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

Teverovsky, Vadim; Taqqu, Murad

J. Time Ser. Anal. 18, No. 3, 279-304 (1997).

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.

MSC:

62M10

Time series, auto-correlation, regression, etc. in statistics (GARCH)

Keywords:

fractional Gaussian noise; long memory; times series; long-range dependence; non-stationarity