Testing for long‐range dependence in the presence of shifting means or a slowly declining trend, using a variance‐type estimator

Vadim Teverovsky and Murad Taqqu

Journal of Time Series Analysis, 1997, vol. 18, issue 3, 279-304

Abstract: In this paper we examine the effects of certain types of non‐ stationarity on the detection of long‐range dependence and on the estimation of the Hurst parameter H, when using a variance‐type estimator. The resulting estimate of H can be misleading when the series has either a jump in the mean or a slow trend. In such a case, plotting the logarithm of the variance versus the logarithm of the level of aggregation gives a curve which is quite different from a straight line. A method for distinguishing between the effects of long‐range dependence and these types of non‐stationarity is developed.

Date: 1997
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