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A simple integer-valued bilinear time series model

Part of: Stochastic processes Parametric inference Statistics Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

P. Doukhan ,
A. Latour  and
D. Oraichi
P. Doukhan*
Affiliation:
CREST
A. Latour*
Affiliation:
Université Pierre Mendès-France
D. Oraichi*
Affiliation:
CHU Sainte-Justine
*
∗ Postal address: Laboratoire de Statistique, CREST, Timbre J340, 3 avenue Pierre Larousse, 92240 Malakoff Cedex, France. Email address: paul.doukhan@ensae.fr
∗∗ Postal address: Laboratoire de Statistique et Analyse de Données, Université Pierre Mendès-France, Bâtiment Sciences Humaines et Mathématiques, 1251 avenue Centrale, BP 47, 38040 Grenoble Cedex 09, France. Email address: alain.latour@upmf-grenoble.fr
∗∗∗ Postal address: Centre de Recherche du CHU Sainte-Justine, 3175 chemin de la Côte-Sainte-Catherine, Montréal, QC H3T 1C5, Canada. Email address: driss.oraichi@recherche-ste-justine.qc.ca
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Abstract

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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.

Keywords

Integer-valued processbilinear model

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc. 60G10: Stationary processes
Secondary: 62F10: Point estimation 62-07: Data analysis
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 2 , June 2006 , pp. 559 - 578
Copyright
Copyright © Applied Probability Trust 2006 

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