HY-A-PARCH: A Stationary A-PARCH Model with Long Memory

Abstract

The FI-A-PARCH process has been developed by Tse (1998) to model essential characteristics of financial market returns. However, due to the nonstationarity described by Níguez (2002) the process exhibits infinite conditional second moments and no statements about the autocovariance function can be derived. Thus, the new Hyperbolic A-PARCH model is considered, first introduced in Schoffer (2003). Subsequently the characteristics of this extension of the FI-A-PARCH process are inspected. It can be shown, that under certain parameter restrictions the intrinsic process as well as the process of conditional volatilities is stationary. Furthermore, for an asymmetric transformation of the conditional volatilities the presence of long memory is proven. Thus, the introduced model is able to reproduce the main characteristics of financial market returns such as volatility clustering, leptokurtosis, asymmetry and long memory.