X-13ARIMA-SEATS Seasonal Adjustment Program

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

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

ABSTRACT:

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.

KEYWORDS:

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

• Back to Seasonal Adjustment Papers page
• Download PDF file (about 433KB)

⁽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 : Tucker.S.McElroy@census.gov

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