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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

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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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 16424.

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Date of creation: 01 Jul 2009
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Handle: RePEc:pra:mprapa:16424

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Related research
Keywords: rescaled range; modified rescaled range; Hurst exponent; long-range dependence; confidence intervals;

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Find related papers by JEL classification:
G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies
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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  1. T. Di Matteo & T. Aste & Michel M. Dacorogna, 2005. "Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development," Econometrics 0503004, EconWPA. [Downloadable!]
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  2. Berg, Lennart & Lyhagen, Johan, 1998. "Short and Long-Run Dependence in Swedish Stock Returns," Applied Financial Economics, Taylor and Francis Journals, vol. 8(4), pages 435-43, August. [Downloadable!] (restricted)
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  3. Paul Eitelman & Justin Vitanza, 2008. "A non-random walk revisited: short- and long-term memory in asset prices," International Finance Discussion Papers 956, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  4. T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor and Francis Journals, vol. 7(1), pages 21-36. [Downloadable!] (restricted)
  5. chin, wencheong, 2008. "Spurious long-range dependence: evidence from Malaysian equity markets," MPRA Paper 7914, University Library of Munich, Germany. [Downloadable!]
  6. Barkoulas, John T & Baum, Christopher F & Travlos, Nickolaos, 2000. "Long Memory in the Greek Stock Market," Applied Financial Economics, Taylor and Francis Journals, vol. 10(2), pages 177-84, April. [Downloadable!] (restricted)
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  7. Lux, Thomas, 2007. "Applications of statistical physics in finance and economics," Economics Working Papers 2007,05, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
  8. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September. [Downloadable!] (restricted)
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  9. Andreas S. Andreou & George A. Zombanakis, 2006. "Computational Intelligence in Exchange-Rate Forecasting," Working Papers 49, Bank of Greece. [Downloadable!]
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This page was last updated on 2009-11-26.

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