Rao_test: Perform Rao's score test for a STVAR model

In sstvars: Toolkit for Reduced Form and Structural Smooth Transition Vector Autoregressive Models

Perform Rao's score test for a STVAR model

Description

Rao_test performs Rao's score test for a STVAR model

Usage

Rao_test(stvar)

Arguments

stvar

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

Details

Tests the constraints imposed in the model given in the argument stvar. This implementation uses the outer product of gradients approximation in the test statistic.

The test is based on the assumption of the standard result of asymptotic normality!

Value

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

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, Wald_test, fitSTVAR, STVAR, diagnostic_plot, profile_logliks, Portmanteau_test

Examples

## These are long running examples that take approximately 10 seconds to run.

# Logistic Student's t STVAR with p=1, M=2, and the first lag of the second variable
# as the switching variable.

## Test whether the location parameter equal 1:

# The model imposing the constraint on the location parameter (parameter values
# were obtained by maximum likelihood estimation; fitSTVAR is not used here
# because the estimation is computationally demanding):
params12w <- c(0.6592583, 0.16162866, 1.7811393, 0.38876396, 0.35499367, 0.0576433,
  -0.43570508, 0.57337706, 0.16449607, -0.01910167, -0.70747014, 0.75386158, 0.3612087,
  0.00241419, 0.03202824, 1.07459924, -0.03432236, 0.14982445, 6.22717097, 8.18575651)
fit12w <- STVAR(data=gdpdef, p=1, M=2, params=params12w, weight_function="logistic",
 weightfun_pars=c(2, 1), cond_dist="Student",
 weight_constraints=list(R=matrix(c(0, 1), nrow=2), r=c(1, 0)))
fit12w

# Test the null hypothesis of the location parameter equal 1:
Rao_test(fit12w)

## Test whether the means and AR matrices are identical across the regimes:

# The model imposing the constraint on the location parameter (parameter values
# were obtained by maximum likelihood estimation; fitSTVAR is not used here
# because the estimation is computationally demanding):
params12cm <- c(0.76892423, 0.67128089, 0.30824474, 0.03530802, -0.11498402, 0.85942541,
 0.39106754, 0.0049437, 0.03897287, 1.44457723, -0.05939876, 0.20885008, 1.23568782,
 6.42128475, 7.28733557)
fit12cm <- STVAR(data=gdpdef, p=1, M=2, params=params12cm, weight_function="logistic",
 weightfun_pars=c(2, 1), parametrization="mean", cond_dist="Student",
 mean_constraints=list(1:2), AR_constraints=rbind(diag(4), diag(4)))

# Test the null hypothesis of the means and AR matrices being identical across the regimes:
Rao_test(fit12cm)

sstvars documentation built on Sept. 16, 2025, 1:09 a.m.