Asymptotic distribution of maximum likelihood estimators in linear models with autoregressive disturbances

by Clifford Hildreth


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Some statistical properties are established for maximum likelihood estimates of linear model coefficients whose disturbances are generated by a stationary linear first-order autoregressive process with unknown autoregression coefficient. This study describes the model, examines the likelihood function, and gives a detailed proof that the estimates of coefficients of independent variables and the estimate of the autoregression coefficient have a limiting joint multivariate-normal distribution, with the estimate of autoregression distributed independently of the estimates of coefficients of independent variables. This asymptotic covariance matrix of the latter estimates is the same as that of the best linear unbiased estimates for a model in which the autoregression coefficient is known. Up to now, consistency is the only property that has been shown for maximum likelihood estimates. Results of this study should be especially helpful in large-sample applications. 30 pp.

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