Improving Electric Vehicle Speed Forecasting Using a Hybrid LSTM-Based Approach

Researchers have been consistently investigating the prediction of vehicle speed, broadly classifying methodologies into three primary categories: model- based, data-driven, and hybrid techniques [8]. Model-based techniques mainly rely on analytical models, which present design challenges because they require extensive adjustments and calibrations for practical situations. On the other hand, data-driven strategies have shorter development cycles and are simpler to apply [9]. The goal of hybrid approaches is to combine data-driven and model- based techniques [10].

There are two further categories of model-based approaches: parametric and non-parametric. For accuracy, parametric approaches require large amounts of representative training data and assume the structure of the prediction model. Constant Acceleration (CA), Constant Speed (CS), the Simulation of Urban Mobility (SUMO) model, and the Intelligent Driver Model (IDM) are a few examples [11]. However, non-parametric techniques can be calculated from historical data and do not require pre-fixing of the model structure, as demonstrated in Figure 1. The study [12] uses 10-fold cross-validation for different prediction horizons and assessed six models using parametric and non- parametric methods. The findings showed that while advanced parametric models show higher accuracy in long-term forecasting, parametric models perform best in short-term prediction.

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Figure 1. Vehicle speed prediction approaches

In terms of EV or non-EV vehicle speed predictions, numerous works using deep learning have been proposed. Recent studies have leveraged deep learning for vehicle speed prediction using diverse models and data sources. A DNN-based approach using shared EV data from Beijing showed effective short-term speed forecasting with an RMSE of 1.53 [13]. Another study to predict vehicle speed was based on Adaptive neuro fuzzy inference system (ANFIS). The approach outperforming traditional methods with an RMSE of 7.73 mph [14]. The proposed Long Short-Term Memory (LSTM) based speed prediction model in the study [15] demonstrated an average RMSE of 1.797 km/h along the prediction horizon, significantly outperforming the Artificial Neural Network (ANN) which recorded an RMSE of 7.012 km/h. During hyperparameter optimization, the best model achieved an average RMSE of 4.753 km/h on the validation data. Across six distinct driving tests, the LSTM model yielded an average RMSE of 5.023 km/h, with individual test results ranging from 4.030 km/h to 5.820 km/h.

A hybrid BP-LSTM model improved long-term predictions across different road types, with RMSE values ranging from 5.78 to 10.92 [16]. This model was also integrated into an energy management strategy for PHEVs, reducing fuel use by 4.97% and achieving an RMSE of 1.84 m/s [17]. Other efforts include speed prediction under varying road statuses using linear regression and DBN with up to 95% accuracy [18]. In the study [19], a Deep Belief Network model was proposed to predict electric vehicle driveline speed ratios. It achieving an R2 value of 0.9989, alongside a minimal Mean Squared Error (MSE) of 0.01 and a Mean Absolute Percentage Error (MAPE) of 0.0008%, the model significantly enhances the efficiency and reliability of vehicle design processes. Another real-time forecasting for EVs on urban roads was also proposed in which Twizy vehicle data was used and it showed that LSTM outperformed Auto Regressive Integrated Moving Average (ARIMA), CNN, and ConvLSTM [7].

Another related work focusing on the implementation of Deep Belief Network (DBN) to predict the EV speed [20]. The proposed model managed to obtain very low prediction errors (as low as 0.001%). The work also produced high R2 values in the experiments.

In the study [21], a hierarchical LSTM-based vehicle trajectory prediction model was introduced that determines driving intention prediction, lane change time estimation, and interaction information from surrounding vehicles. Tested on the NGSIM dataset, the model achieved superior performance in medium- to long-term prediction horizons. Specifically, at a 5-second forecast horizon, the lateral RMSE was reduced to 0.46 m (a 70% improvement over the Constant Acceleration model and 25% over the S_LSTM model), while the longitudinal RMSE dropped to 4.53 m, marking a 52% and 20% reduction respectively.

