  This article proposes omnibus portmanteau tests for contrasting adequacy of
time series models. The test statistics are based on combining the
autocorrelation function of the conditional residuals, the autocorrelation
function of the conditional squared residuals, and the cross-correlation
function between these residuals and their squares. The maximum likelihood
estimator is used to derive the asymptotic distribution of the proposed test
statistics under a general class of time series models, including ARMA, GARCH,
and other nonlinear structures. An extensive Monte Carlo simulation study shows
that the proposed tests successfully control the type I error probability and
tend to have more power than other competitor tests in many scenarios. Two
applications to a set of weekly stock returns for 92 companies from the S&P 500
demonstrate the practical use of the proposed tests.
