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Subsampling inference for the mean of heavy-tailed long-memory time series
Article first published online: 30 MAY 2011
© 2011 Blackwell Publishing Ltd
Journal of Time Series Analysis
Volume 33, Issue 1, pages 96–111, January 2012
How to Cite
Jach, A., McElroy, T. and Politis, D. N. (2012), Subsampling inference for the mean of heavy-tailed long-memory time series. Journal of Time Series Analysis, 33: 96–111. doi: 10.1111/j.1467-9892.2011.00742.x
- Issue published online: 27 DEC 2011
- Article first published online: 30 MAY 2011
- First Version received January 2010
- Infinite variance;
- weak dependence;
- adaptive block size
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.