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The mis-specification of the expected rescaled adjusted range

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  • Ellis, Craig

Abstract

Rescaled range analysis has regained popularity in the recent econophysics literature as a means of identifying long-term dependence in time-series data. Conclusions derived from the rescaled adjusted range statistic are conditional however upon the choice of an appropriate benchmark against which calculated results can be compared. One recent paper in Physica A by Couillard and Davison [Physica A 348 (2005) 404] concludes that the Anis and Lloyd [Biometrika 63 (1976) 111] model of the expected rescaled adjusted range is more accurate than that proposed by Peters [Fractal Market Analysis, Wiley, New York, 1994]. This finding is contrary to the evidence presented by Peters. This paper reveals significant inconsistencies in the empirical results reported by Peters, which when considered, support the conclusions of Couillard and Davison and explain the apparent contradiction in their results versus those of Peters.

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  • Ellis, Craig, 2006. "The mis-specification of the expected rescaled adjusted range," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 469-476.
    • Handle: RePEc:eee:phsmap:v:363:y:2006:i:2:p:469-476
    DOI: 10.1016/j.physa.2005.08.058
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    References listed on IDEAS

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    1. Graham Newell & Maurice Peat & Max Stevenson, 1996. "Testing for Evidence of Nonlinear Structure in Australian Real Estate Market Returns," Working Paper Series 61, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    2. G. Wenchi Kao & Christopher K. Ma, 1992. "Memories, heteroscedasticity, and price limit in Currency futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 12(6), pages 679-692, December.
    3. Batten, Jonathan & Ellis, Craig, 1996. "Fractal structures and naive trading systems: Evidence from the spot US dollar/Japanese yen," Japan and the World Economy, Elsevier, vol. 8(4), pages 411-421, December.
    4. Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
    5. Brent W. Ambrose & Esther Ancel & Mark D. Griffiths, 1992. "The Fractal Structure of Real Estate Investment Trust Returns: The Search for Evidence of Market Segmentation and Nonlinear Dependency," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 20(1), pages 25-54, March.
    6. Peter W.B. Phillips, 1992. "Analysis," Challenge, Taylor & Francis Journals, vol. 35(1), pages 57-59, January.
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    Cited by:

    1. Howe, John S. & Martin, Deryl W. & WoodJr., Bob G., 1999. "Much ado about nothing: Long-term memory in Pacific Rim equity markets," International Review of Financial Analysis, Elsevier, vol. 8(2), pages 139-151, June.
    2. Batten, Jonathan A. & Ellis, Craig A. & Fethertson, Thomas A., 2008. "Sample period selection and long-term dependence: New evidence from the Dow Jones index," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1126-1140.
    3. Craig Ellis, 1998. "Modelling the Expected Value of the Classical Rescaled Adjusted Range for Long-Term Dependent Series," Working Paper Series 79, Finance Discipline Group, UTS Business School, University of Technology, Sydney.

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