Adaptive Test for Periodicity in Self-Exciting Threshold Autoregressive Models

Abstract

This article is devoted to the study of the periodicity testing problem in a self-exciting threshold autoregressive (SETAR) model. The local asymptotic normality (LAN) property is shown via the adapted sufficient conditions due to Swensen (1985). Moreover, the LAN of the central sequence is established. First, we consider the case where the innovation density is specified and we obtain a parametric local asymptotic test. Second, we construct an adaptive test in the case where this density is unspecified but symmetric. The performances of these established tests are shown via simulation studies.

Keywords:

• Adaptive test
• Local Asymptotic Normality
• Local Asymptotic “most stringent” test
• Periodically correlated process
• Periodic self-exciting threshold autoregressive
• Swensen's conditions

Mathematics Subject Classification:

• 62

Acknowledgments

The authors express their deep gratitude to Professor N. Balakrishnan, Editor in Chief, and their profound acknowledgments to the anonymous referee for the helpful suggestions and very constructive comments which improved the quality and readability of the article. The first author thanks Brahim Bentarzi for his encouragement.