Séminaire d’actuariat, 20 octobre 2011, Université Laval

le 10 octobre 2011 à 11:24
Jean-Francois Plante

Jeudi 20 octobre 2011, 15h30 – 16h30, Salle COP-1168 (auditorium du Pavillon photonique), Université Laval.

Multivariate Integer Autoregressive Models
Dimitris Karlis, Athens University of Economics and Business

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. Representative examples can be found in epidemiology, ecology, finance and elsewhere. Due to their frequent occurrence, a wide variety of models appropriate for treating count time series data have been proposed in the literature. The vast majority of such models consider the univariate case since the 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. We thus define a multivariate integer valued autoregressive process of order 1 (MINAR(1)) 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.