Testing Second-Order Dynamics for Autoregressive Processes in Presence of Time-Varying Variance

This article considers the volatility modeling for autoregressive univariate time series. A benchmark approach is the stationary autoregressive conditional heteroscedasticity (ARCH) model of Engle. Motivated by real data evidence, processes with nonconstant unconditional variance and ARCH effects have been recently introduced. We take into account this type of nonstationarity in variance and propose simple testing procedures for ARCH effects. Adaptive McLeod and Li’s portmanteau and ARCH-LM tests for checking the presence of such second-order dynamics are provided. The standard versions of these tests, commonly used by practitioners, suppose constant unconditional variance. The failure of these standard tests with time-varying unconditional variance is highlighted. The theoretical results are illustrated by means of simulated and real data. Supplementary materials for this article are available online.