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Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Manabu Asai & Michael McAleer & Shelton Peiris, 2017. "Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory," Tinbergen Institute Discussion Papers 17-105/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20170105
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    7. P. de Zea Bermudez & J. Miguel Marín & Helena Veiga, 2020. "Data cloning estimation for asymmetric stochastic volatility models," Econometric Reviews, Taylor & Francis Journals, vol. 39(10), pages 1057-1074, November.
    8. Li, Chenxing & Zhang, Zehua & Zhao, Ran, 2024. "Volatility or higher moments: Which is more important in return density forecasts of stochastic volatility model?," Finance Research Letters, Elsevier, vol. 67(PB).
    9. 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 Polynomial; 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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