Recent studies highlight the effectiveness of deep learning models, particularly LSTM networks for vehicle speed prediction in both short and long-term scenarios. Models integrating LSTM with other techniques, such as Backpropagation or adaptive control, have shown improved accuracy by capturing temporal dependencies and complex driving patterns. While deep models excel in nonlinear pattern recognition, statistical methods like ARIMA are known for modeling linear trends effectively. However, few works have explored the synergy between these two approaches. Therefore, a hybrid model combining LSTM and ARIMA holds strong potential to leverage both temporal pattern recognition and linear trend modeling, offering a more robust and accurate solution for vehicle speed prediction. This integration is particularly valuable for real-time applications and energy-efficient vehicle control strategies.

The experiments of the proposed LSTM-ARIMA hybrid model for speed prediction were done on three trajectory types of trajectories (A, B, C), whole trajectory, segment trajectory, steps (5 and 10), and forecast horizon (30 and 60). The results of the proposed work are compared with benchmark LSTM model for the case of numerical sequences. The results shown will be based on the metrics used which are SMAPE, RMSE and R² for whole trajectory and segmented trajectory.

4.1 Whole trajectory

In terms of the SMAPE metric for the whole trajectory experiments the results are shown in Table 1. For Trajectory A with a collected step of 5 and a forecast horizon of 30 steps, the LSTM model yields a SMAPE of 21.00%, while the LSTM-ARIMA hybrid model trained with 500 epochs improves the result to 19.23%. At a 60-step forecast horizon, the LSTM model achieves a SMAPE of 19.66%, whereas the LSTM-ARIMA model records a slightly higher SMAPE of 21.08%. When the collected step increases to 10, the SMAPE for the LSTM model is 17.93% at 30 steps, while LSTM-ARIMA further reduces this to 15.97%. For a 60-step horizon, the LSTM model yields 16.93%, with the LSTM-ARIMA showing a moderate increase to 20.09%.

Table 1. Symmetric Mean Absolute Percentage Error (SMAPE) results for whole trajectory data

In the case of Trajectory B, the performance gains from the hybrid model are more modest. With a collected step of 5 and a forecast horizon of 30 steps, the LSTM model achieves a SMAPE of 57.79%, and LSTM-ARIMA slightly reduces it to 57.31%. For the 60-step forecast, the SMAPE improves from 61.55% (LSTM) to 58.75% (LSTM-ARIMA). With a collected step of 10, LSTM achieves a SMAPE of 52.66% at 30 steps, and LSTM-ARIMA reduces this to 50.01%. For the 60-step forecast, the LSTM model records 52.39%, while LSTM-ARIMA marginally improves it to 52.04%.

For Trajectory C, with a collected step of 5 and a 30-step forecast horizon, the LSTM model produces a SMAPE of 80.83%, and LSTM-ARIMA slightly improves this to 79.67%. At 60 steps, the SMAPE increases from 73.31% (LSTM) to 74.25% (LSTM-ARIMA). When the collected step is 10, the LSTM model yields a SMAPE of 73.53% for 30-step forecasts, with LSTM-ARIMA reducing it to 71.87%. For a 60-step horizon, the LSTM model records 70.56%, while LSTM-ARIMA shows a slight increase to 72.76%.

In terms of Symmetric Mean Absolute Percentage Error (SMAPE) in whole trajectory setup, the proposed LSTM–ARIMA hybrid model generally demonstrates improved accuracy over the baseline LSTM, particularly for shorter forecast horizons and higher collected steps. For Trajectory A, the hybrid model significantly reduces SMAPE at 30-step forecasts for both collected steps of 5 and 10, confirming its effectiveness in correcting short-term errors. However, for the 60-step forecasts, the LSTM-ARIMA model occasionally yields slightly higher SMAPE values, indicating limited benefit from residual modeling over longer horizons.

In Trajectory B, improvements from the hybrid approach are modest but consistent, especially at 60-step forecasts, where SMAPE is reduced more noticeably. This reflects ARIMA’s strength in capturing residual linear patterns that LSTM may overlook.

For Trajectory C, which exhibits higher prediction difficulty as reflected by overall higher SMAPE values, the LSTM–ARIMA model provides only slight improvements in most cases, with occasional performance drops for longer forecast horizons. This suggests that while the hybrid model offers enhancements in SMAPE, its effectiveness varies depending on the trajectory complexity and temporal resolution. Overall, hybridization offers measurable but context-dependent gains in predictive accuracy.

