QMLE of the General Periodic GARCH Models

Abstract

In this article, we study the necessary and sufficient conditions that guarantee the strict stationarity of general periodic generalized autoregressive conditional heteroskedasticity models (in the periodic sense). We also obtain conditions for the existence of finite higher-order moments under general and tractable assumptions. We propose the quasi-maximum likelihood estimation of general periodic generalized autoregressive conditional heteroskedasticity parameters and derive their asymptotic properties. We demonstrate the strong consistency and asymptotic normality of the quasi-maximum likelihood estimation in special cases.

Key words and phrases. GARCH model and its extension, strict stationarity, QMLE, ergodicity, strong consistency, asymptotic normality.

2010 Mathematics Subject Classification. Primary 62F12 ; Secondary 62M05