"Quantitative Methods in High-Frequency Financial Econometrics: Modeling Univariate and Multivariate Time Series" by Wei Sun We propose a new framework to modeling ultra-high-frequency financial data, i.e., the ARMA-GARCH model with one of the typical self-similar processes, fractional stable noise. We empirically compare this process with several alternative distributional assumptions in either fractal form or i.i.d. form (i.e., normal distribution, fractional Gaussian noise, generalized extreme value distribution, generalized Pareto distribution, and stable distribution) for modeling German equity market volatility. The empirical results suggest that fractional stable noise dominates these alternative distributional assumptions both in in-sample modeling and out-of-sample forecasting. Our findings suggest that models based on fractional stable noise perform better than models based on the Gaussian random walk, the fractional Gaussian noise, and the non-Gaussian stable random walk. We use this modeling framework for analyzing trade duration data. The empirical results suggest that fractional stable noise and stable distribution dominate other alternative distributional assumptions. We introduce a copula ARMA-GARCH model for analyzing the co-movement of international equity markets. The model is implemented with an ARMA-GARCH model for the marginal distributions and a copula for the joint distribution. After goodness of fit testing, we find that the Student's t copula ARMA(1,1)-GARCH(1,1) model with fractional Gaussian noise is superior to alternative models investigated in my study where I model the simultaneous co-movement of nine international equity market indexes. We introduce a skewed Student's t copula ARMA-GARCH model for analyzing the co-movement of indexes in German equity markets that exhibit asymmetric correlation. The empirical findings illustrate the superior performance of this modeling structure.