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Subsampling Inference for the Mean of Heavy-tailed Long Memory Time Series

Agnieszka Jach (1), Tucker S. McElroy (2) and Dimitris N. Politis (3)


In this paper we revisit a time series model introduced by McElroy and Politis (2007a) and generalize it in several ways to encompass a wider class of stationary, nonlinear, heavy-tailed time series with long memory. The joint asymptotic distribution for the sample mean and sample variance under the extended model is derived; the associated convergence rates are found to depend crucially on the tail thickness and long memory parameter. A self-normalized sample mean, that concurrently captures the tail and memory behavior, is defined. Its asymptotic distribution is approximated by subsampling without the knowledge of tail or/and memory parameters; a result of independent interest regarding subsampling consistency for certain long-range dependent processes is provided. The subsampling-based confidence intervals for the process mean are shown to have good empirical coverage rates in a simulation study. The influence of block size on the coverage and the performance of a data-driven rule for block size selection are assessed. The methodology is further applied to the series of packet-counts from Ethernet traffic traces.


Infinite variance, self-normalization, subsampling, weak dependence, adaptive block size

(1) Agnieszka Jach is a professor at Universidad Carlos III de Madrid.

(2) Tucker S. McElroy is Mathematical Statistican, Center for Statistical Research and Methodology U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email :

(3) Dimitris N. Politis is a professor at the Department of Mathematics, University of California, San Diego. email :

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Source: U.S. Census Bureau | Statistical Research Division | (301) 763-1649 (or |  Last Revised: April 02, 2015