Essays On Time Series and Financial Econometrics

This dissertation contains four essays in financial econometrics. In the first essay, some asymptotic results are derived for first-order autoregression with a root moderately deviating from unity and a nonzero drift. It is shown that the drift changes drastically the large sample properties of the least-squares (LS) estimator. The second essay is concerned with the joint test of predictability and stability in the context of predictive regression. The null hypothesis under investigation is that the potential predictors exhibit no predictability and incur no structural break during the sample period. We first show that the IVX estimator provides better finite sample performance than LS when they are used to test for a structural break in the slope coefficient. We then consider a new test by combining the IVX and sup-Wald statistics. The third essay considers the impact of level-shifts in the predicted variable on the performance of the conventional test for predictability when highly persistent predictors are used. It is shown that the limiting distribution of conventional t-statistic depends on the magnitude of break size. When the breaks are ignored, the t-statistic generates a too large type-I error. To alleviate this problem, we propose to base the inference on a sample-splitting procedure. Applications to the prediction of stock return volatility and housing price index are conducted. In the last essay, we consider a new multivariate stochastic volatility (MSV) model, applying a fully flexible parameterization of the correlation matrix, which generalizes Fisher’s z-transformation to the high-dimensional case. In the new model, we can separately model the dynamics in volatilities and correlations. To conduct statistical inference of the proposed model, we propose the Particle Gibbs Ancestor Sampling (PGAS) method. Extensive simulation studies are conducted to show the proposed method works well.