Time series count data models: an empirical application to traffic accidents

Count data are primarily categorised as cross-sectional, time series, and panel. Over the past decade,Poisson and Negative Binomial (NB) models have been used widely to analyse cross-sectional and timeseries count data, and random effect and fixed effect Poisson and NB models have been used to analyse panelcount data. However, recent literature suggests that although the underlying distributional assumptionsof these models are appropriate for cross-sectional count data, they are not capable of taking into accountthe effect of serial correlation often found in pure time series count data. Real-valued time series models,such as the autoregressive integrated moving average (ARIMA) model, introduced by Box and Jenkinshave been used in many applications over the last few decades. However, when modelling non-negativeinteger-valued data such as traffic accidents at a junction over time, Box and Jenkins models may beinappropriate. This is mainly due to the normality assumption of errors in the ARIMA model. Over thelast few years, a new class of time series models known as integer-valued autoregressive (INAR) Poissonmodels, has been studied by many authors. This class of models is particularly applicable to the analysisof time series count data as these models hold the properties of Poisson regression and able to deal withserial correlation, and therefore offers an alternative to the real-valued time series models.The primary objective of this paper is to introduce the class of INAR models for the time series analysis oftraffic accidents in Great Britain. Different types of time series count data are considered: aggregated timeseries data where both the spatial and temporal units of observation are relatively large (e.g., Great Britainand years) and disaggregated time series data where both the spatial and temporal units are relativelysmall (e.g., congestion charging zone and months). The performance of the INAR models is comparedwith the class of Box and Jenkins real-valued models. The results suggest that the performance of thesetwo classes of models is quite similar in terms of coefficient estimates and goodness of fit for the case ofaggregated time series traffic accident data. This is because the mean of the counts is high in which casethe normal approximations and the ARIMA model may be satisfactory. However, the performance of INARPoisson models is found to be much better than that of the ARIMA model for the case of the disaggregatedtime series traffic accident data where the counts is relatively low. The paper ends with a discussion onthe limitations of INAR models to deal with the seasonality and unobserved heterogeneity.