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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.

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Bibliographic Info

Article provided by De Gruyter in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 9 (2005)
Issue (Month): 4 (December)
Pages: 1-43

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Handle: RePEc:bpj:sndecm:v:9:y:2005:i:4:n:1

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Cited by:
  1. 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.
  2. Peter Christoffersen & Kris Dorion & Yintian Wang, 2008. "Volatility Components, Affine Restrictions and Non-Normal Innovations," CREATES Research Papers 2008-10, School of Economics and Management, University of Aarhus.
  3. BAUWENS, Luc & STORTI, Giuseppe, 2007. "A component GARCH model with time varying weights," CORE Discussion Papers 2007019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
  5. Wei, Yu & Wang, Yudong & Huang, Dengshi, 2010. "Forecasting crude oil market volatility: Further evidence using GARCH-class models," Energy Economics, Elsevier, vol. 32(6), pages 1477-1484, November.
  6. Amendola, Alessandra & Storti, Giuseppe, 2008. "A GMM procedure for combining volatility forecasts," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3047-3060, February.
  7. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2008. "Asymmetric multivariate normal mixture GARCH," CFS Working Paper Series 2008/07, Center for Financial Studies (CFS).
  8. Liu, Chun & Maheu, John M., 2012. "Intraday dynamics of volatility and duration: Evidence from Chinese stocks," Pacific-Basin Finance Journal, Elsevier, vol. 20(3), pages 329-348.
  9. William Miles, 2011. "Long-Range Dependence in U.S. Home Price Volatility," The Journal of Real Estate Finance and Economics, Springer, vol. 42(3), pages 329-347, April.
  10. Lin, Xiaoqiang & Fei, Fangyu, 2013. "Long memory revisit in Chinese stock markets: Based on GARCH-class models and multiscale analysis," Economic Modelling, Elsevier, vol. 31(C), pages 265-275.
  11. Chun Liu & John M Maheu, 2010. "Intraday Dynamics of Volatility and Duration: Evidence from the Chinese Stock Market," Working Papers tecipa-401, University of Toronto, Department of Economics.

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