An integer-valued bilinear type model

Alain Latour (1) , Lionel Truquet (2, 3, 4, 5)

1 SMS - Statistique et Modélisation Stochatisque
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 CREST - Centre de Recherche en Économie et Statistique
4 CES - Centre d'économie de la Sorbonne
5 IRMAR - Institut de Recherche Mathématique de Rennes

A integer-valued bilinear type model is proposed. It can take positive as well as negative values. The existence of the process is established in Lm. In fact, this process is the unique causal solution to an equation that is similar to a classical bilinear type model equation. For the estimation of the parameters, we suggest a quasi-maximum likelihood approach. The estimator is strongly consistent and asymptotically normal.

Mots clés: Times series; Bilinear Processes; Stable Processes; Point estimation; Asymptotic properties of estimators; Asymptotically normal estimators

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

Alain Latour, Lionel Truquet. An integer-valued bilinear type model. 2009. ⟨hal-00373409⟩