This dissertation considers choice criteria and test statistics for non-nested time series regression models that are stationary or non-stationary. The non-nestedness of models includes differences in linear parameter restrictions, and models are estimated by the IV method. The choice criterion proposed for non-nested stationary models is asymptotically valid in probability. This choice criterion is also asymptotically valid for non-nested non-stationary models, but only in distribution. Incorporating the correct linear constraints can enhance the selection of rival models. The test statistic proposed for non-nested stationary models has an asymptotically standard normal distribution. It includes many existing tests as special cases. When models are nonstationary, the test statistic has an asymptotically standard normal distribution only under the very restrictive conditions that the disturbance terms are serially uncorrelated and uncorrelated with the first difference of regressors and instrument variables. This implies that the existing tests which are our special cases cannot be applied generally to non-nested non-stationary models. We construct a test with a non-parametric modification when the conditions are violated. When the test is valid for both stationary and non-stationary models, the consistency and the asymptotic power of the test under the local null are analyzed. The test is consistent if the true model is not nested within the alternative model at the true value of the parameter. The asymptotic power against the local null is higher for nonstationary models than for stationary models. In the stationary case, the computation of the test statistic can be implemented using several restricted OLS regressions. Monte Carlo simulation demonstrates that the testing procedure with the non-parametric modification performs very well in large samples. The empirical test of major competing exchange rate models indicates that the monetary model with flexible prices and different domestic and foreign demand for money functions performs best
