Wald_test() R function from [uGMAR]

Perform Wald test

Wald_test performs a Wald test for a GMAR, StMAR, or G-StMAR model.


Wald_test(gsmar, A, c, h = 6e-06)

Arguments

gsmar: a class 'gsmar' object, typically generated by fitGSMAR or GSMAR.
A: a size $(k x n_params)$ matrix with full row rank specifying a 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 a part of the null hypothesis. See details for more information.
h: the difference used to approximate the derivatives.

Returns

A list with class "htest" containing the following components: - statistic: the value of the Wald statistics.

parameter: the degrees of freedom of the Wald 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 (Wald test).
data.name: a character string giving the names of the supplied model, constraint matrix A, and vector c.
gsmar: the supplied argument gsmar.
A: the supplied argument A.
c: the supplied argument c.
h: the supplied argument h.

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

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).

Examples


# GMAR p=1, M=2 model:
fit12 <- fitGSMAR(simudata, p=1, M=2, model="GMAR", ncalls=1, seeds=1)

# Test with Wald test whether the AR coefficients are the same in both
# regimes:
# There are 7 parameters in the model and the AR coefficient of the
# first regime is the 2nd element, whereas the AR coefficient of the second
# regime is in the 5th element.
A <- matrix(c(0, 1, 0, 0, -1, 0, 0), nrow=1, ncol=7)
c <- 0
Wald_test(fit12, A=A, c=c)

References

Kalliovirta L., Meitz M. and Saikkonen P. 2015. Gaussian Mixture Autoregressive model for univariate time series. Journal of Time Series Analysis, 36 (2), 247-266.
Meitz M., Preve D., Saikkonen P. 2023. A mixture autoregressive model based on Student's t-distribution. Communications in Statistics - Theory and Methods, 52 (2), 499-515.
Virolainen S. 2022. A mixture autoregressive model based on Gaussian and Student's t-distributions. Studies in Nonlinear Dynamics & Econometrics, 26 (4) 559-580.

Wald_test function