Improved finite‐sample Hurst exponent estimates using rescaled range analysis

Abstract

Rescaled range analysis is one of the classical methods used for detecting and quantifying long‐term dependence in time series. However, rescaled range analysis has been shown in several studies to give biased estimates of the Hurst exponent in finite samples. A new estimator based on a modified expression of the expected value of the rescaled range is proposed. A comparison of the modified estimator with other alternatives shows that the modified estimator offers a great improvement over the classical rescaled range estimator in terms of bias and root mean square error, which makes it comparable to some of the leading estimators. The application of the proposed modified rescaled range estimator to a group of temperature, rainfall, river flow, and tree‐ring time series in the Midwest USA demonstrates the extent to which classical rescaled range analysis can give misleading results. Based on a statistical test of significance, the number of time series exhibiting the Hurst effect is reduced from 36 to only 11 out of 56 temperature series, and from 23 to 7 out of 60 rainfall series. On the other hand, the number of time series exhibiting the Hurst effect marginally increased from 8 to 9 out of 49 river flow series, and from 49 to 54 out of 88 tree‐ring series.