Simulation and bootstrap of bivariate VECM/TVECM

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Description

Estimate or bootstraps a multivariate Threshold VAR

Usage

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VECM.sim(data, B, VECMobject, beta, n = 200, lag = 1, type = c("simul",
  "boot", "check"), include = c("const", "trend", "none", "both"),
  starting = NULL, innov = rmnorm(n, varcov = varcov), varcov = diag(1,
  k), show.parMat = FALSE, seed)

VECM.boot(VECMobject, show.parMat = FALSE, seed, check = TRUE)

TVECM.boot(TVECMobject, show.parMat = FALSE, seed, check = TRUE)

TVECM.sim(data, B, TVECMobject, nthresh = 1, Thresh, beta, n = 200,
  lag = 1, type = c("simul", "boot", "check"), include = c("const",
  "trend", "none", "both"), starting = NULL, innov = rmnorm(n, varcov =
  varcov), varcov = diag(1, k), show.parMat = FALSE, seed)

Arguments

data

matrix of parameter to simulate

B

Matrix of coefficients to simulate

beta

The cointegrating value

n

Number of observations to create when type="simul"

lag

Number of lags to include in each regime

type

Whether a bootstrap or simulation is to employ. See details

include

Type of deterministic regressors to include. NOT WORKING PROPERLY CURRENTLY if not const

starting

Starting values when a simulation with given parameter matrix is made

innov

Innovations used for simulation. Should be matrix of dim nxk. By default multivariate normal.

varcov

Variance-covariance matrix for the innovations. By default multivariate normal is used.

show.parMat

Logical. Should the parameter matrix be shown? Useful to understand how to give right input

seed

Optional. Seed for the random number generation.

check

When performing a bootstrap replication, check if taking original residuals (instead of resampled) leads to the original data.

TVECMobject,VECMobject

Object computed by function TVECM or linear VECM

nthresh

number of threshold (see details)

Thresh

The threshold value(s). Vector of length nthresh

Details

This function offers the possibility to generate series following a VECM/TVECM from two approaches: bootstrap or simulation. VECM.sim is just a wrapper for TVECM.sim.

When the argument matrix is given, on can only simulate a VECM (nthresh=0) or TVECM (nthresh=1 or 2). One can have a specification with constant ("const"), "trend", "both" or "none" (see argument include). Order for the parameters is ECT/include/lags for VECM and ECT1/include1/lags1/ECT2/include2/lags2 for TVECM. To be sure that once is using it correctly, setting show.parMat = TRUE will show the matrix of parameters together with their values and names.

The argument beta is the contegrating value on the right side of the long-run relationship, and hence the function use the vector (1,-beta). The innov argument specifies the innovations. It should be given as a matrix of dim nxk, (here n does not include the starting values!), by default it uses a multivariate normal distribution, with covariance matrix specified by varcov.

The starting values (of dim lags x k) can be given through argument starting. The user should take care for their choice, since it is not sure that the simulated values will cross the threshold even once. Notice that only one cointegrating value is allowed. User interested in simulating a VECM with more cointegrating values should do use the VAR representation and use TVAR.sim.

The second possibility is to bootstrap series. This is done on a object generated by TVECM (or VECM). A simple residual bootstrap is done, or one can simulate a series with the same parameter matrix and with normal distributed residuals (with variance pre-specified), corresponding to Monte-carlo simulations.

One can alternatively give only the series, and then the function will call internally TVECM.

Value

A matrix with the simulated/bootstraped series.

Author(s)

Matthieu Stigler

See Also

TVECM to estimate a TVECM, VAR.sim to simulate/bootstrap a VAR.

Examples

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###reproduce example in Enders (2004, 2 edition) p. 350,
# (similar example in Enders (2010, 3 edition) 301-302).

if(require(mnormt)){
#see that the full "VAR" coefficient matrix is:
 A <- matrix(c(-0.2, 0.2, 0.2, -0.2), byrow=TRUE, ncol=2)

# but this is not the input of VECM.sim. You should decompose into the a and b matrix:
 a<-matrix(c(-0.2, 0.2), ncol=1)
 b<-matrix(c(1,-1), nrow=1)

# so that:
 a%*%b

# The a matrix is the input under argument B, while the b matrix is under argument beta:
# (the other zeros in B are for the not-specified lags)
 innov<-rmnorm(100, varcov=diag(2))
 startVal <- matrix(0, nrow=2, ncol=1)
 Bvecm <- rbind(c(-0.2, 0,0), c(0.2, 0,0))
 vecm1 <- VECM.sim(B=Bvecm, beta=1,n=100, lag=1,include="none", innov=innov, starting=startVal)
 ECT <- vecm1[,1]-vecm1[,2]

#add an intercept as in panel B
 Bvecm2 <- rbind(c(-0.2, 0.1,0,0), c(0.2,0.4, 0,0))
 vecm2 <- VECM.sim(B=Bvecm2,  n=100,beta=1, lag=1,include="const", innov=innov, starting=startVal)

 par(mfrow=c(2,1))
 plot(vecm1[,1], type="l", main="Panel a: no drift or intercept", ylab="", xlab="")
 lines(vecm1[,2], lty=2)
 plot(vecm2[,1], type="l", main="Panel b: drift terms (0.1)", ylab="", xlab="")
 lines(vecm2[,2], lty=2)
}
##Bootstrap a TVAR with 1 threshold (two regimes)
data(zeroyld)
dat<-zeroyld
TVECMobject<-TVECM(dat, nthresh=1, lag=1, ngridBeta=20, ngridTh=20, plot=FALSE)
TVECM.sim(TVECMobject=TVECMobject,type="boot")

##Check the bootstrap
TVECM.sim.check <- TVECM.sim(TVECMobject=TVECMobject,type="check")
all(TVECM.sim.check==dat)

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