Seminar by Prof. Marie Huskova

Change point analysis concerns  procedures on stability of statistical models.  The basic scheme can be formulated as follows: a sequence of observations $Y_1,￥dots,Y_n$ obtained at the ordered time points $t_1<¥dots<_n$ such that the first $m$ observations follow a certain statistical model and after the $m$-th observation the model changes and the remaining $n-m$ observations follow another model.  The point $m$ is unknown and is called change point. The problems are to detect changes (to test $H_0$: no change vs. $H_1$: there is a change),  to identify the location of such a change (estimate $m$) and estimate model before and after a change $m$.

There are numerous applications in meteorology, climatology, hydrology or environmental studies, econometric time series, statistical quality control among others.

After an introduction the talk will focus on robust and rank based procedures for detection of changes. Their description will be accompanied by theoretical properties and simulation results.

The last part of the talk will concern robust sequential procedures for detection of changes in Capital Assets Pricing Model (CAPM). Theoretical results together with an application to real data set will be presented.