sstvars (version 1.1.6)

Wald_test: Perform Wald test for a STVAR model

Description

Wald_test performs a Wald test for a STVAR model

Usage

Wald_test(stvar, A, c)

Value

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

Arguments

stvar

an object of class 'stvar' generated by fitSTVAR or STVAR, containing the model specified by the alternative hypothesis (i.e., the unconstrained model).

A

a size \((k\times\)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.

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

The test is based on the assumption of the standard result of asymptotic normality! Also note that this function does not check whether the model assumptions hold under the null.

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, fitSTVAR, STVAR, diagnostic_plot, profile_logliks, Portmanteau_test

Examples

 # Logistic Student's t STVAR with p=1, M=2, and the first lag of the second variable
 # as the switching variable (parameter values were obtained by maximum likelihood estimation;
 # fitSTVAR is not used here because the estimation is computationally demanding).
 params12 <- c(0.62906848, 0.14245295, 2.41245785, 0.66719269, 0.3534745, 0.06041779, -0.34909745,
  0.61783824, 0.125769, -0.04094521, -0.99122586, 0.63805416, 0.371575, 0.00314754, 0.03440824,
  1.29072533, -0.06067807, 0.18737385, 1.21813844, 5.00884263, 7.70111672)
 fit12 <- STVAR(data=gdpdef, p=1, M=2, params=params12, weight_function="logistic",
  weightfun_pars=c(2, 1), cond_dist="Student")
 fit12

 # Test whether the location parameter equals 1.
 # For this model, the parameter vector has the length 21 and
 # location parameter is in the 19th element:
 A <- matrix(c(rep(0, times=18), 1, 0, 0), nrow=1, ncol=21)
 c <- 1
 Wald_test(fit12, A=A, c=c)

 # Test whether the intercepts and autoregressive matrices are identical across the regimes:
 # fit12 has parameter vector of length 21. In the first regime, the intercepts are in the
 # elements 1,2 and the AR parameters in the elements 5,...,8. In the second regime,
 # the intercepts are in the elements 3,4, and the AR parameters the elements 9,...,12.
 A <- rbind(cbind(diag(2), -diag(2), matrix(0, nrow=2, ncol=17)), # intercepts
            cbind(matrix(0, nrow=4, ncol=4), diag(4), -diag(4), matrix(0, nrow=4, ncol=9))) # AR
 c <- rep(0, times=6)
 Wald_test(fit12, A=A, c=c)