gmvarkit (version 2.1.4)

Wald_test: Perform Wald test for a GMVAR, StMVAR, or G-StMVAR model

Description

Wald_test performs a Wald test for a GMVAR, StMVAR, or G-StMVAR model

Usage

Wald_test(gsmvar, A, c, custom_h = NULL)

Value

A list with class "hypotest" containing the test results and arguments used to calculate the test.

Arguments

gsmvar

an object of class 'gsmvar', typically created with fitGSMVAR or GSMVAR.

A

a size \((k x n_params)\) matrix with full row rank specifying part of the null hypothesis where \(n_params\) is the number of parameters in the (unconstrained) model. See details for more information.

c

a length \(k\) vector specifying part of the null hypothesis. See details for more information.

custom_h

a numeric vector with the same length as x specifying the difference h for each dimension separately. If NULL (default), then the difference 1e-6 used for all but overly large degrees of freedom parameters. For them, the difference is adjusted to avoid numerical problems.

Details

Denoting the true parameter value by \(\theta_{0}\), we test the null hypothesis \(A\theta_{0}=c\). Under the null, the test statistic is asymptotically \(\chi^2\)-distributed with \(k\) (=nrow(A)) degrees of freedom. The parameter \(\theta_{0}\) is assumed to have the same form as in the model supplied in the argument gsmvar and it is presented in the documentation of the argument params in the function GSMVAR (see ?GSMVAR).

Finally, note that this function does not check whether the specified constraints are feasible (e.g. whether the implied constrained model would be stationary or have positive definite error term covariance matrices).

References

• Buse A. (1982). The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note. The American Statistician, 36(3a), 153-157.

See Also

LR_test, Rao_test, fitGSMVAR, GSMVAR, diagnostic_plot, profile_logliks, quantile_residual_tests, cond_moment_plot

Examples

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

 # Test whether the lambda parameters (of the second regime) are identical
 # (due to the zero constraint, the model is identified under the null):
 # fit22s has parameter vector of length 26 with the lambda parameters
 # in elements 24 and 25.
 A <- matrix(c(rep(0, times=23), 1, -1, 0), nrow=1, ncol=26)
 c <- 0
 Wald_test(fit22s, A=A, c=c)

 # Test whether the off-diagonal elements of the first regime's first
 # AR coefficient matrix (A_11) are both zero:
 # fit22s has parameter vector of length 26 and the off-diagonal elements
 # of the 1st regime's 1st AR coefficient matrix are in the elements 6 and 7.
 A <- rbind(c(rep(0, times=5), 1, rep(0, times=20)),
            c(rep(0, times=6), 1, rep(0, times=19)))
 c <- c(0, 0)
 Wald_test(fit22s, A=A, c=c)
# }