Forecasting the number of road accidents in Poland by day of the week and the impact of pandemics and pandemic-induced changes

Abstract

The COVID19 pandemic has significantly affected the performance of the transport sector and its overall intensity. Reduced mobility has a large impact on the number of road accidents. The aim of this study is to forecast the number of road accidents in Poland and to assess the impact of the COVID19 pandemic on the variation in road crashes. For this purpose, day-wise historical crash data from 2011 onwards have been collected and analysed. Based on real historical field data, the future has been forecasted for both pandemic and nonpandemic variants. Forecasting of the number of accidents has been carried out using selected time series models and exponential models. Based on obtained data, it can be stated that pandemic resulted in a decrease in number of road accidents in Poland with ranges of reduction varying from 11% to 30% based on different days of week. Most visible decrease is observed on 3 days viz. Monday, Wednesday, and Saturday. Further, the projections show that in view of the current situation one may expect further decrease in the number of road accidents in Poland.

Keywords:

• Road accident
• pandemic
• Poland
• forecasting
• exponential smoothing

1. Introduction

Road accidents are incidents that cause not only injury or death to road users, but also material damage. According to World Health Organization (WHO) data, about 1.3 million people die every year as a result of road accidents. In most countries, road accidents take up an average of 3% of their gross domestic product (GDP). Road accidents are the leading cause of death for minors and young people aged between 5–29 years (WHO. The Global status on road safety, 2018). The UN General Assembly has set an ambitious target of halving the number of deaths and injuries from road accidents by 2030 with respect to the numbers in 2018.

The extent of a road accident is an attribute to determine the severity of the accident. Predicting accident severity is crucial for relevant authorities while developing transport safety policies to eliminate accidents, reduce injuries, fatalities and property damage (Tambouratzis et al., 2014; Zhu et al., 2019). Identification of critical factors affecting accident severity is a prerequisite for developing countermeasures to eliminate and mitigate accident severity (Arteaga et al., 2020). Yang et al. (2022) proposed a multi-node Deep Neutral Network (DNN) to predict different levels of severity of injury, death and property loss. According to the authors, DNN technique allows for a comprehensive and accurate analysis of the severity of road accidents.

There are several sources of accident data. Most commonly, they are collected and analysed by government authorities through relevant government agencies. Data are collected through police reports, insurance databases or hospital records. Partial information on road accidents is then processed for the transport sector on a larger scale (Gorzelanczyk et al., 2020).

Intelligent transport systems are currently the most important source of data related to road accident analysis and forecasting. This data can be processed through the use of GPS devices in vehicles (Chen, 2017). Roadside vehicle detection microsystems can continuously record vehicle data (speed, traffic volume, vehicle type, etc.; Khaliq et al., 2019). A vehicle number plate recognition system also enables the collection of large amounts of traffic data over a monitored period of time (Rajput et al., 2015). Social media can be another source of traffic and accident data, but its accuracy may be insufficient due to the incompetence of reporters (Zheng et al., 2018).

To ensure the relevance of accident data, it is necessary to work with several data sources, which are needed to be confronted appropriately. Combining different data sources by consolidating heterogeneous road accident data helps in increasing the accuracy of analysis results (Abdullah & Emam, 2016).

A statistical study to assess the severity, finding the relationship between road accidents and road users was conducted by Vilaça et al. (2017). The result of the study is a suggestion to improve road safety standards and adopt other policies related to transport safety.

Bąk et al. (2019) conducted a statistical study of road safety in a selected region of Poland based on the number of road accidents, and attempted to learn various causes for the causes of road accidents. Their study used multivariate statistical analysis to examine safety data on those responsible for missing.

The choice of accident data source for analysis depends on the type of traffic problem being addressed. The combination of statistical models with other natural driving data or other data obtained through intelligent transport systems contributes to the accuracy of accident forecasts and contributes to the elimination of accidents (Chand et al., 2021).

Different methods for forecasting the number of accidents can be found in the literature. Most commonly, time series methods are used to forecast the number of road accidents (Helgason, 2016; Lavrenz et al., 2018), the disadvantages of which are the inability to assess the quality of the forecast based on expired forecasts and the often-occurring autocorrelation of the residual component (Forecasting based on time series, 2022). Procházka et al. (2017) utilized the multiple seasonality model for forecasting and Sunny et al. (2018) used the Holt-Winters exponential smoothing method (Sunny et al., 2018). The drawbacks of these methods include the inability to introduce exogenous variables into the model (Dudek, 2013; Szmuksta-Zawadzka & Zawadzki, 2009).