In terms of RMSE for whole trajectory experiments, the results are shown in Table 2. For Trajectory A with a collected step of 5, the LSTM model records an RMSE of 8.69 for a 30-step forecast horizon, whereas the proposed LSTM–ARIMA hybrid model achieves a lower RMSE of 7.33 at 500 epochs. For the 60-step forecast horizon, the LSTM outperforms the hybrid with an RMSE of 7.25 compared to 9.44 from the LSTM–ARIMA model. When the collected step is increased to 10, the LSTM model yields an RMSE of 5.96 for the 30-step horizon, while the hybrid improves performance with an RMSE of 5.25. For the 60-step horizon, the LSTM achieves 5.47, whereas the LSTM–ARIMA gives 7.00.

Table 2. RMSE results for whole trajectory data

For Trajectory B, with a collected step of 5, the LSTM model produces an RMSE of 10.21 for the 30-step forecast horizon, while the LSTM–ARIMA hybrid model at 500 epochs yields a nearly identical RMSE of 10.22. However, for the 60-step horizon, the hybrid model improves upon the LSTM's RMSE of 11.98 by achieving 10.49. When the collected step is increased to 10, the LSTM model records an RMSE of 7.62 for the 30-step horizon, with the LSTM–ARIMA reducing it further to 7.06. For the 60-step forecast, the LSTM model attains an RMSE of 8.27, and the hybrid model shows a slight improvement with 8.20.

For Trajectory C, the LSTM-ARIMA hybrid model showed slight improvements in RMSE performance over the baseline LSTM model at most configurations. With a collected step of 5 and a 30-step forecast horizon, the LSTM model yielded an RMSE of 11.00, while the LSTM-ARIMA model reduced this to 10.88. For a 60-step forecast horizon, the LSTM model achieved a lower RMSE of 9.37, although the hybrid model recorded a slightly higher RMSE of 9.62.

When the collected step increased to 10, the hybrid model continued to show modest gains. For the 30-step forecast horizon, the LSTM model recorded an RMSE of 8.22, while LSTM-ARIMA improved this to 7.96. At the 60-step horizon, the LSTM model achieved an RMSE of 7.43, with the LSTM-ARIMA model showing a marginal increase to 7.67.

In terms of Root Mean Squared Error (RMSE), the LSTM–ARIMA hybrid model demonstrates consistent improvements over the standalone LSTM model in several configurations, particularly for shorter forecast horizons and higher collected steps. Notably, in Trajectories A and B, the hybrid model outperforms LSTM when the collected step is 10, indicating better short-term error correction. However, for longer forecast horizons—especially in Trajectories A and C—the hybrid model occasionally underperforms compared to LSTM, suggesting that ARIMA's residual correction is more effective in scenarios with stronger short-term dependencies. Overall, the hybrid approach enhances prediction accuracy in most settings, validating its suitability for electric vehicle speed forecasting where capturing both linear and nonlinear patterns is critical.

In terms of coefficient of determination (R²), the LSTM-ARIMA hybrid model generally outperformed the standalone LSTM model across various configurations and trajectories, indicating improved explanatory power in modeling electric vehicle speed. The full results of R² for the Whole Trajectory experiments are shown in Table 3.

Table 3. R² results for whole trajectory data

For Trajectory A, with a collected step of 5 and a 30-step forecast horizon, the LSTM model attained an R² of 82.16%, which was further improved by the LSTM-ARIMA model to 87.31%. However, for the 60-step forecast horizon, the LSTM model yielded an R² of 86.61%, while the hybrid model showed a slight reduction to 77.27%, suggesting that the integration may be less effective for longer horizons under this configuration. When the collected step increased to 10, both models showed higher performance: the LSTM model achieved 91.50% R² for the 30-step forecast, and the LSTM-ARIMA model enhanced it further to 93.40%. For the 60-step forecast, the LSTM model reached 92.34%, while the hybrid model recorded a slightly lower R² of 87.48%.

