LR_test() R function from [sstvars]

Perform likelihood ratio test for a STVAR model

LR_test performs a likelihood ratio test for a STVAR model


LR_test(stvar1, stvar2)

Arguments

stvar1: an object of class 'stvar' generated by fitSTVAR or STVAR, containing the freely estimated model.
stvar2: an object of class 'stvar' generated by fitSTVAR or STVAR, containing the constrained model.

Returns

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

Details

Performs a likelihood ratio test, testing the null hypothesis that the true parameter value lies in the constrained parameter space. Under the null, the test statistic is asymptotically $\chi^2$ -distributed with $k$ degrees of freedom, $k$ being the difference in the dimensions of the unconstrained and constrained parameter spaces.

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

Also, note that this function does not verify that the two models are actually nested.

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:

# Same as the original model but with the location parameter constrained to 1
# (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)))

# Test the null hypothesis of the location parameter equal 1:
LR_test(fit12, fit12w)

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

# Same as the original model but with the mean and AR matrices constrained identical
# across the regimes (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:
LR_test(fit12, fit12cm)

References

Buse A. (1982). The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note. The American Statistician, 36(3a), 153-157.

LR_test function