A vector autoregression model is used to forecast the number of road accidents, whose limitation is the requirement of a large number of observations of the variables in order to correctly estimate their parameters (Wójcik, 2014). While forecasting the number of road accidents in the vector autoregression model, the major limitation faced is the requirement of a large number of points in order to correctly conduct the estimation of the parameters (Wójcik, 2014). Monederoa et al. (2021) have also successfully used the autoregression models to predict the number of fatalities. Similarly, Boom’s regression models have been used by Al-Madani (2018). These models require one single-line connection (Mamczur 2022, Piłatowska, 2012).

Biswas et al. (2019) used Random Forest regression to predict the number of road accidents. In another study, the data contain groups of correlated features with similar significance to the original data, where smaller groups are favoured over larger groups (Random forest, 2022), and there is instability in the method and spike prediction (Fijorek et al., 2010). Chudy-Laskowska and Pisula (2014) used the following in the prediction problem under discussion: an autoregressive model with quadratic trend, a model with univariate periodic trend and an exponential equalization model. A moving average model can be used for the prediction of the discussed issue; however, the disadvantages of the technique are low prediction accuracy, loss of data in the sequence, lack of consideration of trends and seasonal effects (Kaszpruk, 2010). Prochozka and Camej used the GARMA method. In this method, some restrictions are imposed in the parameter space to guarantee the stationarity of the process (Prochazka & Camaj, 2017). Very often, the ARMA model for a stationary process or ARIMA or SARIMA for a non-stationary process is used for forecasting (Dutta et al., 2020; Karlaftis & Vlahogianni, 2009; Procházka et al., 2017; Sunny et al., 2018). This results in very high flexibility of the discussed models, but it is also their disadvantage, as good model identification requires more experience from the researcher than, for example, regression analysis (Łobejko, 2015). Another disadvantage is the linear nature of the ARIMA model (Dudek, 2013).

Chudy-Laskowska and Pisula (2015) used the ANOVA method to forecast the discussed issue. The disadvantage of this method is the adoption of additional assumptions, in particular the assumption of sphericity, the violation of which may lead to erroneous conclusions (Road safety assessment handbook). Neural network models are also used to predict the number of road accidents. The disadvantages of the model used are the need for experience in this field (Chudy-Laskowska & Pisula, 2014; Wrobel, 2017) and the dependence of the final solution on the initial conditions of the network, as well as the lack of interpretability in the traditional way (Data mining techniques StatSoft).

A new prediction method is the use of Hadoop model by Kumar et al. (2019). The disadvantage of this method is its inability to work with small data files (Top Advantages and Disadvantages of Hadoop, 2022). Karlaftis and Vlahogianni (2009) used the Garch model for prediction. The disadvantages of this method are its complex form and complicated model (Fiszeder, 2009; Perczak & Fiszeder, 2014). On the other hand, McIlroy and his team used the ADF test (McIlroy et al., 2019), which has the drawback of poor power in the case of autocorrelation of the random component (Muck, 2022).

Various researchers (Li et al., 2017; Shetty et al., 2017) have also used Data-Mining techniques for forecasting, which usually have the disadvantage of huge sets of general descriptions (Marcinkowska, 2015). One also encounters the combination of models proposed by Sebego et al. (2008) as a combination of different models. Parametric models were also proposed in the work of Bloomfield (1973).

Given the above analysis, the purpose of this study is to forecast the number of road accidents in Poland and to assess the impact of the COVID-19 pandemic on the variability of road accidents. For this purpose, daily historical accident data since 2011 were collected and analyzed. Based on actual historical field data, forward-looking forecasts were made for both the pandemic and non-pandemic variants. Selected time series models and exponential models were used to forecast the number of accidents.

