Book Description

The first essay reexamines regression-based tests for evaluating one-step-ahead prediction errors in a nested regression framework when the model fitting is based upon the out-of-sample method. We reaffirm the asymptotic equivalence between frequently used test statistics for out-of-sample predictive accuracy and F statistics in the in-sample case. When the out-of-sample window size is variable, it is shown that asymptotically the corresponding test statistics converge weakly to functionals of Brownian motion. In addition, the asymptotic densities under the alternative are shown to be related to densities of the null hypothesis by a simple convolution operation. Simulation results confirm that the empirically approximated statistics are functions of the in-sample ratios, and the terms omitted are negligible in size. Also, it is revealed that the empirical powers of out-of-sample tests are quite close to those in the in-sample case. Three stocks from the US stock market are modeled and analyzed to illustrate the proposed methodology. The second essay investigates consistent tests of stochastic dominance to select among nested models. Similar to the first essay, we compute one-step-ahead out-of-sample predictive errors and obtain predictive accuracy of two nested models. Then, we define and develop stochastic tests at both lower orders (first-order and second-order) and higher orders (third-order and fourth-order). We propose a recursive method to obtain critical values by bootstrapping and conduct power tests. We find that this method works perfectly for small sample size and small estimation size. When the sample size gets larger, two series of predictive accuracy might cross multiple times. We solve this problem by investigating on higher-order stochastic dominance. In the end, we apply this stochastic dominance (SD) rule to financial data. Three stocks from the US stock market are modeled and reaffirm the efficiency and correctness of our theory.