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Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

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  • Asai, M.
  • McAleer, M.J.
  • Peiris, S.

Abstract

In recent years fractionally differenced processes have received a great deal of attention due to their exibility in nancial applications with long memory. In this paper, we develop a new re- alized 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 infor- mation 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 rst step, and the remaining parameters based on the Whittle likelihood in the second step. We conduct Monte Carlo experiments for investigating the nite sample properties of the estimators, with a quasi-likelihood ratio test of RSV-SLM model against theRSV-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.

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  • Asai, M. & McAleer, M.J. & Peiris, S., 2017. "Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory," Econometric Institute Research Papers EI2017-29, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:102576
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    4. Li, Chenxing & Zhang, Zehua & Zhao, Ran, 2023. "Volatility or higher moments: Which is more important in return density forecasts of stochastic volatility model?," MPRA Paper 118459, University Library of Munich, Germany.
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    8. Webel, Karsten, 2022. "A review of some recent developments in the modelling and seasonal adjustment of infra-monthly time series," Discussion Papers 31/2022, Deutsche Bundesbank.
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    More about this item

    Keywords

    Stochastic Volatility; Realized Volatility Measure; Long Memory; Gegenbauer Poly-nomial; Seasonality; Whittle Likelihood;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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