Testing for long-range dependence in the presence of shifting means or a slowly declining trend, using a variance-type estimator. (English) Zbl 0934.62094

Summary: 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 develepod.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Full Text: DOI