nested models

We consider the problem of model selection in vector autoregressive model with Normal innovation. Tests such as Vuong's and Cox's tests are provided for order and model selection, i.e. for selecting the order and a suitable subset of regressors, in vector autoregressive model. We propose a test as a modified log-likelihood ratio test for selecting subsets of regressors. The Europe oil prices, Brent, and the real gross domestic product, GDP, data are considered as real data. Since the Brent data does Granger-cause the GDP data, so we suggest the vector autoregressive model and select optimal model based on the model selection test. The analysis provides analytic results show that the Vuong's, Cox's and proposed test are the appropriate test for order and model selection for vector autoregressive models with Normal innovation. In simulation study, the power of proposed test at least is as good as the power of Vuong's test.

The problem of obtaining the optimum design، which is able to discriminate between several rival models has been considered in this paper. We give an optimality-criterion، using a Bayesian approach. This is an extension of the Bayesian KL-optimality to more than two models. A modification is made to deal with nested models. The proposed Bayesian optimality criterion is a weighted average، where the weights are corresponding probabilities of models to let them be true. We consider these probabilities coming from a Poisson distribution.