tsDyn (version 0.7-60)

TVECM.sim: Simulation and bootstrap of bivariate VECM/TVECM

Description

Estimate or bootstraps a multivariate Threshold VAR

Usage

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, mean=0, varcov=varcov), varcov=diag(1,k), show.parMat=FALSE)

Arguments

data

matrix of parameter to simulate

B

Matrix of coefficients to simulate

TVECMobject

Object computed by function TVECM() or linear VECM

nthresh

number of threshold (see details)

Thresh

The threshold value(s). Vector of length nthresh

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 inov when default multivariate normal is used.

show.parMat

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

Value

• A matrix with the simulated/bootstraped series.

Details

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

When the parameter matrix is given, on can only simulate a VECM (nthresh=0) or TVECM (nthresh=1 or 2). One can have a specification with constant (default), trend, both or none (see arg include). Order in parameters is ECT/include/lags for VECM and ECT1/include1/lags1/ECT2/include2/lags2 for TVECM.

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 innovations can be given by the user (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. 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 serie 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()

References

TODO

See Also

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

Examples

###reproduce example in Enders 2004, p. 350
#see that:
a<-matrix(c(-0.2, 0.2), ncol=1)
b<-matrix(c(1,-1), nrow=1)
a
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]

#add an intercept as in panel B
b<-TVECM.sim(B=rbind(c(-0.2, 0.1,0,0), c(0.2,0.4, 0,0)), nthresh=0, n=100,beta=1, lag=1,include="const", innov=innov)



##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
all(TVECM.sim(TVECMobject=TVECM(dat, nthresh=1, lag=2, ngridBeta=20, ngridTh=20, plot=FALSE, include="none"),type="check")==dat)