gmvarkit (version 1.5.0)

LR_test: Perform likelihood ratio test for a GMVAR or SGMVAR model

Description

LR_test performs a likelihood ratio test for a GMVAR or SGMVAR model

Usage

LR_test(gmvar1, gmvar2)

Arguments

gmvar1

an object of class 'gmvar' generated by fitGMVAR or GMVAR, containing the freely estimated model.

gmvar2

an object of class 'gmvar' generated by fitGMVAR or GMVAR, containing the constrained model.

Value

A list with class "htest" containing the following components:

statistic

the value of the likelihood ratio statistics.

parameter

the degrees of freedom of the likelihood ratio statistic.

p.value

the p-value of the test.

alternative

a character string describing the alternative hypothesis.

method

a character string indicating the type of the test (likelihood ratio test).

data.name

a character string giving the names of the supplied models, gsmar1 and gsmar2.

gmvar1

the supplied argument gmvar1

gmvar2

the supplied argument gmvar2

Details

Performs a likelihood ratio test, testing the null hypothesis that the true parameter value lies in the constrained parameter space. Under the null, the test statistic is asymptotically \(\chi^2\)-distributed with \(k\) degrees of freedom, \(k\) being the difference in the dimensions of the unconstrained and constrained parameter spaces.

Note that this function does not verify that the two models are actually nested.

References

• Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.

• Virolainen S. 2020. Structural Gaussian mixture vector autoregressive model. Unpublished working paper, available as arXiv:2007.04713.

@keywords internal

See Also

Wald_test, fitGMVAR, GMVAR, diagnostic_plot, profile_logliks, quantile_residual_tests, cond_moment_plot

Examples

# NOT RUN {
 ## These are long running examples that use parallel computing!
 ## The below examples take around 1 minute to run.

 # Structural GMVAR(2, 2), d=2 model with recursive identification
 W22 <- matrix(c(1, NA, 0, 1), nrow=2, byrow=FALSE)
 fit22s <- fitGMVAR(gdpdef, p=2, M=2, structural_pars=list(W=W22),
                    ncalls=1, seeds=2)

 # The same model but the AR coefficients restricted to be the same
 # in both regimes:
 C_mat <- rbind(diag(2*2^2), diag(2*2^2))
 fit22sc <- fitGMVAR(gdpdef, p=2, M=2, constraints=C_mat,
                     structural_pars=list(W=W22), ncalls=1, seeds=1)

 # Test the AR constraints with likelihood ratio test:
 LR_test(fit22s, fit22sc)
 
# }