## 6 Discussion and Conclusions  
Traffic accident incidence results from various factors. Spatial and temporal structures are traffic accidents' inherent traits. Traffic accidents usually follow Poisson or Negative Binomial distribution. This study used a time series Negative Binomial count data model to capture traffic crash features, investigate influential factors, and predict future crash number. Daily crash incidence is difficult to forecast. This study achieved 0.7 error of RMSD for crash prediction. Results show that previous crash occurrence is the most significant factor of future crashes happening. Other traffic operation data, such as speed, traffic flow, weather, and vehicle types, may not play a significant role in crash prediction. Although deep learning forecasting methods such as Long Short Term Memory model (LSTM), Bayesian Neural Network (BNNs), or machine learning methods, such as Support Vector Machine (SVM) as well as multivariate adaptive regression splines (MARS), achieved moderate accuracy in crash prediction, the difficulty of interpreting modeling structure compromises the real application of deep learning models in crash forecasting [13]. Linear regression is a statistical technique known as multimodal adaptable rehabilitation shafts (MARS). It is a non-parametric extrapolation approach that dynamically analyzes intermodulation distortion and interconnections among factors, acting as an augmentation of model parameters. For instance, even though the forecasting number is close to the real number, police officers do not know the specific reason leading to crashes. Therefore, duty arrangement is hard to allocate accordingly. In addition, due to the large scale of the modeling parameter, any small parameter change may influence model stability. Robustness of modeling is becoming an issue. The mathematical statistical model in time series count data distribution for crash forecasting is more robust, and the relationship between explanatory variables and traffic crash accidents is easy to interpret. This paper compared the Negative Binomial time series model with the Poisson time series model and selected Negative Binomial time series model to account overdispersion. As an alternative, the Quasi-Poisson model may also be considered to account for overdispersion by adding a conditional variance of \(\varphi\lambda\) as linearly and not quadratically increasing in the conditional mean of \(\lambda\)[34]. Additionally, zero-inflation hurdle GARCH processes can also be used as generalizations of time series count data model to deal with excess zeros, which is typical in real time traffic accidents for future analysis. Hourly and daily crash prediction can help traffic police and the freeway control center to devise corresponding regulations to prevent crashes. However, since a crash is a small probability and random event, prediction of a crash incidence with high accuracy is very hard. Therefore, predicting crash risk may also be an alternative to predicting the real number. For actual crash number prediction, when the predicted value is larger than 0.5, then it will be rounded to 1. Roundness will also introduce some errors. This paper compares several machine learning and time series forecasting methods in predicting short time traffic crashes. It shows that the count data time series Negative binomial model outperforms typical machine learning methods. The novelty of this research is to compare different forecasting methods for both machine learning and conventional time series models in crash prediction, and it proposes a count data time series model with loosening the strict assumption of ARIMA and introducing intervention and seasonal effect in INGARCH time series generalized linear regression. However, this research has some potential limitations. In the first place, it does not consider excess zero in crash data. For further improvement, the zero inflation or hurdle model structure can be involved.