Detection of long range dependence in the time domain for (in)finite-variance time series

Abstract

Empirical detection of long range dependence (LRD) of a time series often consists of deciding whether an estimate of the memory parameter d corresponds to LRD. Surprisingly, the literature offers only a few estimators for d in the time domain. And those that exist are criticized for relying on visual inspection to determine an observation window [ n 1 , n 2 ] for a linear regression. Here, we provide rigorous asymptotic conditions on [ n 1 , n 2 ] to ensure consistency of the well-known variance plot estimator under LRD. We do this for a large class of square-integrable time series models so that the estimator can be used to detect LRD for infinite-variance time series in the sense of indicators of excursion sets. Thus, detection of LRD for infinite-variance time series is another novelty of our paper. Finally, a simulation study compares the variance plot estimator with a popular spectral domain estimator.