gmvarkit (version 1.4.1)

Wald_test: Perform Wald test for a GMVAR or SGMVAR model

Description

Wald_test performs a Wald test for a GMVAR or SGMVAR model

Usage

Wald_test(gmvar, A, c, h = 6e-06)
# S3 method for wald
print(x, ..., digits = 4)

Arguments

gmvar

an object of class 'gmvar' created with fitGMVAR or GMVAR.

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.

h

difference used to approximate the derivatives.

x

object of class 'wald' generated by the function Wald_test.

...

other arguments passed to fn

digits

how many significant digits to print?

Value

Returns an object of class \('wald'\) containing the test statistic and the related p-value.

Methods (by generic)

• print: print method

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 gmvar and it is presented in the documentation of the argument params in the function GMVAR (see ?GMVAR).

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

• 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 Unpublished working paper, available as arXiv:2007.04713.

See Also

LR_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 40 seconds to run.
 # Load the data
 data(eurusd, package="gmvarkit")
 data <- cbind(10*eurusd[,1], 100*eurusd[,2])
 colnames(data) <- colnames(eurusd)

 # Structural GMVAR(2, 2), d=2 model identified similarly to Cholesky:
 W22 <- matrix(c(1, NA, 0, 1), nrow=2, byrow=FALSE)
 fit22s <- fitGMVAR(data, p=2, M=2, structural_pars=list(W=W22),
                    ncalls=1, seeds=4)
 fit22s

 # Test whether the lambda parameters (of the second regime) are identical:
 # 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)
# }