Rescaled Range R/S analysis and Hurst Exponents are widely used as emasures of long-term mrmory structures in stochastic processes. Our empirical studies show, however, that these statistics can incorrectly indicate departures from rando walk behavior on short and intermediate time scales when very short-term correlations re present. A modification of rescaled range estimation(R/S analysis) intended to correct bias due to short-term dependencies was proposed by Lo (1991). We show, however, that Lo's R/S statistic is itself baised and introduces other problems, including distortion of the Hurst exonents. We propose a new statistic R/S that corrects for mean bias in the range R, but does not suffer for the short term biases of R/S or Lo's R/S. We support our conclusion with experiments on simulated random walk and AR(1) processes and experiments using high frequency interbank DEM/USD exchange rate quotes. We conclude that the DEM/USD series is mildly trending on time scales of 10 to 100 ticks, and that the mean reversion usggested on these time scales by R/S or R/S analysis is spurious.
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