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Can GARCH Models Capture Long-Range Dependence?

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  • Maheu John

    (University of Toronto)

Abstract

This paper investigates if component GARCH models introduced by Engle and Lee(1999) and Ding and Granger(1996) can capture the long-range dependence observed in measures of time-series volatility. Long-range dependence is assessed through the sample autocorrelations, two popular semiparametric estimators of the long-memory parameter, and the parametric fractionally integrated GARCH (FIGARCH) model. Monte Carlo methods are used to characterize the finite sample distributions of these statistics when data are generated from GARCH(1,1), component GARCH and FIGARCH models. For several daily financial return series we find that a two-component GARCH model captures the shape of the autocorrelation function of volatility, and is consistent with long-memory based on semiparametric and parametric estimates. Therefore, GARCH models can in some circumstances account for the long-range dependence found in financial market volatility.

Suggested Citation

  • Maheu John, 2005. "Can GARCH Models Capture Long-Range Dependence?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-43, December.
    • Handle: RePEc:bpj:sndecm:v:9:y:2005:i:4:n:1
    DOI: 10.2202/1558-3708.1269
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    8. Jozef Barunik & Josef Kurka, 2021. "Risks of heterogeneously persistent higher moments," Papers 2104.04264, arXiv.org, revised Mar 2024.
    9. Ahmed, Shamim & Valente, Giorgio, 2015. "Understanding the price of volatility risk in carry trades," Journal of Banking & Finance, Elsevier, vol. 57(C), pages 118-129.
    10. Harris, Richard D.F. & Stoja, Evarist & Yilmaz, Fatih, 2011. "A cyclical model of exchange rate volatility," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 3055-3064, November.
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