**by Mattias
Villani**

** Research
Report 1998:14**

Department of Statistics, Stockholm University, S-106 91 Stockholm, Sweden

**Abstract**

The posterior distribution of the number of lags in a multivariate autoregression is derived under the Jeffreys prior. Not only can this distribution aid in the choice of a particular lag length, but it should also be used to incorporate the uncertainty regarding the lag length into the analysis of other quantities which depend on the number of lags. The fractional Bayes approach is used to settle the indeterminacy in the model selection caused by the improperness of the Jeffreys prior. The Bayesian solution to the problem of choosing a particular lag length depends on both the prior distribution of the lag length and the utility function. A uniform prior over the lag length and a simple zero-one utility function are assumed in a small simulation study where the fractional Bayes approach performs very well compared to the three most widely used information criteria.

**Key words:** Fractional
Bayes factor, Improper priors, Information criteria, Lag length, Vector
autoregression.

*Last update: 990916/CE*