Statistical Modelling 11 (2011), 325–349
A bivariate INAR(1) process with application
Xanthi Pedeli
Department of Statistics,
Athens University of Economics and Business
Greece
Dimitris Karlis
Department of Statistics,
Athens University of Economics and Business
76 Patisien Str.
10434 Athens
Greece
eMail: karlis@aueb.gr
Abstract:
The study of time series models for count data has become a topic of special
interest during the last years. However, while research on univariate time
series for counts now flourishes, the literature on multivariate time series
models for count data is notably more limited. In the present paper, a
bivariate integer-valued autoregressive process of order 1 (BINAR(1)) is
introduced. Emphasis is placed on models with bivariate Poisson and bivariate
negative binomial innovations. We discuss properties of the BINAR(1) model
and propose the method of conditional maximum likelihood for the estimation
of its unknown parameters. Issues of diagnostics and forecasting are
considered and predictions are produced by means of the conditional forecast
distribution. Estimation uncertainty is accommodated by taking advantage of
the asymptotic normality of maximum likelihood estimators and constructing
appropriate confidence intervals for the fe-step-ahead conditional probability
mass function. The proposed model is applied to a bivariate data series
concerning daytime and nighttime road accidents in the Netherlands.
Keywords:
BINAR; bivariate time series; count data; negative binomial; Poisson
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