A simple integer-valued bilinear time series model

Paul Doukhan (1, 2, 3) , Alain Latour (4, 5) , D. Oraichi (5)

1 CREST - Centre de Recherche en Économie et Statistique
2 CES - Centre d'économie de la Sorbonne
3 SAMOS - Statistique Appliquée et MOdélisation Stochastique
4 LABSAD - Laboratoire de Statistiques et Analyse des Données
5 UQAM - Université du Québec à Montréal = University of Québec in Montréal

In this paper, we extend the integer-valued model class to give a nonnegative integer-valued bilinear process, denoted by INBL(p,q,m,n), similar to the real-valued bilinear model. We demonstrate the existence of this strictly stationary process and give an existence condition for it. The estimation problem is discussed in the context of a particular simple case. The method of moments is applied and the asymptotic joint distribution of the estimators is given: it turns out to be a normal distribution. We present numerical examples and applications of the model to real time series data on meningitis and Escherichia coli infections.

Mots clés: Integer-valued process; bilinear model

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Paul Doukhan, Alain Latour, D. Oraichi. A simple integer-valued bilinear time series model. Advances in Applied Probability, 2006, 38 (2), pp.559-578. ⟨10.1239/aap/1151337085⟩. ⟨hal-00267627⟩