Bojan Basrak: On dependence structure of multivariate heavy tailed time series

Na prvem seminarju iz finančne matematike v drugem semestru bo predaval prof. Bojan Basrak z Univerze v Zagrebu. 

Povzetek predavanja:

On dependence structure of multivariate heavy tailed time series Extreme values of a stationary, multivariate time series may exhibit dependence across coordinates and over time. We will discuss a new and potentially useful tool called tail process to describe and model such extremes. The key property is the following fact: existence of the tail process is equivalent to multivariate regular variation of finite cuts of the original process. Certain re- markable properties of the tail process are exploited to shed new light on known results on certain point processes of extremes. The theory is shown to be applica- ble with great ease to stationary solutions of autoregressive processes with random coefficient matrices, this includes certain examples of multivariate GARCH models frequently used in financial modeling. In this class of models, the distribution of the tail process is calculated by a combination of analytical methods and a novel sampling algorithm.

(joint work with Johan Segers, Université catholique de Louvain, Institut de statistique)