A JOINT PORTMANTEAU TEST FOR CONDITIONAL MEAN AND VARIANCE TIME-SERIES MODELS

In this article, we propose a new joint portmanteau test for checking the specification of parametric conditional mean and variance functions of linear and nonlinear time-series models. The use of a joint test is motivated for complete control of the asymptotic size since marginal tests for the conditional variance may lead to misleading conclusions when the conditional mean is misspecified. The new test is based on an asymptotically distribution-free transformation on the sample autocorrelations of both normalized residuals and squared normalized residuals. This makes it unnecessary to full detail the asymptotic properties of the estimates used to obtain residuals, which could be inefficient two-step ones, avoiding also choices of maximum lag parameters increasing with sample length to control asymptotic size. The robust versions of the new test also properly account for higher-order moment dependence at a reduced cost. The finite-sample performance of the new test is compared with that of well-known tests through simulations.