Researchers from the Czech Republic have demonstrated that a traditional statistical model known as Seasonal Autoregressive Integrated Moving Average (SARIMA) provides more accurate short-term forecasts of daily road traffic accidents than a complex hybrid system that integrates recurrent neural networks. The study, published in the European Transport Research Review, conducted a controlled comparative evaluation of baseline SARIMA and hybrid SARIMA-LSTM frameworks using accident data from the Czech Republic between 2010 and 2023. The central finding is that while Long Short-Term Memory (LSTM) networks effectively captured temporal dependencies in the residual errors of the statistical model, integrating these neural network predictions into the final forecast did not improve accuracy relative to the standalone SARIMA model. In fact, the hybrid approach yielded only minor increases in error metrics, suggesting that for one-step-ahead daily forecasting, the added complexity of neural residual modelling offers no practical benefit over the robust baseline.
The investigation utilized a comprehensive dataset of 1,114,777 road accident incidents reported to the Czech Republic Police from January 2010 to December 2023. According to Czech law, accidents are reported to the police if they involve a fatality or property damage exceeding 4,000 EUR, meaning the dataset represents a significant sample of the total population of road accidents during this period. The researchers aggregated this raw data by day, resulting in a time series of 5,113 daily observations. This daily granularity was selected to facilitate seasonal modelling and to reduce the noise commonly present in hourly counts, thereby enabling the detection of long-term trends and recurring seasonal patterns essential for effective forecasting.
To mitigate heteroscedasticity in the daily road accident counts, the study applied a natural logarithm transformation to the data. This preprocessing step stabilizes the variance and reduces the influence of extreme values, enhancing the suitability of the time series for linear modelling techniques. The initial dataset was divided into two distinct parts: a training and model development period from January 2010 to December 2022, and an implementation and evaluation period from January 2023 to December 2023. This temporal split ensured that the models were trained on historical data and tested on unseen future data, providing a rigorous assessment of predictive performance.
The baseline SARIMA model was selected through a systematic model selection strategy involving statistical criteria and diagnostic tests. The optimal specification, identified as Model 3 with parameters (4,1,2)(1,1,1)7, demonstrated the lowest Akaike Information Criterion (AIC) value of -2710.2031, indicating the best trade-off between model complexity and fit. Diagnostic tests, including the Ljung-Box and Box-Pierce tests, showed non-significant p-values, suggesting that the residuals approximated white noise with no remaining autocorrelation. For the 2023 evaluation period, this baseline SARIMA model achieved a Root Mean Squared Error (RMSE) of 81.5317 and a Mean Absolute Percentage Error (MAPE) of 33.2427%.
To address potential non-linearities not captured by the linear SARIMA model, the researchers extended the approach by modelling the SARIMA residuals using Recurrent Neural Networks (RNNs). Four network architectures were evaluated: Simple RNN, Bidirectional RNN, LSTM, and Bidirectional LSTM. The LSTM architecture, which includes mechanisms to mitigate the vanishing gradient problem, was found to be the most effective for capturing temporal dependencies in the log-residual space. Within the residual-domain model selection, the unidirectional LSTM achieved the lowest RMSE of 0.184 and MAPE of 1.0966% among the tested architectures, confirming its effectiveness in isolating non-linear patterns from the residuals.
The hybrid SARIMA-LSTM approach was constructed by integrating the SARIMA forecasts with the LSTM-based residual predictions. This method was applied to the 2023 implementation dataset using a one-step-ahead rolling-origin strategy with a 7-day sliding window. The 7-day input window corresponds to one full seasonal cycle, allowing the model to capture weekly dependencies. Despite the LSTM’s strong performance on the residuals, the hybrid model did not improve accuracy relative to the baseline SARIMA. Across all forecast intervals, the differences between the two models were minimal, with the hybrid approach showing slight increases in both RMSE and MAPE.
Diagnostic examination of the LSTM-predicted residuals revealed that they were consistently near zero, with a mean value of 4.67 × 10^-5. This indicates that the neural network effectively produced a null output across the forecasting period. The researchers proposed three plausible explanations for this outcome. First, the aggressive differencing pipeline, which included log transformation, seasonal differencing at lag 7, and second-order differencing, may have removed all exploitable non-linear structure before the residuals reached the LSTM. Second, the statistical tests confirmed that the post-fitting residuals closely approximated white noise, leaving no systematic temporal pattern for the LSTM to learn. Third, architectural constraints, such as the shallow single-layer LSTM and limited training epochs, may have been insufficient to detect any remaining non-linearity.
The study highlights the importance of careful validation in hybrid modelling. While previous studies in other domains, such as wind power forecasting and vehicle speed prediction, have reported substantial improvements from hybrid ARIMA-LSTM models, these benefits were often associated with more stable trends and predictable short-term fluctuations. In contrast, daily accident counts exhibit high variability, making the baseline SARIMA model a robust and interpretable choice for operational forecasting. The minor increases in error metrics observed in the hybrid model suggest that the added complexity of modelling residual non-linearities did not consistently enhance accuracy for this specific dataset.
The achieved MAPE exceeding 33% indicates substantial relative error, which is within the expected bounds for univariate daily accident forecasting studies that typically report MAPEs in the range of 20–45%. However, a MAPE below approximately 15% would be required for precise day-level operational deployment. Therefore, the current model is best interpreted as a directional decision-support signal rather than a precise count predictor. The study emphasizes that while LSTM networks are promising for capturing temporal dependencies, their integration with SARIMA residuals requires careful consideration to avoid introducing new biases or degrading forecast quality.
Limitations of the study include its strictly univariate nature, which does not incorporate exogenous variables known to influence daily accident occurrence, such as meteorological conditions, public holiday calendars, and traffic volume dynamics. These factors can drive sudden spikes in accident frequency that a univariate model cannot anticipate. The authors recommend incorporating these covariates through a SARIMAX framework or a multivariate LSTM as a promising immediate extension. Additionally, the study does not generate multi-year projections, as compounding uncertainty at daily resolution with a univariate model renders long-term point forecasts unreliably wide.
The findings suggest that for one-step-ahead forecasting, the baseline SARIMA model remains highly competitive and robust. The hybrid approach, while methodologically sound, did not deliver consistent gains in this instance. Future research should focus on multi-step-ahead predictions, larger datasets, and the inclusion of exogenous variables to fully explore the potential of hybrid approaches in modelling accident patterns. The study underscores that model simplicity and interpretability, as demonstrated by SARIMA, can often be more valuable than algorithmic complexity if that complexity is not managed with extreme care and rigorous validation of intermediate outputs.
Subject of Research: Hybrid SARIMA-recurrent neural network approach for road accident forecasting
Article Title: Hybrid SARIMA-recurrent neural network approach for road accident forecasting
Article References: Gavrilov, I., Hrubes, P., & Pelikan, E. (2026). Hybrid SARIMA-recurrent neural network approach for road accident forecasting. European Transport Research Review, 18(1), Article 72. https://doi.org/10.1186/s12544-026-00835-z
Image Credits: AI Generated
DOI: 10.1186/s12544-026-00835-z
Keywords: Hybrid, SARIMA-recurrent, neural, network, approach, road, accident, forecasting, scientific research
News Source: Cassandra Pierce. (November 9, 2026). SARIMA Model Outperforms Hybrid Neural Network in Accident Forecasts. Scienmag.
