R Under development (unstable) (2024-10-28 r87274 ucrt) -- "Unsuffered Consequences"
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> library(tsDyn)
> library(mnormt)
> suppressWarnings(RNGversion("3.5.3"))
>
> TVECM.boot.check <- tsDyn:::TVECM.boot.check
> options(useFancyQuotes=FALSE) # useful for all.equal comparison
>
> ################################################################
> ######### From man file:
> ################################################################
> #see that:
> a<-matrix(c(-0.2, 0.2), ncol=1)
> b<-matrix(c(1,-1), nrow=1)
> a%*%b
[,1] [,2]
[1,] -0.2 0.2
[2,] 0.2 -0.2
>
> set.seed(123)
> innov<-rmnorm(100, varcov=diag(2))
> vecm1<-TVECM.sim(B=rbind(c(-0.2, 0,0), c(0.2, 0,0)), nthresh=0, beta=1,n=100, lag=1,include="none", innov=innov)
> ECT<-vecm1[,1]-vecm1[,2]
> ECT[1:5]
[1] -0.3302982 1.2900210 -0.8117646 1.2389187 0.5021603
>
> #add an intercept as in panel B
> B2 <- rbind(c(-0.2, 0.1,0,0), c(0.2,0.4, 0,0))
> b<- TVECM.sim(B=B2, nthresh=0, n=100,beta=1, lag=1,include="const", innov=innov, show.parMat=TRUE)
ECT Const Trend L{x1}{1} L{x2}{1}
Equ x1: -0.2 0.1 0 0 0
Equ x2: 0.2 0.4 0 0 0
> b_2 <- VECM.sim(B=B2, n=100,beta=1, lag=1,include="const", innov=innov, show.parMat=TRUE)
ECT Const Trend L{x1}{1} L{x2}{1}
Equ x1: -0.2 0.1 0 0 0
Equ x2: 0.2 0.4 0 0 0
> b[1:5,]
[,1] [,2]
[1,] -0.4604756 0.1698225
[2,] 1.3242923 0.5142713
[3,] 1.3915758 2.7913405
[4,] 2.2324450 1.6463263
[5,] 1.5283684 1.7178881
> all.equal(b, b_2)
[1] TRUE
>
> ## other ways to input beta:
> b_beta_vec <- TVECM.sim(B=B2, nthresh=0, n=100,beta=c(1,-1), lag=1,include="const", innov=innov, show.parMat=TRUE)
ECT Const Trend L{x1}{1} L{x2}{1}
Equ x1: -0.2 0.1 0 0 0
Equ x2: 0.2 0.4 0 0 0
> b_beta_vec_2 <- VECM.sim(B=B2, n=100,beta=c(1,-1), lag=1,include="const", innov=innov, show.parMat=TRUE)
ECT Const Trend L{x1}{1} L{x2}{1}
Equ x1: -0.2 0.1 0 0 0
Equ x2: 0.2 0.4 0 0 0
> b_beta_vec[1:5,]
[,1] [,2]
[1,] -0.4604756 0.1698225
[2,] 1.3242923 0.5142713
[3,] 1.3915758 2.7913405
[4,] 2.2324450 1.6463263
[5,] 1.5283684 1.7178881
> all.equal(b,b_beta_vec)
[1] TRUE
> all.equal(b_beta_vec, b_beta_vec_2)
[1] TRUE
>
> beta_mat <- matrix(c(1,-1), ncol=1)
> b_beta_mat <- TVECM.sim(B=B2, nthresh=0, n=100,beta=beta_mat, lag=1,include="const", innov=innov, show.parMat=TRUE)
ECT Const Trend L{x1}{1} L{x2}{1}
Equ x1: -0.2 0.1 0 0 0
Equ x2: 0.2 0.4 0 0 0
> b_beta_mat[1:5,]
[,1] [,2]
[1,] -0.4604756 0.1698225
[2,] 1.3242923 0.5142713
[3,] 1.3915758 2.7913405
[4,] 2.2324450 1.6463263
[5,] 1.5283684 1.7178881
> all.equal(b,b_beta_mat)
[1] TRUE
>
>
> ########################
> ######## TVECM
> ########################
>
> ##Bootstrap a TVECM with 1 threshold (two regimes)
> data(zeroyld)
> dat<-zeroyld
