Volume:13, Issue: 11, 2019 Page No: 193 - 196

ISSN: 2517-9934

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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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