Subsampling Inference for the Autocovariances and Autocorrelations of Long‐Memory Heavy‐Tailed Linear Time Series

19 Pages Posted: 17 Oct 2012

See all articles by Tucker McElroy

Tucker McElroy

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

Agnieszka Jach

Hanken School of Economics

Date Written: November 2012

Abstract

We provide a self‐normalization for the sample autocovariances and autocorrelations of a linear, long‐memory time series with innovations that have either finite fourth moment or are heavy‐tailed with tail index 2 < α < 4. In the asymptotic distribution of the sample autocovariance there are three rates of convergence that depend on the interplay between the memory parameter d and α, and which consequently lead to three different limit distributions; for the sample autocorrelation the limit distribution only depends on d. We introduce a self‐normalized sample autocovariance statistic, which is computable without knowledge of α or d (or their relationship), and which converges to a non‐degenerate distribution. We also treat self‐normalization of the autocorrelations. The sampling distributions can then be approximated non‐parametrically by subsampling, as the corresponding asymptotic distribution is still parameter‐dependent. The subsampling‐based confidence intervals for the process autocovariances and autocorrelations are shown to have satisfactory empirical coverage rates in a simulation study. The impact of subsampling block size on the coverage is assessed. The methodology is further applied to the log‐squared returns of Merck stock.

Keywords: Linear time series, parameter‐dependent convergence rates, self‐normalization, subsampling confidence intervals

Suggested Citation

McElroy, Tucker and Jach, Agnieszka, Subsampling Inference for the Autocovariances and Autocorrelations of Long‐Memory Heavy‐Tailed Linear Time Series (November 2012). Journal of Time Series Analysis, Vol. 33, Issue 6, pp. 935-953, 2012, Available at SSRN: https://ssrn.com/abstract=2162324 or http://dx.doi.org/10.1111/j.1467-9892.2012.00808.x

Tucker McElroy (Contact Author)

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

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

Agnieszka Jach

Hanken School of Economics

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