Long memory in stochastic volatility

Abstract

It is well established that while financial variables such as stock returns are serially uncorrelated over time, their squares are not. The most common way of modeling this serial correlation in volatility is by means of the generalized autoregressive conditional heteroscedasticity (GARCH) class. This chapter provides a long memory stochastic volatility model. Its dynamic properties are derived and shown to be consistent with empirical findings reported in the literature on stock returns. The model is parsimonious and appears to be a viable alternative to the asymmetric power ARCH (A-PARCH) class.