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Journal Article

Distribution of the Estimators for Autoregressive Time Series With a Unit Root

David A. Dickey and Wayne A. Fuller
Journal of the American Statistical Association
Vol. 74, No. 366 (Jun., 1979), pp. 427-431
DOI: 10.2307/2286348
Stable URL: http://www.jstor.org/stable/2286348
Page Count: 5
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Distribution of the Estimators for Autoregressive Time Series With a Unit Root
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Abstract

Let n observations Y1, Y2, ..., Yn be generated by the model Yt = ρ Yt - 1 + et, where Y0 is a fixed constant and {et}t = 1n is a sequence of independent normal random variables with mean 0 and variance σ2. Properties of the regression estimator of ρ are obtained under the assumption that ρ = ± 1. Representations for the limit distributions of the estimator of ρ and of the regression t test are derived. The estimator of ρ and the regression t test furnish methods of testing the hypothesis that ρ = 1.

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