X-13ARIMA-SEATS Seasonal Adjustment Program

Fixed-B Asymptotics for the Studentized Mean from Time Series with Short, Long, or Negative Memory

Tucker S. McElroy ⁽¹⁾ and Dimitris N. Politis ⁽²⁾

ABSTRACT:

This paper considers the problem of variance estimation for the sample mean in the context of long memory and negative memory time series dynamics, adopting the fixed-bandwidth approach now popular in the econometrics literature. The distribution theory generalizes the short memory results of Kiefer and Vogelsang (2005, Econometric Theory 21, 1130–1164). In particular, our results highlight the dependence on the kernel (we include flat-top kernels), whether or not the kernel is nonzero at the boundary, and, most important, whether or not the process is short memory. Simulation studies support the importance of accounting for memory in the construction of confidence intervals for the mean.

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⁽¹⁾ 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

⁽²⁾ Dimitris N. Politis is a professor at the Department of Mathematics, University of California, San Diego. email : dpolitis@ucsd.edu