2. Materials and methods

The number of road accidents on Polish roads is decreasing year by year. Based on the day of crash occurrence, it is observed that the drop in accidents is more than 60% on Saturdays and Sundays. Further, day-wise fluctuations and variations in the number of crashes are also recorded with a decreasing trend. However, when compared with the European Union, the number of accidents is still very high in Poland. Next, when the accidents happened during pandemic are observed, a drop in the number of road crashes is observed. As compared to 2019, 23% less road crashes have been recorded in 2020. Figure 1 graphically represents the trend in road crashes in Poland over the years across 7 days of a week.

Figure 1. Comparison of the number of accidents in Poland from 2001–2021.

Selected exponential alignment models were used to forecast the number of road accidents by day of the week. The essence of these methods is that the time series of the forecast variable is pronounced with a weighted moving average and the weights are determined according to the exponential function. These weights were optimally selected by the Statistica software in which the analysis was conducted. The forecast in this case is based on a weighted average of the current and historical series. The result of the forecast using this method depends on the choice of the model and its parameters. Forecasting the number of accidents in Poland was carried out using selected time series models.

The following errors of expired forecasts determined from equations (1(1) $\mathit{ME}=\frac{1}{n}{\sum }_{i=1}^n\left(Y_i-Y_p\right)$(1) –5(5) $\mathit{SSE}=\sqrt{\frac{1}{\mathit{n}}{\sum }_{i=1}^n{\left(Y_i-Y_p\right)}^2\mathit{\hspace{0.17em}}}$(5) ) were used to calculate measures of analytical forecasting perfection:

• ME—mean error

(1) $\mathit{ME}=\frac{1}{n}{\sum }_{i=1}^n\left(Y_i-Y_p\right)$(1)

• MAE—mean average error

(2) $\mathit{MAE}=\frac{1}{\mathit{n}}{\sum }_{i=1}^n\left|Y_i-Y_p\right|$(2)

• MPE—mean percentage error

(3) $\mathit{MPE}=\frac{1}{\mathit{n}}{\sum }_{i=1}^n\frac{Y_i-Y_p}{Y_i}$(3)

• MAPE—mean absolute percentage error

(4) $\mathit{MAPE}=\frac{1}{\mathit{n}}{\sum }_{i=1}^n\frac{\left|Y_i-Y_p\right|}{Y_i}$(4)

• SSE—Error Sum of Squares

(5) $\mathit{SSE}=\sqrt{\frac{1}{\mathit{n}}{\sum }_{i=1}^n{\left(Y_i-Y_p\right)}^2\mathit{\hspace{0.17em}}}$(5)

where:

n—the length of the forecast horizon,

Y—observed value of road accidents,

Y_p—forecasted value of road accidents.

In order to compare the number of accidents during a pandemic and if it did not exist, the mean percentage error was minimized.

The day-wise variation in the number of road accidents was tested by conducting a Kruskal-Wallis test. The value of the test statistic is 14.4 with test probability p < 0.05. The value states that according to the hypothesis, equality of the average level of road accidents should be rejected. This means that the number of accidents we are dealing with, is exhibiting a systematic decrease in the average level of accidents over the years. Further, day-wise there is a marked variation among the crashes as is presented in Figure 2. Figure 2 clearly reveals that the highest number of road accidents takes place during the weekend, on Friday and Saturday. This is due to increased traffic on weekends which propels a high number of road accidents. Sundays exhibit least number of road crashes as the workplaces are closed on that day leading to less traffic flow on roads.

Figure 2. Comparison of the average number of road accidents in Poland by days of the week in 2001–2021.

Selected time series models were used for further analysis to forecast the number of road accidents.

3. Forecasting the road accidents

Data from the Polish Police from 2001 to 2021 were used to forecast the weekly number of accidents. To examine the role of pandemic on the number of road accidents in Poland, the study was divided into two timelines:

• From the end of 2011 to 2021 (with pandemic), and

• From the end of 2011 till the end of 2019 (without pandemic)

The study assumes that the beginning of the pandemic is 2020, due to the lack of statistics from the police on the number of road accidents by days of the week and breakdown by months. The day-wise forecasting results of the study where the effect of pandemic is included (upto 2021) are shown in Figures 3 to 9. Similarly, the day-wise crash forecasting without considering the data from pandemic (upto 2019) is shown in Figures 10 to 16. The various forecasting methods used in the study are coded as M1, M2, …, Mn. The various forecasting techniques used for the study are as follows.

