Seminar: Modelling multivariate time series for counts

SpeakerDimitris Karlis
AffiliationDepartment of Statistics, Athens University of Economics and Business
DateThursday, 08 Mar 2012
Time16:00 - 17:00
LocationRoom 102, 1-19 Torrington Place
Event seriesStatistical Science Seminars
Description

Non-negative integer-valued time series are often encountered in many different scientific fields, usually in the form of counts of events at consecutive time points. Such examples can be found in epidemiology, ecology, finance just to name a few. A wide variety of models appropriate for treating count time series data have been proposed in the literature mainly for the univariate case. Analysis of multivariate counting processes presents much more difficulties. In specific, the need to account for both serial and cross-correlation complicates model specification, estimation and inference. Many of the models that have been built for count time series data are based on the thinning operator of Steutel and van Harn (1979). The model in its simplest form. i.e. the first order integer valued autoregressive model (INAR(1)), was introduced by McKenzie (1985) and Al-Osh and Alzaid (1987).

In this talk, extensions to the multi-dimensional space will be discussed. and examine its basic statistical properties. To help the exposition special care will be given to the bivariate case. The multivariate case has certain challenges especially as far as estimation is concerned. Such estimation problems do not arise in the bivariate case where estimation can be achieved using either the maximum likelihood approach or the method of Yule-Walker. Extensions to incorporate covariate information are also discussed while emphasis is placed on models with multivariate Poisson and multivariate negative binomial innovations. Real data problems are used to illustrate the model. An actuarial application will be also discussed.

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