Remark on the asymptotic distribution of the OLS estimator in a simple Gaussian unit-root autoregression

Dimitrios Vougas

Statistics & Probability Letters, 2006, vol. 76, issue 1, 27-34

Abstract: This paper considers the asymptotic distribution of the OLS estimator in a simple, Gaussian unit-root AR(1) with fixed, non-zero startup. All asymptotic possibilities are considered. The approach is new, relatively simple, and relies on observing and determining the asymptotic/limiting behavior of the underlying finite sample distribution. It does not rely on inversion of joint moment generating or characteristic functions to derive limiting distributions. The paper introduces small-sigma/parameter-based asymptotic theory and re-examines large-sample asymptotic theory. In addition, combinations of these asymptotic approaches are considered explicitly. The analysis provides a set of very interesting and sometimes surprising results.

Keywords: AR(1); OLS; estimator; Unit-root; process; Parameter-based; asymptotic; theory; Small-sigma; asymptotic; theory; Large-sample; asymptotic; theory (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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