Stationarity of Gtarch Processes

Abstract

The study of the volatility, present in some time series, provoked the appearance of models with autoregressive conditional heteroscedasticity, called ARCH (ENGLE (1982)).

In order to account for asymmetries in the volatility, RABEMANANJARA & ZAKOIAN (1992) introduced a new formulation for the conditional variance expressing it as a piecewise linear function of past values of the process as well as of past values of the conditional variance itself. The aim of this paper is to study the strong stationarity and the ergodicity of this kind of models, called GTARCH. As a consequence, we obtain, for some concrete models, regions of stationarity for thier coefficients.

Keywords:

• AMS subject classification
• 62G20

Keywords:

• Conditionally heteroscedastic models
• strict stationarity
• ergodicity