Statistical Methods for Data Analysis with Applications to Financial Engineering

Introduction to modern methods of statistical data analysis. Data will be used primarily from the financial industry. The course is both computational and mathematical in nature. Most facts will be stated in a rigorous manner, motivated by applications and justified at an intuitive level, but usually not proven rigorously. Emphasis will be on the relevance of concepts and the practical use of tools. A broad range of topics will be covered, including some standard techniques of univariate and multivariate data analysis (histograms, kernel density estimators, Q-Q plots), Monte Carlo simulations and calculations, analysis of heavy tailed data, use of copulas, various parametric and non-parametric regression models, both local and nonlocal, as well as analysis of time series data and Kalman filtering. Methods will be demonstrated on numerous concrete examples, with extensive use of the programming language R.