Adaptive test for periodicity in restrictive EXPAR(p) models

Abstract

Locally asymptotically most stringent test for testing the periodicity in the restricted exponential autoregressive model EXPAR(1) has been constructed by Merzougui et al. This test is generalized here to the restricted EXPAR of order p. On the other hand, we construct a semi-parametric optimal test of periodicity when the innovation density is unknown. The sufficient conditions of the Local Asymptotic Normality (LAN) property are adapted to the periodic model.

Keywords:

• Periodically correlated process
• periodic exponential autoregressive model
• local asymptotic normality (LAN)
• local asymptotic “most stringent” test
• adaptive test

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F12; 62M10

Acknowledgments

The authors would like to thank the anonymous expert for his important comments which gave more insight to the model under consideration and refined the quality of the paper.