IMPACT OF INFORMATION ON THE NUMBER OF TRAFFIC ACCIDENTS ON THE OUTCOME OF THE FORECAST

traffic


Introduction
Road accidents have been and continue to be a significant social problem for every country.Their causes depend on many factors, which include weather conditions, the state of intoxicated drivers, the speed of the car.etc.According to the World Health Organization (The Global Status on Road Safety 2018), every year more than 1.35 million people die in road accidents, and millions more suffer serious injuries and long-term negative health consequences.For this reason, road accidents also generate economic losses.The number of traffic accidents is decreasing year by year.This has also happened in recent years, primarily due to the COVID-19 pandemic.However, the number of road accidents on Polish roads is very high (Fig. 1), with an average of 62 road accidents every day, in which 6 people are killed and 72 injured.This causes an increase in medical costs, the need for repairs to vehicles and road infrastructure, and a negative impact on the environment (e.g., through leaks of fuel and operating fluids).Therefore, various measures are being taken to prevent traffic accidents and reduce their number.One such measure is forecasting the number of traffic accidents using known forecasting methods.Here it should also be taken into account that the number of vehicles on Polish roads is increasing (Fig. 2).The problem of traffic safety has been addressed in the following articles (Bartuska et al. 2016, Čubranić--DobroDolac et al. 2020, Gorzelanczyk, bazela 2021, Gorzelanczyk, Huk 2022, Gorzelanczyk, Tylicki 2023, Gorzelanczyk et al. 2020, 2022a, 2022b, 2022c, 2022d, Gorzelanczyk 2023a, 2023b, 2023c, 2023d).A vector autoregression model has also been used to forecast the number of traffic accidents, the drawback of which is the need to have a large number of observations of variables in order to correctly estimate their parameters (wójcik 2014), as well as the autoregression models of moneDero et al. (2021) for analyzing the number of fatalities (moneDero et al. 2021) and the curve--fit regression models of al-maDani (2018).These, in turn, require only simple linear relationships (mamczuk 2020), and an order of autoregression (assuming the series is already stationary) (PiłaTowska 2012).
biswas et al. ( 2019) used Random Forest regression to predict the number of traffic accidents.In this case, the data contains groups of correlated features of similar significance to the original data, smaller groups are favored over larger ones (Las losowy 2022), and there is instability in the method and spike prediction (Fijorek et al. 2010).cHuDy-laskowska and Pisula (2014) used an autoregressive quadratic trend model, a univariate periodic trend model and an exponential equalization model for the forecasting issue at hand.A moving average model can also be used to forecast the number of traffic accidents, which has the disadvantages of low forecast accuracy, loss of data in the sequence, and lack of consideration of trends and seasonal effects (kasHpruk 2010).ProcHozka and camej (2017) used the GARMA method, in which certain constraints are imposed in the parameter space to guarantee the stationarity of the process.Very often, the ARMA model for a stationary process or ARIMA or SARIMA for a non-stationary process is used for forecasting (ProcHazka, camaj 2017, sunny at al. 2018, DuTTa et al. 2020, karlaFTis, vlaHoGianni 2009).There is great flexibility in the models in question, but this is also a disadvantage, as good model identification requires researchers to have more experience than, for example, regression analysis (łobejko 2015).Another disadvantage is the linear nature of the ARIMA model (DuDek 2013).
Based on the presented literature analysis, it can be concluded that the problem of forecasting the number of traffic accidents has been considered by many researchers, but none of the analyzed researchers have studied how the number of historical inputs affects the quality of prediction of the number of traffic accidents?For this reason, the author addressed this issue.In this case, it is important to remember that the data on the number of traffic accidents is seasonal, and not all forecasting methods work well for this type of forecasting.

Materials and methods
The purpose of the article is to answer the question: how the number of historical inputs affects the quality of prediction of the number of traffic accidents.For this purpose, the author analyzed the annual number of road accidents in Poland from 1990-2021 from the statistics of the Police (Statystyka -Portal polskiej Policji 2022).Taking into account the above review of methods, the author used the following forecasting methods in his research to determine the forecast horizon of the number of road accidents: • As we can see, there are many forecasting methods.Their results of forecasting the number of accidents are even more.The author selected only a part of them.For this reason, for further analysis, on the basis of previous detailed studies (jurkovic et al. 2022), the author chose an adaptive method -with exponential smoothing of the seasonal component of the linear trend: none -HOLTA, for which, for the assumed data (Tab.1, 2), the average absolute percentage error MAPE (4), of the forecast of the number of traffic accidents was the smallest.The following forecast errors, determined from equations (1-5), were used to calculate measures of analytical forecast excellence: • ME -mean error (1) • MAE -mean absolute error (2) • MPE -mean percentage error (3) • MAPE -mean absolute percentage error • RMSE -root mean square error (5) where: n -number of observations, lwd(t i )number of traffic accidents over time t i , lwd(t i ) -forecasts number of traffic accidents over time t i .Using the data presented in Table 1, for the assumed forecasting method (HOLTA), the author examined how reducing the number of inputs, historical data from 32 (years 1990-2021) to 4 years (2019-2021), affected the value of the average absolute percentage error MAPE (1) of the forecast for the following years.Based on previous research, the author concluded that the forecast of the number of traffic accidents for the next 6 years using annual data can be successfully applied.The research was conducted on the basis of police statistics (Statystyka -Portal polskiej Policji 2022) on the number of traffic accidents in 1990-2021 using Statistica software.

Results
On the basis of the study, with predetermined input conditions, the average absolute percentage error of MAPE was determined (Tab.2).The last time frame studied was 2017-2021 (5 years).The inability to perform the study for another year, was due to the fact, too little data to perform the study.Considering the number of accidents in the analyzed time interval, taking into account the average absolute percentage error (Fig. 3), a forecast of the number of traffic accidents for the next 6 years was determined (Tab.3).For analysis, on the basis of previous detailed studies (jurkovic et al. 2022), the author chose an adaptive method -with exponential smoothing of the seasonal component of the linear trend: none -HOLTA.

Fig. 3 .
Fig. 3. MAPE error values for the analyzed time periods

Table 1
Number of road accidents in Poland from 1990 to 2021 Source: based on Statystyka -Portal polskiejPolicji (2022).

Table 2
MAPE road accident number forecast error values Impact of Information on the Number of Traffic Accidents… 227

Table 3
Forecasting number of road accidents for 2022-2027