Figure 3. Forecasting the number of road accidents on Monday from 2022–2031.

Figure 4. Forecasting the number of road accidents on Tuesday from 2022–2031.

Figure 5. Forecasting the number of road accidents on Wednesday from 2022–2031.

Figure 6. Forecasting the number of road accidents on Thursday from 2022–2031.

Figure 7. Forecasting the number of road accidents on Friday from 2022–2031.

Figure 8. Forecasting the number of road accidents on Saturday in 2022–2031.

Figure 9. Forecasting the number of road accidents on Sunday from 2022–2031.

Figure 10. Forecasting the number of road accidents on Monday from 2020–2029 if there was no pandemic.

Figure 11. Forecasting the number of road accidents on Tuesday from 2020–2029 if there was no pandemic.

Figure 12. Forecasting the number of road accidents on Wednesday from 2020–2029 if there was no pandemic.

Figure 13. Forecasting the number of road accidents on Thursday from 2020–2029 if there was no pandemic.

Figure 14. Forecasting the number of road accidents on Friday from 2020–2029 if there was no pandemic.

Figure 15. Forecasting the number of road accidents on Saturday from 2020–2029 if there was no pandemic.

Figure 16. Forecasting the number of road accidents on Sunday from 2020–2029 if there was no pandemic.

• M1—moving average method 2-points,

• M2—moving average method 3-points,

• M3—moving average method 4-points,

• M4—exponential smoothing no trend seasonal component: none,

• M5—exponential smoothing no trend seasonal component: additive,

• M6—exponential smoothing no trend seasonal component: multiplicative,

• M7—exponential smoothing linear trend seasonal component: none Holt,

• M8—exponential smoothing linear trend seasonal component: additive,

• M9—exponential smoothing linear trend seasonal component: multiplicative Winters,

• M10—exponential smoothing exponential seasonal component: none,

• M11—exponential smoothing exponential seasonal component: additive,

• M12—exponential smoothing exponential seasonal component: multiplicative,

• M13—exponential smoothing fading trend seasonal component: none,

• M14—exponential smoothing fading trend seasonal component: additive,

• M15—exponential smoothing fading trend seasonal component: multiplicative)

4. Results

The charts below show the results of forecasting the number of road accidents in Poland by pandemic and day of the week (Table 1). For Monday, the projected number of traffic accidents from 2022 to 2031, changes for 2022 from 3148 for M8 to 5839—M3. For the last analyzed period, 2031, the value of the number of traffic accidents changes from 1175—M7 to 4080—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 350%. For the weekday studied, the smallest MAPE error value was observed for the M7 method (Figure 3).

