  We examine finite sample performance of the Generalized Covariance (GCov)
residual-based specification test for semiparametric models with i.i.d. errors.
The residual-based multivariate portmanteau test statistic follows
asymptotically a $\chi^2$ distribution when the model is estimated by the GCov
estimator. The test is shown to perform well in application to the univariate
mixed causal-noncausal MAR, double autoregressive (DAR) and multivariate Vector
Autoregressive (VAR) models. We also introduce a bootstrap procedure that
provides the limiting distribution of the test statistic when the specification
test is applied to a model estimated by the maximum likelihood, or the
approximate or quasi-maximum likelihood under a parametric assumption on the
error distribution.
