# Distribution of the Estimators for Autoregressive Time Series with a Unit Root

**David A. Dickey****Wayne A. Fuller**

CiteWeb id: 20120000001

CiteWeb score: 19672

Let n observations Y 1, Y 2, ···, Y n be generated by the model Y t = pY t−1 + e t , where Y **0** is a fixed constant and {e t } t-1 n is a sequence of independent normal random variables with mean **0** and variance σ2. Properties of the regression estimator of p are obtained under the assumption that p = ±1. Representations for the limit distributions of the estimator of p and of the regression t test are derived. The estimator of p and the regression t test furnish methods of testing the hypothesis that p = 1.PDFKey WordsTime series, Autoregressive, Nonstationary, Random walk, DifferencingRelated articlesView all related articlesAdd to shortlist Link Permalink http://dx.doi.org/10.1080/01621459.1979.10482531

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David A. Dickey, Wayne A. Fuller,

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