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

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.