> TVECMobject<-TVECM(dat, nthresh=1, lag=1, ngridBeta=20, th1=list(exact=-1.195), plot=FALSE)
> tv_1_boot <-TVECM.boot(TVECMobject, seed=123, show.parMat=TRUE)
ECT_low Const_low Trend_low L{x1}{1}_low L{x2}{1}_low ECT_upr
Equ x1: 0.2025264 0.4857667 0 0.2252923 -0.09926611 0.001291099
Equ x2: 0.9575983 1.5929831 0 0.8703592 0.02252604 0.058816293
Const_upr Trend_upr L{x1}{1}_upr L{x2}{1}_upr
Equ x1: 0.004290751 0 -0.02328976 0.06741675
Equ x2: -0.007954949 0 0.16032265 0.14668443
> head(tv_1_boot)
short.run long.run
[1,] 2.1830000 1.57500000
[2,] 2.2460000 1.54500000
[3,] 2.2373746 1.40316599
[4,] 1.6102958 0.94029117
[5,] 1.4410637 0.65045167
[6,] 0.6969609 -0.06715804
>
> ##Check the bootstrap
> TVECM.boot.check(TVECMobject)
[1] TRUE
>
> ## check correspondence bootstrap/simul:
> tv_1_sim <-TVECM.sim(B=tsDyn:::coefMat.nlVar(TVECMobject),beta=TVECMobject$model.specific$beta,
+ Thresh=getTh(TVECMobject), show.parMat=TRUE, innov=matrix(0,200,2))
ECT_low Const_low Trend_low L{x1}{1}_low L{x2}{1}_low ECT_upr
Equ x1: 0.2025264 0.4857667 0 0.2252923 -0.09926611 0.001291099
Equ x2: 0.9575983 1.5929831 0 0.8703592 0.02252604 0.058816293
Const_upr Trend_upr L{x1}{1}_upr L{x2}{1}_upr
Equ x1: 0.004290751 0 -0.02328976 0.06741675
Equ x2: -0.007954949 0 0.16032265 0.14668443
> head(tv_1_boot)
short.run long.run
[1,] 2.1830000 1.57500000
[2,] 2.2460000 1.54500000
[3,] 2.2373746 1.40316599
[4,] 1.6102958 0.94029117
[5,] 1.4410637 0.65045167
[6,] 0.6969609 -0.06715804
>
> tv_1_sim <-TVECM.sim(B=tsDyn:::coefMat.nlVar(TVECMobject),
+ beta=TVECMobject$model.specific$beta,
+ Thresh=getTh(TVECMobject), show.parMat=TRUE)
ECT_low Const_low Trend_low L{x1}{1}_low L{x2}{1}_low ECT_upr
Equ x1: 0.2025264 0.4857667 0 0.2252923 -0.09926611 0.001291099
Equ x2: 0.9575983 1.5929831 0 0.8703592 0.02252604 0.058816293
Const_upr Trend_upr L{x1}{1}_upr L{x2}{1}_upr
Equ x1: 0.004290751 0 -0.02328976 0.06741675
Equ x2: -0.007954949 0 0.16032265 0.14668443
> head(tv_1_boot)
short.run long.run
[1,] 2.1830000 1.57500000
[2,] 2.2460000 1.54500000
[3,] 2.2373746 1.40316599
[4,] 1.6102958 0.94029117
[5,] 1.4410637 0.65045167
[6,] 0.6969609 -0.06715804
>
> ##Bootstrap a TVAR with two threshold (three regimes)
> tv_2_const <- TVECM(dat, lag=1, nthresh=2, plot=FALSE, trace=FALSE, th1=list(exact=-1.312),
+ th2=list(exact=0.774))
> tv_2_none <- TVECM(dat, lag=1, nthresh=2, plot=FALSE, trace=FALSE, th1=list(exact=-1.312),
+ th2=list(exact=0.774), include="none")
> tv_2_trend <- TVECM(dat, lag=1, nthresh=2, plot=FALSE, trace=FALSE, th1=list(exact=-1.312),
+ th2=list(exact=0.774), include="trend")
> tv_2_both <- TVECM(dat, lag=1, nthresh=2, plot=FALSE, trace=FALSE, th1=list(exact=-1.312),
+ th2=list(exact=0.774), ngridBeta=5, include="both")
