Asymptotic inference for periodic ARCH processes

Abstract

In this paper, we consider the conditional least squares (CLS) estimators for periodic ARCH models (P-ARCH). The CLS estimators applied to the square-transformed P-ARCH model have an explicit form which does not depend on the distribution of the innovation. Since the CLS are not asymptotically efficient in general, we give a necessary and sufficient condition ensuring the asymptotic efficiency of the CLS based on the local asymptotic normality (LAN) approach.