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

David A. Dickey; Wayne A. Fuller · Journal of the American Statistical Association · 1979

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Author / responsible party

David A. Dickey; Wayne A. Fuller

Publisher

Journal of the American Statistical Association

Year

1979

Language

English

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Abstract 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 é 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.

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APA 7

Dickey, D. A. & Fuller, W. A. (1979). Distribution of the Estimators for Autoregressive Time Series with a Unit Root. https://doi.org/10.1080/01621459.1979.10482531

MLA

Dickey, David A, and Wayne A. Fuller. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." 1979. https://doi.org/10.1080/01621459.1979.10482531.

Chicago

Dickey, David A. and Wayne A. Fuller. 1979. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root.". https://doi.org/10.1080/01621459.1979.10482531.

Harvard

Dickey, D. A. and Fuller, W. A. 1979, Distribution of the Estimators for Autoregressive Time Series with a Unit Root, Journal of the American Statistical Association, available at: https://doi.org/10.1080/01621459.1979.10482531 [Accessed 7 Aug. 2026].

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

Author / contributors: David A. Dickey; Wayne A. Fuller

Publisher: Journal of the American Statistical Association

Publication year: 1979

Language: English

Subjects

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Mathematics; Autoregressive model; Estimator; Statistics; Series (stratigraphy); Regression analysis; Combinatorics; Paleontology; Biology