>
> tv_2_const_common <- TVECM(dat, lag=1, nthresh=2, plot=FALSE, trace=FALSE, th1=list(exact=-1.451),
+ th2=list(exact=0.754), include="const", common="only_ECT")
> tv_2_const_l2 <- TVECM(dat, nthresh=2, lag=2, ngridBeta=5, plot=FALSE, include="none",
+ th1=list(exact=-1.312),th2=list(exact=0.774), trace=FALSE)
>
> TVECM.boot(tv_2_const, show.parMat=TRUE, seed=456)[1:5,]
ECT_low Const_low Trend_low L{x1}{1}_low L{x2}{1}_low ECT_mid
Equ x1: 0.2343191 0.5627267 0 0.2133872 -0.13045497 -0.01031875
Equ x2: 1.1492230 1.9445867 0 0.7652367 0.02490849 0.01991474
Const_mid Trend_mid L{x1}{1}_mid L{x2}{1}_mid ECT_upr
Equ x1: 0.007322243 0 0.09944158 0.06907443 -0.04920032
Equ x2: -0.005735839 0 0.32699066 0.23687489 0.10732160
Const_upr Trend_upr L{x1}{1}_upr L{x2}{1}_upr
Equ x1: 0.06691590 0 -0.11216037 0.04637838
Equ x2: -0.09079342 0 0.08524092 -0.02873180
short.run long.run
[1,] 2.183000 1.575000
[2,] 2.246000 1.545000
[3,] 2.255825 1.664895
[4,] 2.289260 1.701369
[5,] 2.151199 1.412521
> TVECM.boot(tv_2_none, show.parMat=TRUE, seed=456)[1:5,]
ECT_low Const_low Trend_low L{x1}{1}_low L{x2}{1}_low ECT_mid
Equ x1: -0.03252245 0 0 0.3508268 -0.2229371 -0.01855284
Equ x2: 0.17029747 0 0 1.2574671 -0.3689984 -0.02128513
Const_mid Trend_mid L{x1}{1}_mid L{x2}{1}_mid ECT_upr Const_upr
Equ x1: 0 0 0.09248489 0.05361497 0.008401237 0
Equ x2: 0 0 0.25119037 0.19618437 0.061539636 0
Trend_upr L{x1}{1}_upr L{x2}{1}_upr
Equ x1: 0 -0.18027015 0.1024449
Equ x2: 0 0.01649033 0.1198955
short.run long.run
[1,] 2.183000 1.575000
[2,] 2.246000 1.545000
[3,] 2.228665 1.598876
[4,] 2.254419 1.609751
[5,] 2.198737 1.570296
> TVECM.boot(tv_2_trend,show.parMat=TRUE, seed=456)[1:5,]
ECT_low Const_low Trend_low L{x1}{1}_low L{x2}{1}_low ECT_mid
Equ x1: 0.3391893 0 0.002350986 0.07245793 -0.05503711 0
Equ x2: 1.4764723 0 0.007927246 0.30567992 0.26850260 0
Const_mid Trend_mid L{x1}{1}_mid L{x2}{1}_mid ECT_upr
Equ x1: -0.009627084 -1.272937e-05 0.0967326 0 0.07017931
Equ x2: 0.019137028 -2.862608e-05 0.3246202 0 0.23703865
Const_upr Trend_upr L{x1}{1}_upr L{x2}{1}_upr
Equ x1: -0.004106742 1.678226e-05 -0.11558062 0.04875773
Equ x2: 0.080441375 -1.830732e-04 0.08127482 -0.02692949
short.run long.run
[1,] 2.183000 1.575000
[2,] 2.246000 1.545000
[3,] 2.251418 1.638299
[4,] 2.273142 1.657000
[5,] 2.133514 1.377453
> TVECM.boot(tv_2_both, show.parMat=TRUE, seed=456)[1:5,]
ECT_low Const_low Trend_low L{x1}{1}_low L{x2}{1}_low ECT_mid
Equ x1: 0.3344445 -0.1764324 0.002892201 0.06269098 -0.04669461 -0.01913800
Equ x2: 1.4605964 -0.2530547 0.008833043 0.30094440 0.27609545 0.02432369
Const_mid Trend_mid L{x1}{1}_mid L{x2}{1}_mid ECT_upr
Equ x1: 0.0329355255 -1.274667e-04 0.06886216 0.07908553 -0.05978909
