Prof. Noelle Samia : ON THE ANALYSIS OF NON-NORMAL NONLINEAR TIME SERIES

Posted by , part of the Statistics and Data Science Seminar.

At

April 14, 2010, 3 p.m.

In

SEO 636

Abstract

The open-loop Threshold Model proposed by Tong (1990) is a stochastic piecewise-linear regression model useful for modeling conditionally normal response time-series data. How- ever, in many applications, the response variable is conditionally non-normal, e.g. Poisson or binomially distributed. We generalize the open-loop Threshold Model by introducing the Generalized Threshold Model (GTM). Specifically, it is assumed that the conditional probability distribution of the response variable belongs to the exponential family, and the conditional mean response is linked to some piecewise-linear stochastic regression function. The consistency and limiting distribution of the maximum likelihood estimator are derived. We illustrate the GTM with a real application on the annual number of human bubonic plague cases in Kazakhstan. This is based on joint work with Professor Kung-Sik Chan (University of Iowa) and Professor Nils C. Stenseth (University of Oslo).