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

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Traditional count data models (Poisson, Negative Binomial) struggle with serial correlation in time series data.
• Real-valued time series models like ARIMA may be inappropriate for non-negative integer-valued data due to normality assumptions.
• Integer-valued autoregressive (INAR) Poisson models offer a promising alternative for time series count data.

Purpose of the Study:

• To introduce and evaluate Integer-valued Autoregressive (INAR) Poisson models for analyzing traffic accident time series data in Great Britain.
• To compare the performance of INAR models against traditional Box-Jenkins real-valued models (ARIMA) for both aggregated and disaggregated traffic data.

Main Methods:

• Application of Integer-valued Autoregressive (INAR) Poisson models to time series count data of traffic accidents.
• Comparison of INAR models with Autoregressive Integrated Moving Average (ARIMA) models using aggregated (e.g., Great Britain, years) and disaggregated (e.g., zone, months) data.
• Evaluation of model performance based on coefficient estimates and goodness-of-fit metrics.

Main Results:

• For aggregated traffic accident data with high counts, INAR and ARIMA models showed similar performance.
• For disaggregated traffic accident data with low counts, INAR Poisson models significantly outperformed ARIMA models.
• INAR models demonstrate superior ability to handle serial correlation in time series count data, especially at lower count levels.

Conclusions:

• INAR Poisson models are a more appropriate and effective tool for analyzing time series count data, particularly when counts are low and serial correlation is present.
• The study highlights the limitations of traditional ARIMA models for specific types of count data, advocating for the adoption of INAR models in such scenarios.
• Further research is needed to address limitations of INAR models regarding seasonality and unobserved heterogeneity.