Adaptive Test for Periodicity in Autoregressive Conditional Heteroskedastic Processes

Abstract

This article is concerned with the periodicity testing problem in Autoregressive Conditional Heteroskedastic ARCH process. Adaptive locally asymptotically optimal test is derived, when the innovation density is unspecified but symmetric satisfying only some general technical assumptions, for the null hypothesis of classical ARCH process against an alternative of periodically correlated ARCH dependence. The main technical tool is LeCam's (1960) Local Asymptotic Normality LAN property. The LAN property of the central sequence is shown via the adapted sufficient Swensen's conditions (1985). The performance of the established test is shown via simulation studies.