Fast exact computation of the MLE for AR(1) by solving the likelihood equation. The sample mean correction is used, so the method is not strickly speaking exact but the name derives from the fact that if the mean is known and was used instead of the sample mean the estimate would be an exact MLE estimate of the parameter in the AR(1) model. It has been shown that effect of estimating the sample mean is negligible.
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The exact MLE for mean-zero an AR(1) time series satisfies a cubic equation. The solution of this equation for the MLE given by Zhang (2002) is used. This approach is more reliable as well as faster than the usual approach to the exact MLE using a numerical optimization technique which can occasionally have convergence problems.
MLE for the parameter
A.I. McLeod and Ying Zhang
Zhang, Y. (2002). Topics in Autoregression, Ph.D. Thesis, University of Western Ontario.
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