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Approximating the Distribution of the R/s Statistic

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  • Denis Conniffe

    (The Economic and Social Research Institute)

  • John E. Spencer

    (The Queen’s University of Belfast)

Abstract

The R/s statistic, used for many years in hydrology, is increasingly employed in economics, although deficiencies in knowledge about its exact distribution have inhibited progress. Harrison and Treacy (1997) described some applications where R/s arises as a test statistic and they derived close to exact critical values for conventional (5 per cent etc.) significance levels for a range of sample values through Monte Carlo simulation. This paper examines two approaches. One is a simple adjustment to the asymptotic distribution that improves its upper tail accuracy greatly and the other is an approximation to the whole distribution, easily computed and suitable for “P-value” calculation, which is also reasonably precise in the upper tail. The Harrison and Treacy values and Monte Carlo simulation are used to confirm accuracy.

Suggested Citation

  • Denis Conniffe & John E. Spencer, 2000. "Approximating the Distribution of the R/s Statistic," The Economic and Social Review, Economic and Social Studies, vol. 31(3), pages 237-248.
    • Handle: RePEc:eso:journl:v:31:y:2000:i:3:p:237-248
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    File URL: http://www.esr.ie/vol31_3/3Conniffe.pdf
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    References listed on IDEAS

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    1. Mandelbrot, Benoit B, 1971. "When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 225-236, August.
    2. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    3. Benoit B. Mandelbrot, 1972. "Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290, National Bureau of Economic Research, Inc.
    4. Michael Harrison & Glenn Treacy, 1997. "On the Small Sample Distribution of the R/S Statistic," Economics Technical Papers 976, Trinity College Dublin, Department of Economics.
    5. Denis Conniffe & John E. Spencer, 1999. "Approximating the Distribution of the Maximum Partial Sum of Normal Deviates," Papers WP102, Economic and Social Research Institute (ESRI).
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    2. Marwan Izzeldin & Anthony Murphy, 2000. "Bootstrapping the Small Sample Critical Values of the Rescaled Range Statistic," The Economic and Social Review, Economic and Social Studies, vol. 31(4), pages 351-359.
    3. Sánchez Granero, M.A. & Trinidad Segovia, J.E. & García Pérez, J., 2008. "Some comments on Hurst exponent and the long memory processes on capital markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5543-5551.

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