Journal of Time Series Analysis

APPROXIMATE DISTRIBUTION OF PARAMETER ESTIMATORS FOR FIRST‐ORDER AUTOREGRESSIVE MODELS

Journal Article

Abstract. Formulae for the exact bias and mean square error for the least squares for forward‐backward least squares estimators are obtained based on the explicit expressions for the moment‐generating and characteristic functions of quadratic form in the first‐order autoregressive process. Asymptotic expressions for their cumulants and the maximum likelihood estimator are given. Approximations of the distributions of the above estimators are proposed based on the Ornstein‐Ulenbeck process. A simple computational procedure for the exact distribution is developed, and some numerical comparisons are given which support the overall good accuracy of the approximation and confirm that the maximum likelihood estimator performs better than the others.

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