Equ x2: 0.0003496974 -2.007436e-05 0.29465882 0.24365050 0.12349362
Const_upr Trend_upr L{x1}{1}_upr L{x2}{1}_upr
Equ x1: 0.09243691 -3.868788e-05 -0.11591998 0.04050465
Equ x2: -0.06383229 -1.475473e-04 0.07572181 -0.02512837
short.run long.run
[1,] 2.183000 1.575000
[2,] 2.246000 1.545000
[3,] 2.265084 1.629432
[4,] 2.303443 1.670040
[5,] 2.166667 1.409473
> try(TVECM.boot(tv_2_const_common, show.parMat=TRUE, seed=456)[1:5,], silent=TRUE)
>
> TVECM.boot.check(tv_2_const)
[1] TRUE
> TVECM.boot.check(tv_2_none)
[1] TRUE
> TVECM.boot.check(tv_2_const_l2)
[1] TRUE
> TVECM.boot.check(tv_2_both)
[1] TRUE
>
> ## does not work:
> TVECM.boot.check(tv_2_trend)
[1] "Component \"short.run\": Mean relative difference: 0.2180451"
[2] "Component \"long.run\": Mean relative difference: 0.1916152"
>
> ###############
> #### p>2
> ###############
>
> data(barry)
>
> ve_r1_l1 <- VECM(barry, lag=1)
> ve_r1_l3 <- VECM(barry, lag=3)
> ve_r2_l3 <- VECM(barry, lag=3, estim="ML", r=2)
>
> TVECM.boot.check(ve_r1_l1)
[1] TRUE
> TVECM.boot.check(ve_r1_l3)
[1] TRUE
> TVECM.boot.check(ve_r2_l3)
[1] TRUE
>
> VECM.boot(ve_r1_l1, show.parMat=TRUE, seed=234)[1:5,]
ECT Const Trend L{x1}{1} L{x2}{1} L{x3}{1}
Equ x1: -0.002537673 0.002202355 0 0.1587853 -0.003002494 0.0001286435
Equ x2: 0.055320874 0.135043876 0 0.5426890 0.483673616 -0.0353661496
Equ x3: 0.179057392 0.157670998 0 0.2897487 0.327296468 -0.0224027426
dolcan cpiUSA cpiCAN
[1,] 0.9993000 27.98000 25.86000
[2,] 0.9956000 28.17000 26.00000
[3,] 0.9836973 28.47662 25.99240
[4,] 1.0075128 28.86076 25.35688
[5,] 1.0154009 28.92388 25.50034
> VECM.boot(ve_r1_l3, show.parMat=TRUE, seed=234)[1:5,]
ECT Const Trend L{x1}{1} L{x2}{1} L{x3}{1}
Equ x1: -0.001338343 0.003662911 0 0.1611940 -0.002242126 0.0003953115
Equ x2: 0.029339845 0.108353256 0 0.8711430 0.468684873 -0.0510243367
Equ x3: 0.133099298 0.100383436 0 0.6925224 0.272239507 -0.0494533196
L{x1}{2} L{x2}{2} L{x3}{2} L{x1}{3} L{x2}{3}
Equ x1: -0.04139589 0.002012077 -0.006607018 0.0202477 -0.002153848
Equ x2: -0.49404335 -0.023189036 0.071589503 -0.3943149 0.007943649
Equ x3: -0.13395315 0.009117886 0.164960151 -0.6081994 0.022337674
L{x3}{3}
Equ x1: -0.0003941692
Equ x2: 0.0928680566
Equ x3: 0.1324489696
dolcan cpiUSA cpiCAN
[1,] 0.9993000 27.98000 25.86000
[2,] 0.9956000 28.17000 26.00000
[3,] 0.9967000 28.44000 26.07000
[4,] 1.0007000 28.63000 26.36000
[5,] 0.9916491 28.93368 26.32038
> VECM.boot(ve_r2_l3, show.parMat=TRUE, seed=234)[1:5,]
ECT ECT Const Trend L{x1}{1} L{x2}{1}
Equ x1: -0.02128737 0.0005968341 0.02324814 0 0.1622498 -0.003419996
Equ x2: -0.05886126 0.0019115449 0.19169805 0 0.8619558 0.462197612
Equ x3: 0.13234280 -0.0025774055 0.10561308 0 0.6225139 0.266045773