For Trajectory B, with a collected step of 5, the LSTM model registered an R² of 66.92% for a 30-step forecast horizon. The LSTM-ARIMA model improved this marginally to 68.85%. At a 60-step forecast, the LSTM model achieved an R² of 54.31%, and the hybrid model demonstrated a substantial improvement, reaching 65.00%. With a collected step of 10, the LSTM model achieved an R² of 81.59% for the 30-step forecast, while the LSTM-ARIMA model further improved this to 84.18%. For the 60-step forecast, both models performed similarly, with the LSTM at 78.22% and the hybrid model slightly better at 78.57%.

For Trajectory C, performance differences between the two models were less pronounced. With a collected step of 5 and a 30-step forecast horizon, the LSTM model recorded an R² of 71.29%, while the LSTM-ARIMA model showed a modest improvement to 71.96%. At a 60-step forecast, the LSTM model reached 79.24%, while the hybrid model slightly decreased to 78.14%. When the collected step was increased to 10, the LSTM model attained an R² of 84.01% for the 30-step horizon, with the hybrid model improving this to 85.00%. For the 60-step forecast, the LSTM model scored 86.98%, and the LSTM-ARIMA model followed closely with 86.11%.

These results indicate that the hybrid LSTM-ARIMA approach can effectively enhance the prediction accuracy in most scenarios, particularly for shorter forecast horizons and smaller input step sizes. However, the performance gains diminish or slightly regress when applied to longer horizons or more stable patterns, particularly in Trajectories A and C. This suggests that while ARIMA enhances the residual correction capability of LSTM, its contribution becomes limited when long-range temporal dependencies dominate the forecast window.

4.2 Segmented Trajectory

As shown in Table 4, for Trajectory A at 500 epochs and a collected step size of 5, the LSTM model yields a SMAPE of 12.73% for the 30-step forecast horizon, which is notably improved to 6.11% by the LSTM–ARIMA hybrid model. For the 60-step forecast, the LSTM model records a SMAPE of 12.95%, while the hybrid model reduces it to 6.89%. When the collected step size is increased to 10, the LSTM model produces a SMAPE of 28.51% for the 30-step forecast, whereas the LSTM–ARIMA model achieves a significantly lower SMAPE of 5.51%. For the 60-step horizon, the LSTM model's SMAPE of 11.81% is reduced to 8.46% by the hybrid approach.

Table 4. SMAPE results for segmented trajectory data

In Trajectory B, using a collected step size of 5, the LSTM model attains a SMAPE of 50.81% for the 30-step forecast horizon, while the LSTM–ARIMA model reduces it to 31.14%. For the 60-step forecast, the LSTM model's SMAPE of 49.55% improved to 31.35% by the hybrid model. When the collected step is increased to 10, the LSTM model yields a SMAPE of 44.99% for the 30-step forecast, with the hybrid model reducing it to 31.09%. For the 60-step forecast horizon, the LSTM model records a SMAPE of 46.38%, which is likewise reduced to 31.09% through the hybrid method.

For Trajectory C, with a collected step size of 5, the LSTM model shows a SMAPE of 76.49% for the 30-step forecast, which is improved to 60.08% by the LSTM–ARIMA model. For the 60-step horizon, the SMAPE decreases from 75.86% (LSTM) to 59.97% (hybrid). When the collected step size is increased to 10, the LSTM model records a SMAPE of 73.00% for the 30-step forecast, while the hybrid model achieves a lower SMAPE of 59.14%. For the 60-step horizon, the LSTM model's SMAPE of 71.14% is further reduced to 59.18% by the hybrid model.

As presented in Table 5, for Trajectory A at 500 training epochs and a collected step size of 5, the LSTM model achieves an RMSE of 3.74 for a 30-step forecast horizon. The proposed LSTM–ARIMA hybrid model substantially reduces the error to 0.64. For the 60-step horizon, the RMSE of the LSTM model is 3.37, which is again markedly improved by the hybrid model to 0.72. When the collected step size is increased to 10, the LSTM model records an RMSE of 4.63 for the 30-step forecast, while the hybrid model reduces it to 0.58. Similarly, for the 60-step horizon, the LSTM model yields an RMSE of 2.51, with the LSTM–ARIMA model improving the result to 0.58.

