Inaugural Lectures of the IAS Focus Group “Risk Analysis and Stochastic Modeling“ by Prof. Richard A. Davis and Prof. Jan Rosinski.

Date: July 20th, 2010

Time: 16:00 – 18:00 pm

Location: Zentrum Mathematik, Hörsaal 3, Boltzmannstr. 3, 85748 Garching

Program:

ABSTRACT:

Much of the recent interest in time series modeling has focused on data from financial markets, from communications channels, from speech recognition and from engineering applications, where the need for non-Gaussian, non-linear, and nonstationary models is clear. With faster computation and new estimation algorithms, it is now possible make significant in-roads on modeling more complex-phenomena.

In this talk, we will describe the procedure AutoPARM (Automatic-Piecewise AR Modeling) that can be used for analyzing a wide range of time series data that exhibit various forms of structural breaks. The novelty of the approach taken here is to combine the use of genetic algorithms with the principle of minimum description length (MDL), an idea developed by Rissanan in the 1980s, to find "optimal" models over a potentially large class of models.

This methodology will be demonstrated in a number of applications from environmental science, neuroscience, and finance. In addition to fitting piece-wise autoregressive models, which works well even for locally stationary models that are smooth, we will also consider extensions to piece-wise nonlinear models. The latter presents some formidable challenges since a nonlinear model can often appear to have quite varied behavior over different time epochs.

(This research is joint work with Thomas Lee and Gabriel Rodriguez-Yam.)

17:15 pm:

Prof. Jan Rosinski

University of Tennessee, USA

IAS Visiting Fellow

TITLE: “Infinite Divisible Stochastic Processes”

ABSTRACT:

Infinitely divisible processes are one of the simplest models incorporating jumps in random evolution of systems. Their most natural and best understood examples are Levy processes, which are continuous-time random walks.

Levy processes are also building blocks of more complicated infinitely divisible processes exhibiting long range dependence, stationarity, and high variability. Our understanding of such processes depends on the interaction with several areas of mathematics, economics, and sciences and thrives through the constant input of new ideas from these disciplines leading to a deep and rich theory. Applications are found in mathematical finance, insurance, telecommunications, extreme values theory, quantum theory, meteorology, geophysics, and astrophysics. This talk will outline some basics of the theory and applications.

If you plan to attend or if you have further questions please contact Mrs. Christine Kley (Tel. +49 89 289-17430).

TITLE: “Estimating Structural Breaks in Time Series“

16:15 pm:

Prof. Richard A. Davis

Howard Levene Professor of Statistics, Columbia University, USA

IAS Hans Fischer Senior Fellow