Fractional Bayesian lag length inference in multivariate autoregressive processes (Q2722252)

The multivariate autoregression, also known as the vector autoregression (VAR) model, has become the most widely used model for multiple time series and serves as a base for more complex models such as cointegration models. The first, and perhaps most difficult, problem in using VAR models is confronted with the choice of the number of lags in the model. Using a Bayesian approach the posterior distribution of the number of lags in the 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.NEWLINENEWLINENEWLINEAn asymptotic equivalence between the fractional approach and the Schwarz' Bayesian criterion 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 is reasonable robust to changes in the prior distribution for the lag length, especially under the zero-one loss.