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.