# 16-044/III (2016-06-06)

Shelton Peiris, University of Sydney, Australia; Manabu Asai, Soka University, Japan; Michael McAleer, National Tsing Hua University, Taiwan; Erasmus University Rotterdam, the Netherlands; Complutense University of Madrid, Spain
Stochastic volatility, GARCH models, Gegenbauer Polynomial, Long Memory, Spectral Likelihood, Estimation, Forecasting
JEL codes:
C18, C21, C58

In recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the statistical properties of the new model, suggest using the spectral likelihood estimation for long memory processes, and investigate the finite sample properties via Monte Carlo experiments. We apply the model to three exchange rate return series. Overall, the results of the out-of-sample forecasts show the adequacy of the new GLMSV model.