Portmanteau Autocorrelation Tests under <i>q</i>-Dependence and Heteroskedasticity

Abstract

We propose extensions of the Box-Pierce (1970) portmanteau autocorrelation test to allow for two generalisations: (i) time series that exhibit unconditional heteroskedasticity and (ii) to test for the presence of autocorrelation only after a fixed lag q. These extensions involve a generalised quadratic form of the Box-Pierce test that uses the heteroskedasticity autocorrelation consistent (HAC)-type estimator. While we show this modified test is robust to unconditional heteroskedasticity, the resulting power loss may be substantial. We therefore develop feasible weighted tests that make use of nonparametric estimates of the unobserved variance process. Simulation experiments show that the weighted tests have good size and superior power properties over the unweighted tests.