The Non-Stationary BINARMA(1,1) Process with Poisson Innovations: An Application on Accident Data
This paper considers the modelling of a non-stationary
bivariate integer-valued autoregressive moving average of order
one (BINARMA(1,1)) with correlated Poisson innovations. The
BINARMA(1,1) model is specified using the binomial thinning
operator and by assuming that the cross-correlation between the
two series is induced by the innovation terms only. Based on
these assumptions, the non-stationary marginal and joint moments
of the BINARMA(1,1) are derived iteratively by using some initial
stationary moments. As regards to the estimation of parameters of
the proposed model, the conditional maximum likelihood (CML)
estimation method is derived based on thinning and convolution
properties. The forecasting equations of the BINARMA(1,1) model
are also derived. A simulation study is also proposed where
BINARMA(1,1) count data are generated using a multivariate
Poisson R code for the innovation terms. The performance of
the BINARMA(1,1) model is then assessed through a simulation
experiment and the mean estimates of the model parameters obtained
are all efficient, based on their standard errors. The proposed model
is then used to analyse a real-life accident data on the motorway in
Mauritius, based on some covariates: policemen, daily patrol, speed
cameras, traffic lights and roundabouts. The BINARMA(1,1) model
is applied on the accident data and the CML estimates clearly indicate
a significant impact of the covariates on the number of accidents on
the motorway in Mauritius. The forecasting equations also provide
reliable one-step ahead forecasts.
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