Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

Abstract Fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, new realized stochastic volatility (RSV) models are developed: one is a RSV model with general Gegenbauer long memory (GGLM), while the other is a 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, a two step method is suggested: the location parameters for the peaks of the power spectrum are estimated in the first step, while the remaining parameters are estimated based on the Whittle likelihood in the second step. Monte Carlo experiments give results for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of the RSV–SLM model against the RSV–GGLM model. The RSV–GGLM and RSV–SLM models are applied to three stock market indices, for which the estimation and forecasting results indicate the adequacy of considering general long memory.

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