inference on economic data based on the model selection test

In this paper, we consider the europe oil prices, brent, american stock market index based on the market capitalizations of 500 large companies having common stock listed on the nyse or nasdaq, s&p500, and the real gross domestic product, gdp. based on the rolling test of granger causality, the europe oil prices data does granger-cause the real grossdomestic product data and s&p500 data. so, the vector autoregressive model can be suggested. we consider the estimation and model selection of vector autoregressive time series model with normal innovation and provide the vuong’s test and cox’s test for order and model selection, i.e. for selecting the order and a suitable subset of regressors, in vector autoregressive model. our results show that, the model selection tests confirm the causality test and theresults of predictive method for gdp and s&p500 data.