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Distinguishing between short and long range dependence: Finite sample properties of rescaled range and modified rescaled range

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  • Kristoufek, Ladislav

Abstract

Mostly used estimators of Hurst exponent for detection of long-range dependence are biased by presence of short-range dependence in the underlying time series. We present confidence intervals estimates for rescaled range and modified rescaled range. We show that the difference in expected values and confidence intervals enables us to use both methods together to clearly distinguish between the two types of processes. The estimates are further applied on Dow Jones Industrial Average between 1944 and 2009 and show that returns do not show any long-range dependence whereas volatility shows both short-range and long-range dependence in the underlying process.

Suggested Citation

  • Kristoufek, Ladislav, 2009. "Distinguishing between short and long range dependence: Finite sample properties of rescaled range and modified rescaled range," MPRA Paper 16424, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:16424
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    1. Gomes, Luís M. P. & Soares, Vasco J. S. & Gama, Sílvio M. A. & Matos, José A. O., 2018. "Long-term memory in Euronext stock indexes returns: an econophysics approach," Business and Economic Horizons (BEH), Prague Development Center, vol. 14(4), pages 862-881, August.

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    More about this item

    Keywords

    rescaled range; modified rescaled range; Hurst exponent; long-range dependence; confidence intervals;
    All these keywords.

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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