Statistics and Data Science Seminar
Prof. Noelle Samia
Northwestern University
ON THE ANALYSIS OF NON-NORMAL NONLINEAR TIME SERIES
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).
Wednesday April 14, 2010 at 3:00 PM in SEO 636