Vol. 6, No. 1, 2013

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New confidence intervals for the AR(1) parameter

Ferebee Tunno and Ashton Erwin

Vol. 6 (2013), No. 1, 53–63
Abstract

This paper presents a new way to construct confidence intervals for the unknown parameter in a first-order autoregressive, or AR(1), time series. Typically, one might construct such an interval by centering it around the ordinary least-squares estimator, but this new method instead centers the interval around a linear combination of a weighted least-squares estimator and the sample autocorrelation function at lag one. When the sample size is small and the parameter has magnitude closer to zero than one, this new approach tends to result in a slightly thinner interval with at least as much coverage.

Keywords
confidence interval, autoregressive parameter, weighted least squares, linear combination
Mathematical Subject Classification 2010
Primary: 60G10, 62F12, 62F99, 62M10
Milestones
Received: 31 December 2011
Revised: 26 April 2012
Accepted: 10 May 2012
Published: 23 June 2013

Communicated by Robert B. Lund
Authors
Ferebee Tunno
Department of Mathematics and Statistics
Arkansas State University
P.O. Box 70
State University, AK 72467
United States
Ashton Erwin
Department of Mathematics and Statistics
Arkansas State University
P.O. Box 70
State University, AK 72467
United States