Table 5. RMSE results for segmented trajectory data

For Trajectory B, using a collected step size of 5, the LSTM model produces an RMSE of 7.11 for the 30-step horizon, whereas the LSTM–ARIMA hybrid model lowers the error significantly to 0.87. For the 60-step forecast, the LSTM model records an RMSE of 6.30, which is reduced to 0.92 by the hybrid approach. With a collected step size of 10, the LSTM model attains an RMSE of 4.95 for the 30-step forecast, while the hybrid model achieves a reduced RMSE of 0.86. For the 60-step horizon, the LSTM model's RMSE of 5.80 is improved to 0.84 by the hybrid model.

In the case of Trajectory C, with a collected step size of 5, the LSTM model registers an RMSE of 7.52 for the 30-step forecast, which is significantly decreased to 1.02 by the LSTM–ARIMA model. For the 60-step horizon, the RMSE is reduced from 6.59 to 0.99. When the collected step size is set to 10, the LSTM model records an RMSE of 6.55 for the 30-step forecast, while the hybrid model further reduces it to 0.87. For the 60-step forecast, the LSTM model yields an RMSE of 5.46, which is improved to 0.77 through the hybrid model.

As detailed in Table 6, for Trajectory A at 500 epochs and a collected step size of 5, the LSTM model achieves an R² of 96.81% for the 30-step forecast horizon, which is enhanced to 99.91% by the LSTM–ARIMA hybrid model. For the 60-step forecast, the LSTM model records an R² of 97.32%, while the hybrid model further improves it to 99.88%. When the collected step size is increased to 10, the LSTM model attains an R² of 96.77% for the 30-step forecast, and the hybrid model increases this to 99.92%. For the 60-step horizon, the R² improves from 98.52% (LSTM) to 99.92% (hybrid).

Table 6. R² results for segmented trajectory data

In Trajectory B, with a collected step size of 5, the LSTM model produces an R² of 84.08% for the 30-step forecast, while the LSTM–ARIMA model markedly improves this to 99.76%. For the 60-step horizon, the LSTM model records an R² of 87.50%, which is enhanced to 99.73% by the hybrid model. With a collected step size of 10, the LSTM model yields an R² of 90.80% for the 30-step forecast, and the hybrid model improves it to 99.78%. For the 60-step horizon, the R² increases from 89.36% to 99.78% through the hybrid approach.

For Trajectory C, using a collected step size of 5, the LSTM model achieves an R² of 86.25% for the 30-step forecast horizon, which is significantly improved to 99.75% by the LSTM–ARIMA model. For the 60-step forecast, the LSTM model yields an R² of 89.50%, with the hybrid model raising it to 99.74%. When the collected step is set to 10, the LSTM model attains an R² of 89.58% for the 30-step horizon, while the hybrid model achieves a higher R² of 99.81%. For the 60-step forecast, the LSTM model’s R² of 92.77% is further enhanced to 99.86% by the hybrid approach.

The corresponding predicted versus actual speed plots that support the findings discussed in this section are provided in the Appendix for reference. Figures A1 to A12 present the prediction results of the LSTM model applied to the full trajectory, while Figures A13 to A24 illustrate its performance on segmented trajectories. The prediction outcomes of the hybrid LSTM-ARIMA model on the full trajectory are shown in Figures A25 to A36, and Figures A37 to A48 depict the hybrid model’s performance on segmented trajectories. These figures offer a comprehensive visual representation of the model outputs across different scenarios and further reinforce the quantitative results presented above.

Based on the experimental results across all segmented trajectories (A, B, and C), the LSTM–ARIMA hybrid approach consistently outperforms the standalone LSTM model in terms of RMSE, SMAPE, and R² metrics. The hybrid model demonstrates significantly lower forecast errors and higher predictive accuracy across varying forecast horizons (30-step and 60-step) and collected step sizes (5 and 10). These improvements are particularly pronounced in more complex or variable trajectories, such as Trajectory B and C, indicating the robustness and generalizability of the LSTM–ARIMA model in handling diverse motion patterns. Overall, the findings confirm that integrating ARIMA with LSTM enhances the model’s capability to capture both linear and nonlinear temporal dependencies in segmented trajectory prediction tasks.

The authors would like to express their sincere appreciation to the Faculty of Computer Science and Information Technology, Universiti Putra Malaysia, for the invaluable support, research facilities, and financial assistance provided throughout the course of this study.