  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 numerous spectral
domain estimators for $d$ but there are only a few estimators in the time
domain. Moreover, the latter estimators are criticized for relying on visual
inspection to determine an observation window $[n_1, n_2]$ for a linear
regression to run on. Theoretically motivated choices of $n_1$ and $n_2$ are
often missing for many time series models.
  In this paper, we take the well-known variance plot estimator and provide
rigorous asymptotic conditions on $[n_1, n_2]$ to ensure the estimator's
consistency under LRD. We establish these conditions for a large class of
square-integrable time series models. This large class enables one to use the
variance plot estimator to detect LRD for infinite-variance time series (after
suitable transformation). Thus, detection of LRD for infinite-variance time
series is another novelty of our paper. A simulation study indicates that the
variance plot estimator can detect LRD better than the popular spectral domain
GPH estimator.
