# Forecasting the Number of Road Accidents in Polish Provinces Using Trend Models
## 2 Literature Review  
For accident data to be relevant, multiple data sources must be handled properly. Combining data from many sources, by merging various road accident data, increases the accuracy of analytical results [18]. A statistical study to estimate the severity of road accidents and clarify the relationship between the accidents and road users was conducted by [PERSON] et al. [19]. The result of this research was suggestions for improving traffic safety standards and adopting other traffic safety measures. [PERSON] et al. [20] conducted a statistical study of traffic safety in selected regions of Poland based on the speed at which the number of road accidents and their causes were determined. The study used multivariate statistical analysis to examine the safety aspects of accident perpetrators. The choice of the source of accident data for analysis depends on the type of traffic problem under consideration. Combining statistical models with other natural driving data or other data acquired by intelligent transportation systems can improve the accuracy of accident prediction and contribute to the elimination of accidents [21]. Various methods for predicting the number of accidents can be found in the literature. Time series methods are most commonly used to predict the number of traffic accidents [22; 23]. The disadvantages are the inability to assess the quality of the prediction based on outdated forecasts and the frequent autocorrelation of the residual components of the accident rates [24]. [PERSON] et al. [25] used multiple seasonality models for forecasting, and [PERSON] et al. [26] used Holt-Winters exponential smoothing. Its limitations include the inability to introduce exogenous variables into the model [27; 28]. The vector autoregression model has also been used to predict the number of traffic accidents. The disadvantage is that it requires a large number of variable observations to properly estimate the parameters [29]. To analyze the number of deaths [30] and the Al-Madani curve-fitting regression model [31], they require only a simple linear relationship [32] and an order of autoregression (assuming the series is already stationary) [33]. [PERSON] et al. [34] used random forest regression to predict the number of traffic accidents. In this case, the data contain clusters of correlated features with similar validity to the original data, with small clusters favored over large clusters [35] and method instability and spike prediction [36]. [PERSON] and [PERSON] [37] applied autoregressive quadratic trend models, one-dimensional cyclical trend models and exponentially adjusted models to the forecasting problem at hand. Moving average models can also be used to predict the problem at hand. Its drawbacks are poor prediction accuracy, the resulting loss of data, and failure to account for trends and seasonal effects [38]. [PERSON] and [PERSON] [39] used the GARMA method. This method imposes some restrictions on the parameter space to ensure the stationarity of the process. ARMA models for steady-state processes and ARIMA or SARIMA models for transient processes are often used for forecasting [25; 40; 41]. Although these models lead to great flexibility of the models in question, they are also a disadvantage, as identifying good models requires more experience from the researcher than, for example, regression analysis [42]. Another disadvantage is the linearity of ARIMA models [43]. [PERSON] and [PERSON] used the ANOVA method in a study [44] to predict the number of traffic accidents. The disadvantage of this method is additional assumptions, especially the assumption of sphericity, the violation of which can lead to erroneous conclusions [45]. Neural network models are also used to predict the number of traffic accidents. The disadvantages of SSNs are the need for experience in this area [44; 46] and the dependence of the final solution on the initial conditions of the network and the lack of interpretability in the traditional way.