Fractional Bayesian Lag Length Inference in Multivariate Autoregressive Processes

The posterior distribution of the number of lags in a multivariate autoregression is derived under an improper prior for the model parameters. The fractional Bayes approach is used to handle the indeterminacy in the model selection caused by the improper prior. An asymptotic equivalence between the fractional approach and the Schwarz Bayesian Criterion (SBC) is proved. Several priors and three loss functions are entertained in a simulation study which focuses on the choice of lag length. The fractional Bayes approach performs very well compared to the three most widely used information criteria, and it seems to be reasonably robust to changes in the prior distribution for the lag length, especially under the zero-one loss.