Wald_test | R Documentation |
Wald_test
performs a Wald test for a GMVAR, StMVAR, or G-StMVAR model
Wald_test(gsmvar, A, c, custom_h = NULL)
gsmvar |
an object of class |
A |
a size |
c |
a length |
custom_h |
a numeric vector with the same length as |
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).
A list with class "hypotest" containing the test results and arguments used to calculate the test.
Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.
Virolainen S. 2022. Structural Gaussian mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks. Unpublished working paper, available as arXiv:2007.04713.
Virolainen S. 2022. Gaussian and Student's t mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks in the Euro area. Unpublished working paper, available as arXiv:2109.13648.
@keywords internal
LR_test
, Rao_test
, fitGSMVAR
, GSMVAR
, diagnostic_plot
,
profile_logliks
, quantile_residual_tests
, cond_moment_plot
# 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)
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