])
lambdas <- LambdaSeq(YStd = YStd, XStd = XStd, n_lambdas = 100)
FitVARLassoSearch(YStd = YStd, XStd = XStd, lambdas = lambdas,
crit = "ebic", max_iter = 1000, tol = 1e-5)
#> [,1] [,2] [,3]
#> [1,] 0.3372619 0.0000000 0.0000000
#> [2,] 0.0000000 0.4718716 0.0000000
#> [3,] 0.0000000 0.0000000 0.5638745Dynr
dynr_model <- ModelVARP1Dynr(data = dat_p1)
coef(
object = dynr_model,
dynr_cook = FitVARDynr(model = dynr_model, hessian_flag = FALSE)
)
#> $constant
#> [1] 0.9099447 0.9914348 1.0581366
#>
#> $coef
#> [,1] [,2] [,3]
#> [1,] 0.37660403 0.03434456 0.015729610
#> [2,] 0.00325585 0.51111108 0.003139214
#> [3,] -0.03962967 0.02120156 0.602733814
#>
#> $cov
#> [,1] [,2] [,3]
#> [1,] 0.990292758 -0.054644587 -0.005531848
#> [2,] -0.054644587 1.010813947 0.006040567
#> [3,] -0.005531848 0.006040567 0.984040302Multiple individuals
n <- 10 # n individuals
dat_p1_mult <- lapply(
X = seq_len(n),
FUN = function(i) {
return(
SimVAR(
time = 1000L,
burn_in = 10,
constant = constant,
coef = coef,
chol_cov = chol_cov
)
)
}
)Single VAR model on the entire data set.
dynr_model <- ModelVARP2Dynr(data = dat_p1_mult)
coef(
object = dynr_model,
dynr_cook = FitVARDynr(model = dynr_model, hessian_flag = FALSE)
)
#> $constant
#> [1] 1.0462309 0.9953261 1.0179085
#>
#> $coef
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.40217196 -0.012849009 -0.007795745 0.006281066 -0.006239730
#> [2,] -0.00682165 0.505751441 -0.011788660 -0.003103103 0.008279539
#> [3,] -0.01854566 0.006197221 0.583717514 -0.001061644 0.017521378
#> [,6]
#> [1,] 0.003882397
#> [2,] 0.007311607
#> [3,] 0.006326369
#>
#> $cov
#> [,1] [,2] [,3]
#> [1,] 0.99881717 0.017241274 -0.016248986
#> [2,] 0.01724127 0.982213749 0.004933834
#> [3,] -0.01624899 0.004933834 0.998348889Multiple VAR models on each individual.
dynr_cook <- FitMLVARDynr(data = dat_p1_mult, p = 2, hessian_flag = FALSE)
dynr_model <- ModelVARP2Dynr(data = dat_p1_mult[[1]])
lapply(
X = dynr_cook,
FUN = function(dynr_cook,
dynr_model) {
coef(
object = dynr_model,
dynr_cook = dynr_cook
)
},
dynr_model = ModelVARP2Dynr(data = dat_p1_mult[[1]])
)
#> [[1]]
#> [[1]]$constant
#> [1] 1.1017634 0.7634997 0.9670509
#>
#> [[1]]$coef
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.36097118 -0.01713410 -0.042502492 0.004367851 0.020536307
#> [2,] -0.01903862 0.51109857 -0.002247776 0.044978193 0.009195141
#> [3,] -0.02660230 0.05839538 0.567272983 -0.005447317 0.017287901
#> [,6]
#> [1,] 0.0310427870
#> [2,] 0.0638127797
#> [3,] -0.0000542151
#>
#> [[1]]$cov
#> [,1] [,2] [,3]
#> [1,] 1.0114534 0.02528320 -0.03518680
#> [2,] 0.0252832 0.98699864 -0.05133939
#> [3,] -0.0351868 -0.05133939 0.97359100
#>
#>
#> [[2]]
#> [[2]]$constant
#> [1] 1.0033993 1.0993408 0.9661149
#>
#> [[2]]$coef
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.423513702 -0.03411393 -0.003712766 0.01439074 -0.031420978
#> [2,] -0.016955314 0.49429593 0.047977376 -0.01516280 0.005647594
#> [3,] 0.005422916 0.03998445 0.588044675 -0.02085193 0.004753246
#> [,6]
#> [1,] 0.014931860
#> [2,] -0.078030388
#> [3,] 0.009803849
#>
#> [[2]]$cov
#> [,1] [,2] [,3]
#> [1,] 0.99019460 -0.01599217 0.02035365
#> [2,] -0.01599217 1.04791966 0.01537336
#> [3,] 0.02035365 0.01537336 0.98573510
#>
#>
#> [[3]]
#> [[3]]$constant
#> [1] 1.0731253 1.0464261 0.9749728
#>
#> [[3]]$coef
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.39419898 0.034788587 0.03524879 0.012620809 -0.055239557 -0.04472302
#> [2,] 0.00139402 0.494954867 -0.00108530 0.023029403 0.009304307 -0.01789489
#> [3,] -0.02312133 -0.008491763 0.57661567 -0.001305735 0.009584453 0.05267844
#>
#> [[3]]$cov
#> [,1] [,2] [,3]
#> [1,] 1.01208388 0.03615487 0.05255972
#> [2,] 0.03615487 0.89524687 -0.02744158
#> [3,] 0.05255972 -0.02744158 1.01995676
#>
#>
#> [[4]]
#> [[4]]$constant
#> [1] 1.0955841 0.9579219 1.0467878
