A necessary and sufficient condition for the existence of the maximum likelihood estimate in autoregressive models

The author studies the existence of a maximum likelihood estimate (MLE) for the parameters of a pth-order autoregressive (AR) model from n⩾1 independent records of length m of a complex time series. It is shown that, for almost all such set of observations, the MLE exists if and only if the n records be exactly fitted by complex undamped sinusoids using the same set of p distinct frequencies