L{x3}{1} L{x1}{2} L{x2}{2} L{x3}{2} L{x1}{3}
Equ x1: 0.0006640453 -0.03681695 0.001110734 -0.006387489 0.02526483
Equ x2: -0.0485913611 -0.48826864 -0.028412522 0.073825879 -0.38942643
Equ x3: -0.0476408945 -0.19364163 0.004214840 0.166485918 -0.68004445
L{x2}{3} L{x3}{3}
Equ x1: -0.0036154386 -0.0002821687
Equ x2: -0.0005587153 0.0944265013
Equ x3: 0.0141090720 0.1337360507
dolcan cpiUSA cpiCAN
[1,] 0.9993000 27.98000 25.86000
[2,] 0.9956000 28.17000 26.00000
[3,] 0.9967000 28.44000 26.07000
[4,] 1.0007000 28.63000 26.36000
[5,] 0.9939164 28.94688 26.34743
>
> ################################################################
> ######### Check error message when matrix badly specified:
> ################################################################
>
> B <- matrix(rnorm(14), byrow=TRUE,ncol=7)
>
> ## 0 thresh
> try(a<-TVECM.sim(B=B, beta=1, nthresh=0, n=100, lag=1,show.parMat=TRUE, include="none"))
Matrix B badly specified: should have 3 columns, but has 7
ECT L{x1}{1} L{x2}{1}
Equ x1 NA NA NA
Equ x2 NA NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
> try(a<-TVECM.sim(B=B, beta=1, nthresh=0, n=100, lag=1,show.parMat=TRUE, include="const"))
Matrix B badly specified: should have 4 columns, but has 7
ECT const L{x1}{1} L{x2}{1}
Equ x1 NA NA NA NA
Equ x2 NA NA NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
> try(a<-TVECM.sim(B=B, beta=1, nthresh=0, n=100, lag=1,show.parMat=TRUE, include="both"))
Matrix B badly specified: should have 5 columns, but has 7
ECT const trend L{x1}{1} L{x2}{1}
Equ x1 NA NA NA NA NA
Equ x2 NA NA NA NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
> try(a<-TVECM.sim(B=B, beta=1, nthresh=0, n=100, lag=1,show.parMat=TRUE, include="trend"))
Matrix B badly specified: should have 4 columns, but has 7
ECT trend L{x1}{1} L{x2}{1}
Equ x1 NA NA NA NA
Equ x2 NA NA NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
>
> try(a<-TVECM.sim(B=B, beta=1, nthresh=0, n=100, lag=2,show.parMat=TRUE, include="none"))
Matrix B badly specified: should have 5 columns, but has 7
ECT L{x1}{1} L{x2}{1} L{x1}{2} L{x2}{2}
Equ x1 NA NA NA NA NA
Equ x2 NA NA NA NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
> try(a<-TVECM.sim(B=B, beta=1, nthresh=0, n=100, lag=2,show.parMat=TRUE, include="const"))
Matrix B badly specified: should have 6 columns, but has 7
ECT const L{x1}{1} L{x2}{1} L{x1}{2} L{x2}{2}
Equ x1 NA NA NA NA NA NA
Equ x2 NA NA NA NA NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
>
> ## 1 thresh
> try(a<-TVECM.sim(B=B, beta=1, nthresh=1, Thresh=0, n=100, lag=1,show.parMat=TRUE, include="none"))
Matrix B badly specified: should have 6 columns, but has 7
ECT_low L{x1}{1}_low L{x2}{1}_low ECT_upr L{x1}{1}_upr L{x2}{1}_upr
Equ x1 NA NA NA NA NA NA
