Time Series and Extreme Value Theory

The course consists of two parts: Extreme Value Theory and Time Series.

The course considers questions such as: What is the chance that the price of oil will be higher than $120/Barrel coming week? Can we expect that UK interest rates will rise next year? How can we assess if global warming is occurring? What is the chance that the daily loss of the stock price of ABN-AMRO is larger than, say 20%, which has never occurred before? How to determine the height of a dike such that the probability of a flood, i.e., the water level exceeding the dike, in a given year is 1/10,000? What is the impact of a dramatic decline in the US stock market on DAX 30 index?

In this course students will build up some theoretical basis, mainly probabilistic results within the area of time series and extreme value theory. Moreover, students will learn statistical methods for dealing with non-stationary data, multivariate data and rare events and assessing extreme risks for data from various fields such as finance, actuarial science, hydrology and environmental science.

Furthermore the student is capable to perform a statistical analysis with the statistical package R.

The Extreme Value Theory part considers topics such as max-domain attractions, peak over threshold approach, estimations of extreme value index, tail probability and high quantile, and tail dependence and independence.

The Time Series part will cover topics such as ARMA models, spectral analysis, non-stationarity, GARCH models, state space models.

Implementations of statistical methods in R will be part of the course. Examples of real applications from environmental science and finance will also be discussed.