My dissertation includes two essays studying the forecasting of financial returns. In the first essay, I study the temporal dependence structures of financial returns by using a mixture copula model. A mixture copula is a linear combination of several single copulas. It is more flexible than a single copula and can capture various dependence structures in financial data. Therefore, instead of choosing a single copula based on certain statistical criteria, I propose to use a model average approach to estimate the temporal dependence structure of a stationary Markov process in a mixture copula framework. The asymptotic properties of the model average estimator are established under some regularity conditions. Simulations show that the model average approach gives the most accurate estimation and predicting results compared to some competing methods, when the working mixture model is misspecified. Using a real data example, we demonstrate the usefulness of our proposed method. In the second essay, I suggest a robust test that is a data-dependent weighted average of the regression-based test and the covariance-based test. This new test allows for multivariate cases and yields chi-squared inference regardless of whether predictors are stationary, local-to-unity or I(1). No prior knowledge of the orders of integration or bias corrections are required. Furthermore, the new test does not force the dependent variable and predictors to share the same order of integration under the alternative hypothesis. It is very important because in practice the dependent variable usually appears to be stationary while predictors may be (near) nonstationary. This test shows good simulation results. In the empirical application section, we test for the predictability of excess stock returns using a large set of predictors.
