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This paper considers maximum likelihood estimation for Gaussian MA(l) processes when the moving average parameter is on or near the unit circle. A unified framework for the derivation of the asymptotic distribution of the MLE of the moving average parameter is given. Of practical significance is the fact that the asymptotic distribution is surprisingly accurate even for small sample sizes and for values of the moving average parameter considerably far from the unit circle. In the latter case, where the normal limit approximation is thought to be reasonably good, the approximation based on our limiting results is often more accurate than the normal approximation. The theoretical results are applied to inference problems of hypothesis testing and confidence interval construction and is demonstrated by simulation to have superior properties than procedures based on a normal distribution approximation.