Asymptotic properties of the least squares estimator in periodic ARCH (p) models

Abstract

We study the asymptotic properties of the least squares estimator (LSE) for periodic ARCH (p) (PARCH (p)) models constructed through the periodic  AR representation (PAR) on the squared observations of the PARCH model. After linearization, we show that the LSE is strongly consistent, asymptotically normal, and we investigate their asymptotic properties in stationary and integrated cases (in a periodic sense). The theory is applied to the study of goodness-of-fit tests and specification tests for some restrictions of PARCH models via Wald statistics.