Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors when the Root Lies on the Unit Circle

This paper considers the maximum likelihood estimator of the first order moving average process when the true value of the coefficient is one. The results are also extended to regression analysis. It is shown that there is a local maximum of the likelihood function within an interval of O(T^-^1) of the true value and also that the probability that the maximum occurs exactly at the true value and also that the probability that the maximum occurs exactly at the true value can be calculated in finite samples.