The course develops the students’ theoretical and empirical grasp of statistical analysis of returns of financial assets. It contains a review of inference methods such as Maximum Likelihood and Generalized Method of Moments (GMM), which are used for estimating parameters of the models considered in the subsequent parts of the course. Emphasis is on associated statistical tests and linear time series models. In addition to statistical techniques we discuss how to interpret the outcomes of statistical analysis in order to answer practical financial questions. In the process, students will perform several hands-on data tasks by computing risk measures, such as expected shortfall or value at risk, based on an estimated model.
Initially the explanatory data analysis is treated in a financial context. Thereafter we cover estimation of linear factor asset pricing models based on linear regression and GMM techniques. We also study time-series properties of financial returns. In this context we discuss predictability of financial returns, methods for comparing forecasting accuracy and the validity of the efficient market hypothesis. Further we concentrate on more details on volatility modeling. We cover discrete time volatility models from the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) class. We also investigate multivariate extensions of GARCH models such as Dynamic Conditional Correlation models. Finally we study continuous time models for high frequency data analysis with the emphasis on intraday volatility and correlation measurement and forecasting. In particular, we study realized variance and multipower variation estimators of volatility and the Heterogeneous Autoregressive (HAR) model for volatility dynamics.