Time series forecasting is one of the most critical aspects of big data analytics. However, conventional time series forecasting models cannot effectively identify appropriate sequence features, often leading to a lack of forecast accuracy. A crucial concept is stationarity, which indicates that a series' behavior remains constant over time despite variations. Stationary series have a well-understood theory and are fundamental to studying time series, although many non-stationary ones are related.

In this paper, we will investigate some stationarity time series features deeply, considering endogenous mathematical aspects that arose from observations related to a class of big data. We will show that implementing Machine Learning (ML) algorithms, like eXtreme Gradient Boosting (XGBoost), will be more effective regarding a more robust model, as Long Short-Term Memory (LSTM) is usually determined with this issue.

Many authors have preferred to resort to dataset manipulations to eliminate stationarity, for example, by applying restrictions (where possible) or working with decompositions of the latter to obtain higher accuracy values of Deep Learning (DL) models. However, models characterized by a lower complexity are more accurate in the prediction phase than competitors in this type of time series.

The prediction tests between ML and DL algorithms were carried out on a dataset relating to the number of vehicles passing through 5 Italian tollbooths on different days. Sequential numbering indicates the “interest” for each of them, linked, for example, to geographical factors. In this sense, Tollbooth 1 is of greater interest than Tollbooth 5 and is the subject of the prediction task. Specifically, the dataset used represents a restriction of the originally collected data, which included a series of additional variables linked to climatic conditions and extended over a longer period. These data show how the different time series are characterized by stationarity, in which many hours are characterized by the passage of no vehicles, especially at night, followed by hours of heavy traffic.

We have tested the predictive capabilities of SVM, Random Forest, XGBoost, and RNN-LSTM on the Tollbooth 1 feature. After searching for the best combination of hyperparameters, the algorithm that outperforms the competitors was found to be XGBoost, as evident in Figure 1 on a 200-hour vehicle flow prediction.

Specifically, even graphically, the prediction with LSTM tends to be less stationary and smoother while maintaining the prediction around a trend. At the same time, XGBoost optimally adapts the detrended predicted series to the original one, which is the best choice for a prediction with this type of time series. A similar behavior is adopted by Random Forest (which still uses Decision Trees) but achieves lower performance than XGBoost.

https://www.nature.com/articles/s41598-024-70341-6/figures/1

https://www.nature.com/articles/s41598-024-70341-6/figures/2

https://www.nature.com/articles/s41598-024-70341-6/figures/3

On the explainability side, the SHAP framework allowed us to study which features were the most important in influencing the prediction of Tollbooth 1 with the XGBoost algorithm. Considering Tollbooth 1 as the target feature, as shown in Figure 2, the most important feature that affects the prediction is  Tollbooth 3 linked to the highest Shapley value, followed by Tollbooth 4. The distribution can explain this relationship over time of vehicles that passed through Tollbooths 2 to 5. Assuming that Tollbooth 1 is the most significant interest to travelers and absorbs the greatest number of vehicles that pass through at different times of the day, various types of users use the remaining toll booths. In this case, Tollbooth 3 has a distribution of vehicles very similar to Tollbooth 1 at different times of the day, albeit with a much smaller number of vehicles, which is why it is the feature that most influences the model. Instead, Tollbooth 2, despite having a very high average number of vehicles passed through, has a different temporal distribution, which makes it a feature characterized by minimal importance and almost on par with Tollbooth 5. The summary plot, however, illustrates different Shapley values as the instances vary, considering the increase in feature values depending on the color intensity of each point. Although not the most important, the Tollbooth 2 feature reaches higher values (regarding vehicles passed through), pushing towards an increase in the Shapley value.

https://www.nature.com/articles/s41598-024-70341-6/figures/4