VAR.LR: The Likelihood Ratio test for parameter restrictions

In VAR.etp: VAR Modelling: Estimation, Testing, and Prediction

The Likelihood Ratio test for parameter restrictions

Description

Likelihood Ratio test for zero parameter restrictions based on system VAR estimation

Bootstrap option is available: iid bootstrap or wild bootstrap

Bootstrap is conducted under the null hypothesis using estimated GLS estimation: see Kim (2014)

Usage

VAR.LR(x, p, restrict0, restrict1, type = "const",bootstrap=0,nb=500)

Arguments

x	data matrix in column
p	VAR order
restrict0	Restriction matrix under H0
restrict1	Restriction matrix under H1, if "full", the full VAR is estimated under H1
type	"const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend
bootstrap	0 for no bootstrap; 1 for iid bootstrap; 2 for wild bootstrap
nb	the number of bootstrap iterations

Details

Restriction matrix is of m by 3 matrix where m is the number of restrictions. A typical row of this matrix (k,i,j), which means that (i,j) element of Ak matrix is set to 0. Ak is a VAR coefficient matrix (k = 1,....p).

The bootstrap test is conducted using the GLS estimation under the parameter restrictions implied by the null hypothesis: see Kim (2014) for details.

Kim (2014) found that the bootstrap based on OLS can show inferior small sample properties.

There are two versions of the bootstrap: the first is based on the iid resampling and the second based on wild bootstrapping.

The Wild bootstrap is conducted with Mammen's two-point distribution.

Value

LRstat	LR test statistic
pval	p-value of the LR test
Boot.pval	p-value of the test based on bootstrapping

Note

See Chapter 4 of Lutkepohl (2005)

Author(s)

Jae H. Kim

References

Lutkepohl, H. 2005, New Introduction to Multiple Time Series Analysis, Springer

Kim, J.H. 2014, Testing for parameter restrictions in a stationary VAR model: a bootstrap alternative. Economic Modelling, 41, 267-273.

Examples

data(dat)
#replicating Table 4.4 of Lutkepohl (2005)
restrict1="full";
restrict0 = rbind(c(4,1,1), c(4,1,2), c(4,1,3), c(4,2,1),
c(4,2,2),c(4,2,3),c(4,3,1),c(4,3,2),c(4,3,3))
VAR.LR(dat,p=4,restrict0,restrict1,type="const")

VAR.etp documentation built on Aug. 31, 2023, 9:08 a.m.