Mathematical Statistics and Financial Time Series

Course content

The students understand the of the complex links between their previous mathematical knowledge and the contents of the lecture, understand the theoretical body of the lecture as a whole and master the corresponding methods, are able to analyze and apply the methods of the lecture, remember and understand core methods of mathematical statistics in order to assess power and optimality of statistical methods, are able to construct (optimal) confidence sets, understand selected statistical methods for high dimensional data, understand the basic probabilistic treatment of financial time series, understand properties of statistical methods in theory and application, are to model real data.

Content

• Optimal statistical decisions
• Asymptotical statistical inference
• Statistical methods for high-dimensional regression and classification
• Bagging, Boosting and Random Forests
• Volatility modelling
• Statistical inference for GARCH models and heteroscedastic time series models
• Application to real data