Subsampling Inference for the Autocovariances of Heavy-Tailed Long-Memory Time Series

• Activity Number: 273
• Type: Invited
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Tucker McElroy*+
• Companies: U.S. Census Bureau
• Keywords: heavy tails ; linear time series ; self-normalization ; subsampling ; confidence intervals

Abstract

We provide a self-normalization for the sample autocovariances (acvs) and autocorrelations (acs) of a linear, long-memory time series with innovations that have either finite 4th moment or are heavy-tailed with tail index between 2 and 4. The asymptotic distribution of the sample acv has three rates of convergence that depend on the interplay between the memory parameter d and the tail index alpha, and which consequently lead to three different limiting distributions; for the sample ac the limit distribution only depends on d. We introduce a self-normalized sample acv statistic, which is computable without knowledge of alpha or d (or their relationship), and which converges to a nondegenerate distribution. We also treat self-normalization of the acs. The sampling distributions can then be approximated nonparametrically by subsampling, as the corresponding asymptotic distribution is still parameter-dependent. The subsampling-based confidence intervals for the process acvs and acs are shown to have good empirical coverage rates in a simulation study. The impact of block size on the coverage is assessed.