Joint and Marginal Diagnostic Tests for Conditional Mean and Variance Specifications

This article proposes a general class of joint and marginal diagnostic tests for parametric conditional mean and variance models of possibly nonlinear non-Markovian time series sequences. The use of joint and marginal tests is motivated from the fact that marginal tests for the conditional variance may lead misleading conclusions when the conditional mean is misspecified. The new tests are based on a generalized spectral approach and, contrary to existing procedures, they do not need to choose a lag order depending on the sample size or to smooth the data. Moreover, the proposed tests are robust to higher order dependence of unknown form, in particular to conditional skewness and kurtosis. It turns out that the asymptotic null distributions of the new tests depend on the data generating process, so a new bootstrap procedure is proposed and theoretically justified. A simulation study compares the finite sample performance of the proposed and competing tests and shows that our tests can play a valuable role in time series modeling. Finally, an application to the S&P 500 highlights the merits of our approach.