Existence of Maximum Likelihood Estimators of Autoregressive and Moving Average Models

摘要

There is given a sufficient condition on the observations from a scalar autoregressive process such that the maximum likelihood estimate exists and corresponds to a stationary process. A sufficient condition is given for the likelihood function to fail to have a maximum. In a moving average model the maximum likelihood estimates always exist. Some results are obtained for the autoregressive moving average model and vector models. It is shown that the solution to the sample Yule-Walker equations in the autoregressive case yield a stationary process. (Author)