Augmented ARCH models for financial time series: stability conditions and empirical evidence

Abstract

The class of conditionally heteroskedastic models known as 'augmented ARCH' encompasses most linear 'ARCH'-type models found in the literature and, in particular, two basic ARCH variants for autocorrelated series: Engle (1982) explains conditional variance by lagged errors, Weiss (1984) also by lagged observations. The framework permits an evaluation of whether the restrictions evolving from the Engle or the Weiss models are valid in practice. Time series of stock market indexes for some major stock exchanges yield empirical examples. In most cases, the statistical approximation to actual dynamic behavior is improved substantially by considering augmented ARCH structures.