Minimum message length autoregressive model order selection

We derive a Minimum Message Length (MML) estimator for stationary and nonstationary autoregressive models using the Wallace and Freeman (1987) approximation. The MML estimator's model selection performance is empirically compared with AIC, AIC(C), BIC and HQ in a Monte Carlo experiment by uniformly sampling from the autoregressive stationarity region. Generally applicable, uniform priors are used on the coefficients, model order and log sigma(2) for the MML estimator. The experimental results show the MML estimator to have the best overall average mean squared prediction error and best ability to choose the true model order.