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

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 {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.

Cite this

David Alan Dickey, Wayne Arthur Fuller (1979). Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1979.10482531

@article{alan1979distribution,
  title  = {Distribution of the Estimators for Autoregressive Time Series with a Unit Root},
  author = {Dickey, David Alan and Fuller, Wayne Arthur},
  year   = {1979},
  journal = {Journal of the American Statistical Association},
  doi    = {10.1080/01621459.1979.10482531}
}

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