Improving robust model selection tests for dynamic models

P>We propose an improved model selection test for dynamic models using a new asymptotic approximation to the sampling distribution of a new test statistic. The model selection test is applicable to dynamic models with very general selection criteria and estimation methods. Since our test statistic does not assume the exact form of a true model, the test is essentially non-parametric once competing models are estimated. For the unknown serial correlation in data, we use a Heteroscedasticity/Autocorrelation-Consistent (HAC) variance estimator, and the sampling distribution of the test statistic is approximated by the fixed-b asymptotic approximation. The asymptotic approximation depends on kernel functions and bandwidth parameters used in HAC estimators. We compare the finite sample performance of the new test with the bootstrap methods as well as with the standard normal approximations, and show that the fixed-b asymptotics and the bootstrap methods are markedly superior to the standard normal approximation for a moderate sample size for time series data. An empirical application for foreign exchange rate forecasting models is presented, and the result shows the normal approximation to the distribution of the test statistic considered appears to overstate the data's ability to distinguish between two competing models.