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New confidence
intervals for the AR(1) parameter
Ferebee Tunno and Ashton Erwin
Vol. 6 (2013), No. 1, 53–63
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 60G10, 62F12, 62F99, 62M10
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Milestones
Received: 31 December 2011
Revised: 26 April 2012
Accepted: 10 May 2012
Published: 23 June 2013
Communicated by Robert B. Lund
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Authors |
| Ferebee Tunno | |
| Department of Mathematics and
Statistics Arkansas State University P.O. Box 70 State University, AK 72467 United States |
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| Ashton Erwin | |
| Department of Mathematics and
Statistics Arkansas State University P.O. Box 70 State University, AK 72467 United States |
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