VAR.LR {VAR.etp}

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")