#>
#> [[4]]$coef
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.368264301 -0.03008492 -0.046526228 0.046489811 0.01530563
#> [2,] -0.006035298 0.55316094 0.001634817 -0.004088443 -0.01188639
#> [3,] -0.054025422 0.02373566 0.644006040 0.002229737 0.01291562
#> [,6]
#> [1,] 0.008204661
#> [2,] -0.009020526
#> [3,] -0.074439688
#>
#> [[4]]$cov
#> [,1] [,2] [,3]
#> [1,] 0.99267950 -0.03601439 -0.01794346
#> [2,] -0.03601439 1.01118746 0.02512984
#> [3,] -0.01794346 0.02512984 0.99203419
#>
#>
#> [[5]]
#> [[5]]$constant
#> [1] 1.1230098 0.7289445 1.0865834
#>
#> [[5]]$coef
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.34186273 -0.01996166 0.000643558 0.02548298 0.003957283 -0.01763780
#> [2,] -0.04690538 0.48565824 0.062845154 0.01772940 0.051965057 0.01774022
#> [3,] -0.03399898 -0.02831650 0.583773014 0.03688310 0.014221099 0.01482605
#>
#> [[5]]$cov
#> [,1] [,2] [,3]
#> [1,] 0.960677731 0.029510426 -0.002992873
#> [2,] 0.029510426 0.958748159 -0.006688382
#> [3,] -0.002992873 -0.006688382 1.007289048
#>
#>
#> [[6]]
#> [[6]]$constant
#> [1] 1.014797 1.081760 1.083911
#>
#> [[6]]$coef
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.4270817750 -0.013844690 -0.05401948 0.006247747 0.0068312325
#> [2,] 0.0008373405 0.503101991 -0.04041253 -0.053687015 0.0005065333
#> [3,] 0.0113947394 0.006774978 0.56378127 0.002470871 -0.0094547169
#> [,6]
#> [1,] 0.0381364536
#> [2,] 0.0348464113
#> [3,] -0.0003432213
#>
#> [[6]]$cov
#> [,1] [,2] [,3]
#> [1,] 1.00148500 0.04037216 0.01237155
#> [2,] 0.04037216 0.99416513 0.06312744
#> [3,] 0.01237155 0.06312744 0.94311670
#>
#>
#> [[7]]
#> [[7]]$constant
#> [1] 1.120327 1.013401 1.070235
#>
#> [[7]]$coef
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.44542334 -0.064948349 -0.03353735 -0.04088164 0.02144546 0.016597991
#> [2,] -0.04873178 0.536953103 -0.06295188 0.03588696 -0.05182605 0.046229692
#> [3,] 0.02251002 0.003835118 0.53665477 -0.01522878 0.03173580 0.004814226
#>
#> [[7]]$cov
#> [,1] [,2] [,3]
#> [1,] 1.01830405 0.02442761 -0.07415982
#> [2,] 0.02442761 0.93594437 -0.03664068
#> [3,] -0.07415982 -0.03664068 1.04095910
#>
#>
#> [[8]]
#> [[8]]$constant
#> [1] 1.137525 1.159089 0.913251
#>
#> [[8]]$coef
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.40596772 -7.396216e-05 0.0006065739 -0.01335477 -0.06008688
#> [2,] -0.02245395 4.878523e-01 -0.0010421956 0.03225741 0.00246128
#> [3,] -0.07338679 4.072094e-02 0.5872724646 0.01117234 0.01085849
#> [,6]
#> [1,] 0.003266138
#> [2,] -0.040259607
#> [3,] 0.041918749
#>
#> [[8]]$cov
#> [,1] [,2] [,3]
#> [1,] 1.01682009 0.04521949 -0.05258184
#> [2,] 0.04521949 0.93295083 0.06997025
#> [3,] -0.05258184 0.06997025 1.06046751
#>
#>
#> [[9]]
#> [[9]]$constant
#> [1] 0.8758778 1.0062131 0.9663398
#>
#> [[9]]$coef
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.44219424 0.03190391 0.03581911 -0.017126780 0.01901798 -0.015252033
#> [2,] 0.03762391 0.48711062 -0.02146374 -0.001368921 0.01465021 -0.001774324
#> [3,] 0.03877865 -0.06090510 0.56843929 -0.009729191 0.05944676 0.017721509
#>
#> [[9]]$cov
#> [,1] [,2] [,3]
#> [1,] 0.92184464 0.011662072 -0.020721780
#> [2,] 0.01166207 0.988356978 -0.005038639
#> [3,] -0.02072178 -0.005038639 0.941584282
#>
#>
#> [[10]]
#> [[10]]$constant
#> [1] 0.9422027 1.1603150 1.2124984
#>
#> [[10]]$coef
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.39001207 -0.0067921960 0.02245800 0.003084543 -0.016418828
#> [2,] 0.03611882 0.4857168804 -0.08228752 -0.067336573 0.007828595
#> [3,] -0.05581702 0.0006361164 0.59962708 -0.003292977 -0.002587081
#> [,6]
#> [1,] 0.03019795
#> [2,] 0.03830022
#> [3,] -0.02244364
#>
#> [[10]]$cov
#> [,1] [,2] [,3]
#> [1,] 1.001435739 0.005841893 -0.041826836
#> [2,] 0.005841893 0.987409552 0.008731475
#> [3,] -0.041826836 0.008731475 0.957445319