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The Multivariate Ginar(p) Process

Part of: Multivariate analysis Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Alain Latour
Alain Latour*
Affiliation:
Université du Québec à Montréal
*
∗ Postal address: Université du Québec à Montréal, Département de mathématiques, Case postale 8888, succursale Centre-Ville, Montréal, Québec, H3C 3P8, Canada.
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Abstract

A criterion is given for the existence of a stationary and causal multivariate integer-valued autoregressive process, MGINAR(p). The autocovariance function of this process being identical to the autocovariance function of a standard Gaussian MAR(p), we deduce that the MGINAR(p) process is nothing but a MAR(p) process. Consequently, the spectral density is directly found and gives good insight into the stochastic structure of a MGINAR(p). The estimation of parameters of the model, as well as the forecasting of the series, is discussed.

Keywords

MULTIVARIATE INTEGER-VALUED TIME SERIESAUTOREGRESSIVE MODELMULTIVARIATE MARTINGALEASYMPTOTIC DISTRIBUTION

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 62H12: Estimation
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 1 , March 1997 , pp. 228 - 248
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

Research supported by the Natural Sciences and Engineering Research Council of Canada (NSERCC).

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