Table 1. Forecasting results

year	Monday			Tuesday			Wednesday			Thursday			Friday			Saturday			Sunday
	with pandemic	without pandemic	%	with pandemic	without pandemic	%	with pandemic	without pandemic	%	with pandemic	without pandemic	%	with pandemic	without pandemic	%	with pandemic	without pandemic	%	with pandemic	without pandemic	%
2011	5765	5765	100	5502	5502	100	5730	5730	100	5607	5607	100	6656	6656	100	5942	5942	100	4863	4863	100
2012	5562	5562	100	5142	5142	100	5238	5238	100	5465	5465	100	6140	6140	100	5238	5238	100	4261	4261	100
2013	5255	5255	100	5206	5206	100	5060	5060	100	5109	5109	100	5965	5965	100	4961	4961	100	4291	4291	100
2014	5231	5231	100	5054	5054	100	5054	5054	100	4914	4914	100	5792	5792	100	4843	4843	100	4082	4082	100
2015	4957	4957	100	4737	4737	100	4465	4465	100	4881	4881	100	5510	5510	100	4571	4571	100	3846	3846	100
2016	4894	4894	100	4815	4815	100	4831	4831	100	4945	4945	100	5675	5675	100	4625	4625	100	3879	3879	100
2017	4872	4872	100	4564	4564	100	4744	4744	100	4846	4846	100	5474	5474	100	4398	4398	100	3862	3862	100
2018	4794	4794	100	4437	4437	100	4676	4676	100	4444	4444	100	5230	5230	100	4412	4412	100	3681	3681	100
2019	4584	4584	100	4334	4334	100	4305	4305	100	4370	4370	100	4790	4790	100	4398	4398	100	3507	3507	100
2020	3490	4512	129	3345	4292	128	3411	4231	124	3417	4248	124	3922	4642	118	3319	4270	129	2636	3334	126
2021	3455	4349	126	3262	4033	124	3266	4107	126	3309	3975	120	3912	4333	111	3110	3966	128	2502	3165	126
2022	3230	4194	130	3048	3987	131	3068	3986	130	3091	3879	126	3669	4219	115	3099	4003	129	2332	2996	128
2023	3001	4126	137	2959	3949	133	2850	3868	136	2873	3758	131	3425	3996	117	2859	3891	136	2143	2827	132
2024	2773	3976	143	2769	3700	134	2631	3755	143	2654	3486	131	3182	3701	116	2619	3614	138	1927	2657	138
2025	2545	3834	151	2593	3663	141	2413	3644	151	2436	3391	139	2938	3572	122	2380	3648	153	1741	2488	143
2026	2317	3772	163	2376	3634	153	2194	3537	161	2218	3271	147	2695	3350	124	2140	3545	166	1552	2319	149
2027	2088	3636	174	2268	3393	150	1976	3433	174	2000	3000	150	2451	3068	125	1900	3293	173	1361	2150	158
2028	1860	3506	188	2083	3365	162	1758	3332	190	1782	2906	163	2208	2924	132	1661	3324	200	1153	1981	172
2029	1632	3449	211	1908	3345	175	1539	3234	210	1564	2787	178	1964	2703	138	1421	3230	227	964	1812	188
Average			129			122			128			121			111			130			124,27

On the next analyzed date, the projected number of traffic accidents from 2022 to 2031, changes for 2022 from 2880 for M8 to 5539—M3. For the last analyzed period, 2031, the value of the number of traffic accidents changes from 1319—M8 to 3844—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 291%. For the studied day of the week, the smallest MAPE error value was observed for the M9 method (Figure 4).

For Wednesday, the projected number of traffic accidents from 2022 to 2031, changes for 2022 from 3064 for M8 to 5638—M3. For the last analyzed period, 2031, the value of the number of traffic accidents changes from 1102—M7 to 3914—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 355%. For the weekday studied, the smallest MAPE error value was observed for the M7 method (Figure 5).

On Thursday, the projected number of traffic accidents from 2022 to 2031, changes for 2022 from 2827 for M8 to 5735—M3. For the last analyzed period, 2031, the value of the number of traffic accidents changes from 749—M8 to 3885—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 518%. For the day of the week studied, the smallest MAPE error value was observed for the M7 method (Figure 6).

On Friday, the projected number of traffic accidents from 2022 to 2031, changes for 2022 from 3471 for M14 to 6604—M3. For the last analyzed period, 2031, the value of the number of traffic accidents changes from 1312—M15 to 4463—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 340%. For the weekday studied, the smallest MAPE error value was observed for the M7 method (Figure 7).

On Saturday, the projected number of traffic accidents from 2022 to 2031, changes for 2022 from 2762 for M10 to 5813—M3. For the last analyzed period, 2031, the value of the number of traffic accidents changes from 813—M10 to 3809—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 340%. For the weekday studied, the smallest MAPE error value was observed for the M7 method (Figure 8).

On Sunday, the projected number of traffic accidents from 2022 to 2031, changes for 2022 from 2231 for M8 to 4866—M3. For the last analyzed period, 2031, the value of the number of traffic accidents changes from 542—M7 to 3081—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 568%. For the studied day of the week, the smallest MAPE error value was observed for the M9 method (Figure 9).

On Monday, not including the pandemic, the projected number of road accidents from 2022 to 2029 changes for 2020 from 3956 for M8 to 4786—M3. For the last period analyzed, 2029, the value of the number of traffic accidents changes from 2225—M7 to 4825—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 216%. For the weekday studied, the smallest MAPE error value was observed for the M12 method (Figure 10).

On Tuesday, not including the pandemic, the projected number of road accidents from 2022 to 2029 changes for 2020 from 4123 for M7 to 4537—M3. For the last period analyzed, 2029, the value of the number of traffic accidents changes from 2634—M8 to 4758—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 181%. For the weekday studied, the smallest MAPE error value was observed for the M11 method (Figure 11).

