On estimating the intensity of long-range dependence in finite and infinite variance time series

The goal of this paper is to provide benchmarks to the practitioner for measuring the intensity of long-range dependence in time series. It provides a detailed comparison of eight estimators for long-range dependence , using simulated FARIMA(p; d; q) time series with diierent nite and innnite variance innovations. FARIMA time series model both long-range dependence (through the parameter d) and short-range dependence (through the parameters p and q). We evaluate the biases and standard deviations of several estimators of d and compare them for each type of series used. We consider Gaussian, exponential, lognormal, Pareto, symmetric and skewed stable innovations. Detailed tables and graphs have been included. We nd that the estimators tend to perform less well when p and q are not zero, that is, when there is additional short-range dependence structure. For most of the estimators, however, the use of innnite variance instead of nite variance innovations does not cause a great decline in performance.

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