Subsampling Inference for the Mean of Heavy‐Tailed Long‐Memory Time Series

16 Pages Posted: 28 Dec 2011

See all articles by Agnieszka Jach

Agnieszka Jach

Hanken School of Economics

Tucker McElroy

U.S. Census Bureau - Center for Statistical Research and Methodology

Dimitris N. Politis

University of California, San Diego (UCSD) - Department of Mathematics

Date Written: January 2012

Abstract

In this article, 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 behaviour, 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.

Keywords: Infinite variance, self‐normalization, subsampling, weak dependence, adaptive block size

JEL Classification: C14, C22

Suggested Citation

Jach, Agnieszka and McElroy, Tucker and Politis, Dimitris, Subsampling Inference for the Mean of Heavy‐Tailed Long‐Memory Time Series (January 2012). Journal of Time Series Analysis, Vol. 33, Issue 1, pp. 96-111, 2012, Available at SSRN: https://ssrn.com/abstract=1977400 or http://dx.doi.org/10.1111/j.1467-9892.2011.00742.x

Agnieszka Jach (Contact Author)

Hanken School of Economics

Tucker McElroy

U.S. Census Bureau - Center for Statistical Research and Methodology ( email )

4600 Silver Hill Road
Washington, DC 20233-9100
United States

Dimitris Politis

University of California, San Diego (UCSD) - Department of Mathematics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0112
United States
858-534-5861 (Phone)
858-534-5273 (Fax)

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