On Wednesday, not including the pandemic, the projected number of traffic accidents from 2022 to 2029 changes for 2020 from 4130 for M7 to 4639—M3. For the last period analyzed, 2029, the value of the number of traffic accidents changes from 2558—M7 to 4875—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 190%. For the weekday studied, the smallest MAPE error value was observed for the M10 method (Figure 12).

On Thursday, not including the pandemic, the projected number of road accidents from 2022 to 2029 changes for 2020 from 4178 for M7 to 4651—M3. For the last period analyzed, 2029, the value of the number of traffic accidents changes from 2589—M7 to 4862—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 187%. For the weekday studied, the smallest MAPE error value was observed for the M14 method (Figure 13).

On Friday, not including the pandemic, the projected number of road accidents from 2022 to 2029 changes for 2020 from 4568 for M7 to 5292—M3. For the last period analyzed, 2029, the value of the number of traffic accidents changes from 2573—M7 to 5190—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 201%. For the weekday studied, the smallest MAPE error value was observed for the M9 method (Figure 14).

On Saturday, not including the pandemic, the projected number of road accidents from 2022 to 2029 changes for 2020 from 3995 for M7 to 4477—M5. For the last period analyzed, 2029, the value of the number of traffic accidents changes from 2066—M9 to 4477—M5. The difference between the minimum and maximum results is more than 217%. For the studied day of the week, the smallest MAPE error value was observed for the M12 method (Figure 15).

On Sunday, not including the pandemic, the projected number of road accidents from 2022 to 2029 changes for 2020 from 3333 for M7 to 3732—M3. For the last period analyzed, 2029, the value of the number of traffic accidents changes from 1740—M9 to 3645—M3. As can be seen in this case, moving average methods should not be used. The difference between the minimum and maximum results is more than 210%. For the weekday studied, the smallest MAPE error value was observed for the M7 method (Figure 16).

Based on the results of the conducted research by the inclusion of pandemic, it can be concluded that the number of forecasted road accidents at the end of analysis period of 2031 varies between 542 to 4117 across all days which depends on the usage of specific forecasting technique. Further, results are evident that the number of road accidents in Poland will decrease over years.

To compare the number of road accidents depending on the day of the week during pandemic and had there been no pandemic, the number of road accidents was forecasted based on various forecasting techniques, for which the average percentage error is the smallest. The following methods were selected as the best forecasting methods for various days.

• Presence of pandemic: Monday—M7, Tuesday—M9, Wednesday—M7, Thursday—M7, Friday—M7, Saturday—M7, Sunday—M9.

• Absence of pandemic: Monday—M12, Tuesday—M11, Wednesday—M10, Thursday—M14, Friday—M9, Saturday—M12, Sunday—M7.

Based on the research, it can be concluded that the estimated number of road accidents in Poland for the year 2029 varies from 740.30 to 4824.00, depending on the method and day of the week. Based on the presented research results, it can be concluded that the number of road accidents in Poland will decrease year over year on each day of the week.

5. Discussion

The forecasted number of road accidents in 2020 on each day of the week was compared with the actual number of road accidents reported by the police (Statistic Road Accident, 2022). These data are presented in Figures 17–23. Based on the obtained data, it can be concluded that the pandemic caused a decrease in the number of road accidents in Poland by 11% to 30% depending on the days of the week. This reduction is most evident on Monday, Wednesday, and Saturday. For individual days it is as follows:

Figure 17. Comparison of number of road accidents in Monday with and without pandemic (presence of pandemic—M7, absence of pandemic—M12).

Figure 18. Comparison of number of road accidents in Tuesday with and without pandemic (presence of pandemic—M9, absence of pandemic—M11).

Figure 19. Comparison of number of road accidents in Wednesday with and without pandemic (presence of pandemic—M7, absence of pandemic—M10).

Figure 20. Comparison of number of road accidents in Thursday with and without pandemic (presence of pandemic—M7, absence of pandemic—M15).

Figure 21. Comparison of number of road accidents in Friday with and without pandemic (presence of pandemic—M7, absence of pandemic—M9).

Figure 22. Comparison of number of road accidents in Saturday with and without pandemic (presence of pandemic—M7, absence of pandemic—M12).

