Portmanteau Likelihood Ratio Tests for Model Selection

This paper provides an extension of Vuong’s (1989, Econometrica, 57, pp.307–333) model selection test to the multivariate case. We use the Kullback–Leibler Information Criterion (KLIC) to measure the closeness of a model to the truth to provide a diagnosis of many competing models where the models are not correctly specified. After investigating the asymptotic joint distribution of the likelihood ratio (LR) statistics, we propose LR-based portmanteau test statistics for model selection among many competing models. These tests are easy to compute and are established under any model case, including nested, strictly nested, or overlapping; and are useful where several function forms and exogenous variables give the candidate models. The case of a nested structure yields a test of the best model and the confidence set of the best model from the standpoint of KLIC. We also discuss the use of information criteria instead of LR statistics.