Equ x2 NA NA NA NA NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
> try(a<-TVECM.sim(B=B, beta=1, nthresh=1, Thresh=0, n=100, lag=1,show.parMat=TRUE, include="const"))
Matrix B badly specified: should have 8 columns, but has 7
ECT_low const_low L{x1}{1}_low L{x2}{1}_low ECT_upr const_upr
Equ x1 NA NA NA NA NA NA
Equ x2 NA NA NA NA NA NA
L{x1}{1}_upr L{x2}{1}_upr
Equ x1 NA NA
Equ x2 NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
> try(a<-TVECM.sim(B=B, beta=1, nthresh=1, Thresh=0, n=100, lag=1,show.parMat=TRUE, include="both"))
Matrix B badly specified: should have 10 columns, but has 7
ECT_low const_low trend_low L{x1}{1}_low L{x2}{1}_low ECT_upr const_upr
Equ x1 NA NA NA NA NA NA NA
Equ x2 NA NA NA NA NA NA NA
trend_upr L{x1}{1}_upr L{x2}{1}_upr
Equ x1 NA NA NA
Equ x2 NA NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
> try(a<-TVECM.sim(B=B, beta=1, nthresh=1, Thresh=0, n=100, lag=1,show.parMat=TRUE, include="trend"))
Matrix B badly specified: should have 8 columns, but has 7
ECT_low trend_low L{x1}{1}_low L{x2}{1}_low ECT_upr trend_upr
Equ x1 NA NA NA NA NA NA
Equ x2 NA NA NA NA NA NA
L{x1}{1}_upr L{x2}{1}_upr
Equ x1 NA NA
Equ x2 NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
>
> try(a<-TVECM.sim(B=B, beta=1, nthresh=1, Thresh=0, n=100, lag=2,show.parMat=TRUE, include="const"))
Matrix B badly specified: should have 12 columns, but has 7
ECT_low const_low L{x1}{1}_low L{x2}{1}_low L{x1}{2}_low L{x2}{2}_low
Equ x1 NA NA NA NA NA NA
Equ x2 NA NA NA NA NA NA
ECT_upr const_upr L{x1}{1}_upr L{x2}{1}_upr L{x1}{2}_upr L{x2}{2}_upr
Equ x1 NA NA NA NA NA NA
Equ x2 NA NA NA NA NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
>
> ## 2 thresh
> try(a<-TVECM.sim(B=B, beta=1, nthresh=2, Thresh=0, n=100, lag=1,show.parMat=TRUE, include="none"))
Matrix B badly specified: should have 9 columns, but has 7
ECT_low L{x1}{1}_low L{x2}{1}_low ECT_mid L{x1}{1}_mid L{x2}{1}_mid
Equ x1 NA NA NA NA NA NA
Equ x2 NA NA NA NA NA NA
ECT_upr L{x1}{1}_upr L{x2}{1}_upr
Equ x1 NA NA NA
Equ x2 NA NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
> try(a<-TVECM.sim(B=B, beta=1, nthresh=2, Thresh=0, n=100, lag=2,show.parMat=TRUE, include="const"))
Matrix B badly specified: should have 18 columns, but has 7
ECT_low const_low L{x1}{1}_low L{x2}{1}_low L{x1}{2}_low L{x2}{2}_low
Equ x1 NA NA NA NA NA NA
Equ x2 NA NA NA NA NA NA
ECT_mid const_mid L{x1}{1}_mid L{x2}{1}_mid L{x1}{2}_mid L{x2}{2}_mid
Equ x1 NA NA NA NA NA NA
Equ x2 NA NA NA NA NA NA
ECT_upr const_upr L{x1}{1}_upr L{x2}{1}_upr L{x1}{2}_upr L{x2}{2}_upr
Equ x1 NA NA NA NA NA NA
Equ x2 NA NA NA NA NA NA
Error in TVECM.gen(B = B, n = n, lag = lag, include = include, beta = beta, :
>
>
> proc.time()
user system elapsed
3.29 0.56 3.84