Figure 23. Comparison of number of road accidents in Sunday with and without pandemic (presence of pandemic—M9, absence of pandemic—M7).

• Monday—29%,

• Tuesday—23%,

• Wednesday—29%,

• Thursday—22%,

• Friday—11%,

• Saturday—30%,

• Sunday—24%.

As we can see, the smallest difference is on the day when the highest number of traffic accidents occur.

In the next step, taking into account formulas 1–5, measurement errors were determined for the projected number of traffic accidents (Table 2). Due to the popularity of the MAPE error, its value was used for further analysis. The study assumed the following criteria for MAPE error (Lewis, 1982):

• <10%—Highly accurate forecasting,

• 10%-20%—Good forecasting,

• 20%-50%—Reasonable forecasting,

• > 50%—Inaccurate forecasting.

Table 2. Summary of errors

Errors/Day of week	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
	With COVID-19
ME	3,21E+01	8,69E+01	3,24E+01	2,98E+01	1,69E+01	7,83E+01	2,98E+00
MPE	2,63E+02	3,65E+02	2,85E+02	2,15E+02	2,45E+02	3,30E+02	2,53E+02
SSE	1,36E+05	3,51E+05	1,25E+05	7,97E+04	1,15E+05	1,62E+05	1,03E+05
MAPE	8,23%	38,74%	9,15%	1,64%	12,73%	13,61%	17,47%
MAE	4,75E+00	6,38E+00	5,46E+00	4,04E+00	3,97E+00	6,03E+00	5,41E+00
	Without COVID-19
ME	3,68E+01	1,91E+01	2,07E+01	6,32E+00	1,56E+01	4,49E+00	1,23E+01
MPE	2,32E+02	1,86E+02	2,86E+02	1,88E+02	2,33E+02	2,45E+02	2,25E+02
SSE	1,11E+05	8,37E+04	1,31E+05	7,23E+04	9,03E+04	1,11E+05	8,68E+04
MAPE	15,81%	2,64%	3,68%	8,33%	0,46%	24,98%	3,38%
MAE	3,60E+00	3,15E+00	5,04E+00	3,26E+00	3,38E+00	3,97E+00	4,27E+00

Based on this, the above assumptions, it can be concluded that in most cases the measurement error is at a high level. In contrast, only in two cases it is reasonable. The value of the error varied in the range: 1.64%-38.74%. Its average value with pandemic was 14.51%, while without pandemic it was 8.47%. Based on this, it can be concluded that the received values of forecasts are at a high level.

6. Conclusion

The day-wise forecasting of the number of accidents in Poland was determined using the exponential equalization method with Statistica software. The applied weights were estimated by the program in such a way as to minimize the mean absolute error and the mean absolute percentage error.

Based on the obtained results, it can be concluded that the pandemic caused a reduction in the number of road accidents in Poland. The range of reduction varies between 11% to 30% depending on the day for which forecasting is conducted. Based on the current situation, further reduction in the number of road accidents in Poland can be expected which might be comparable with number of accidents in EU.

Moreover, based on analysis of the obtained results it can be stated that the forecasts of the number of road accidents in Poland for the coming years show a decreasing trend, especially due to the arrival of COVID-19 virus pandemic. The calculated forecast errors prove the accuracy of the used models. Another remarkable finding from the analysis is that variation of crashes is observed for different days of a week. Moreover, based on the day for which forecasting is conducted, specific types of forecasting technique prove to be more accurate.

The forecasts of the number of road accidents obtained in the article may be used in the future to formulate further actions aimed at minimizing the number of accidents in the countries under study. These actions may consist, for example, in introducing higher penalties for traffic offences on Polish roads from beginning of 2022. In further research, the authors plan to consider more factors affecting the level of accidents in Poland. These may include traffic density, weather conditions or the age of the accident perpetrator.

Acknowledgements

This publication was created thanks to support under the Operational Program Integrated Infrastructure for the project: Identification and possibilities of implementation of new technological measures in transport to achieve safe mobility during a pandemic caused by COVID-19 (ITMS code: 313011AUX5), co-financed by the European Regional Development Fund.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Identification and possibilities of implementation of new technological measures in transport to achieve safe mobility during a pandemic caused by COVID-19 [313011AUX5].