Statistics and financial data analysis

Objectives and Learning Outcomes

The course provides a comprehensive introduction to key concepts used in applied statistical work with financial data. The emphasis is both on the key principles of the underlying statistical theory as well as on the economic intuition behind the estimates. At the end of the course, the students will have a good understanding of the “traditional” statistical methods for financial data analysis (outside the machine learning framework), their merits and disadvantages, and will be well equipped to conduct individual data-driven research or industry projects.

Lectures

Financial time series and their characteristics. Linear regression with normal and non-normal data. Transformations, weighted regression and heteroscedasticity. Maximum likelihood estimation. Instrumental variables. Linear time series models: autoregressive, moving average and ARMA models; autocorrelation structure; order identification using AIC and BIC; model checking. State space models and Kalman filter. Forecasting methods. Stationarity. Unit-root tests. ARIMA models. Conditional volatility models (ARCH and GARCH modelling and calibration). Multivariate time series models. Introduction to nonlinear time series models. Regime change detection.

Exercises

Working with financial data using R. Estimating and interpreting linear regression in practice. Testing statistical hypothesis. Estimating weighted least squares. Instrumental variables regressions and the selection of instruments. Univariate linear time series analysis and fitting the best model for forecasting returns. Unobserved component models: estimation, interpretation and forecast. Unit root tests and statistical and economic implications. Vector autoregressive models: estimation, interpretation and forecast. Conditional volatility modelling: estimation, interpretation, selection and forecast.