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Approximating the Distribution of the R/s Statistic


  • Denis Conniffe

    (Economic and Social Research Institute (ESRI))

  • John E. Spencer

    (The Queen's University of Belfast)


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) have described some applications and addressed distributional problems through Monte Carlo simulation, deriving close to exact significance test points for a range of sample values. But there remain advantages to algebraic approximations to the exact distribution in relaxing restrictions on significance levels or sample sizes and permitting evaluation of ?P-values?. This paper examines two approaches. One is a simple adjustment to the asymptotic distribution (Feller, 1951) that improves its tail accuracy greatly for realistic sample size. The order is an approximation to the whole distribution, suitable for ?P-value? calculation, which is also reasonably precise in the tail. The Harrison and Treacy values and Monte Carlo simulation are used to confirm accuracy.

Suggested Citation

  • Denis Conniffe & John E. Spencer, 1999. "Approximating the Distribution of the R/s Statistic," Papers WP104, Economic and Social Research Institute (ESRI).
  • Handle: RePEc:esr:wpaper:wp104

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    References listed on IDEAS

    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. 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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    Cited by:

    1. 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.
    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.

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