Detection of Long Range Dependence in the Time Domain for (In)Finite-Variance Time Series
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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. The theoretically motivated choice of n_1 and n_2 has been missing so far. In this paper, we take the well-known, yet shunned variance plot estimator and provide rigorous asymptotic conditions on [n_1, n_2] to ensure the estimator's consistency under LRD. Thus, our paper fills a theoretical gap and provides practitioners with a simple to implement estimator that was previously not theoretically justified. Another novelty of our paper is the LRD detection for infinite-variance time series with the variance plot estimator. A simulation study indicates that the variance plot estimator can detect LRD better than the popular spectral domain GPH estimator.
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