A Bayesian estimation of lag lengths in distributed lag models

Dynamic regression models are widely used because they express and model the behaviour of a system over time. In this article, two dynamic regression models, the distributed lag (DL) model and the autoregressive distributed lag model, are evaluated focusing on their lag lengths. From a classical statistics point of view, there are various methods to determine the number of lags, but none of them are the best in all situations. This is a serious issue since wrong choices will provide bad estimates for the effects of the regressors on the response variable. We present an alternative for the aforementioned problems by considering a Bayesian approach. The posterior distributions of the numbers of lags are derived under an improper prior for the model parameters. The fractional Bayes factor technique [A. O'Hagan, Fractional Bayes factors for model comparison (with discussion), J. R. Statist. Soc. B 57 (1995), pp. 99-138] is used to handle the indeterminacy in the likelihood function caused by the improper prior. The zero-one loss function is used to penalize wrong decisions. A naive method using the specified maximum number of DLs is also presented. The proposed and the naive methods are verified using simulation data. The results are promising for the method we proposed. An illustrative example with a real data set is provided.