# 17-105/III (2017-11-03)

Manabu Asai, Soka University, Japan; Michael McAleer, National Tsing Hua University, Taiwan; University of Sydney Business School, Australia; Erasmus University, The Netherlands; Shelton Peiris, School of Mathematics and Statistics University of Sydney, Australia
Stochastic Volatility, Realized Volatility Measure, Long Memory, Gegenbauer Polynomial, Seasonality, Whittle Likelihood
JEL codes:
C18, C21, C58

In recent years fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, we develop a new realized stochastic volatility (RSV) model with general Gegenbauer long memory (GGLM), which encompasses a new RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks apart from the origin in the power spectrum. For estimating the RSV-GGLM model, we suggest estimating the location parameters for the peaks of the power spectrum in the first step, and the remaining parameters based on the Whittle likelihood in the second step. We conduct Monte Carlo experiments for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of RSV-SLM model against the RSV-GGLM model. We apply the RSV-GGLM and RSV-SLM model to three stock market indices. The estimation and forecasting results indicate the adequacy of considering general long memory.