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 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 σ² 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.