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Econometric estimation in long-range dependent volatility models: Theory and practice

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  • Casas, Isabel
  • Gao, Jiti

Abstract

It is commonly accepted that some financial data may exhibit long-range dependence, while other financial data exhibit intermediate-range dependence or short-range dependence. These behaviors may be fitted to a continuous-time fractional stochastic model. The estimation procedure proposed in this paper is based on a continuous-time version of the Gauss–Whittle objective function to find the parameter estimates that minimize the discrepancy between the spectral density and the data periodogram. As a special case, the proposed estimation procedure is applied to a class of fractional stochastic volatility models to estimate the drift, standard deviation and memory parameters of the volatility process under consideration. As an application, the volatility of the Dow Jones, S&P 500, CAC 40, DAX 30, FTSE 100 and NIKKEI 225 is estimated.

Suggested Citation

  • Casas, Isabel & Gao, Jiti, 2006. "Econometric estimation in long-range dependent volatility models: Theory and practice," MPRA Paper 11981, University Library of Munich, Germany, revised Aug 2007.
    • Handle: RePEc:pra:mprapa:11981
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    7. Zhibiao Zhao & Yiyun Zhang & Runze Li, 2014. "Non-Parametric Estimation Under Strong Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 4-15, January.
    8. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2021. "Exploring volatility of crude oil intra-day return curves: a functional GARCH-X Model," MPRA Paper 109231, University Library of Munich, Germany.
    9. Xu, Weijun & Sun, Qi & Xiao, Weilin, 2012. "A new energy model to capture the behavior of energy price processes," Economic Modelling, Elsevier, vol. 29(5), pages 1585-1591.
    10. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2010. "A two-sample test for comparison of long memory parameters," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2118-2136, October.
    11. Mehmet Ugur & Marco Vivarelli, 2020. "Technology, industrial dynamics and productivity: a critical survey," DISCE - Quaderni del Dipartimento di Politica Economica dipe0011, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).
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    14. Sun, Qi & Xu, Weijun & Xiao, Weilin, 2013. "An empirical estimation for mean-reverting coal prices with long memory," Economic Modelling, Elsevier, vol. 33(C), pages 174-181.

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    More about this item

    Keywords

    Continuous-time model; diffusion process; long-range dependence; stochastic volatility;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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