## 5 Discussion
Moreover, increasing automation (especially automated software) has simplified model selection and parameter tuning, making them accessible to a wider range  
Figure 7: Actual and forecasted EF values from different time series models. of users. These advancements have contributed to enhancing the precision, adaptability, and intelligibility of forecasting models [34; 35]. Despite these advances, there are still fundamental challenges in forecasting time series. First, unexpected events and unusual circumstances can significantly affect forecasting models. For example, natural disasters, pandemics, or economic turmoil can make it difficult for models to understand past behavior and predict future trends. Second, accurately modeling nonlinear dynamics such as trends and seasonality in time series data is a challenge that is difficult to overcome using conventional methods [36]. Third, missing values can prevent the model from producing reliable forecasts, and data quality can significantly affect forecast accuracy [37]. Additionally, effective modeling of nonlinear relationships poses another major challenge in time series forecasting, along with technical challenges such as model selection and parameter tuning. Identifying the appropriate model and selecting suitable parameters requires a complex process. The EF dataset used in this study presents two significant challenges. First, the analyzed data are highly non-stationary, making it difficult for time series models to effectively adapt to the non-stationary structures in the dataset. Second, the strict lockdowns imposed in 2020 due to the COVID-19 pandemic caused an unpredictable sudden drop in EF values. Anomalies (sudden decreases or increases) in datasets contradict previous data trends and patterns, making it difficult for models to make accurate predictions. Therefore, these sudden variations have a negative impact on the predictive performance of the models. Forecasting sudden drops in real-world data is a challenging task for models. The substantial decrease in EF levels due to the closures caused by the COVID-19 pandemic in 2020 adversely affects the forecasting capabilities of the models. When assessing the model's performance, it is essential to consider unforeseen circumstances of this nature. In this context, the EF forecasting errors of the time series models used in this study for the year 2020 were examined. Figure 8 illustrates the box-plot graph of the Mean Absolute Percentage Error (MAPE) results for the test set (2013\(-\)2022) for ARIMA (1,1,0), LSTM, ARIMA-SVR, and Holt-Winters models. All models forecast the EF amount in the year 2020 with higher errors compared to other years. However, the ARIMA (1,1,0) model achieved a more successful forecasting with a MAPE of 5.93%. Following that, the LSTM model had a MAPE of 6.44%, the ARIMA-SVR model had a MAPE of 7.73%, and the Holt-Winters model had a MAPE of 7.74%. These results indicate that the ARIMA model adapts better to unexpected situations. The lower forecasting errors demonstrate that the ARIMA model exhibits a more robust and reliable performance in Ecological Footprint (EF) forecasting, especially during extraordinary situations like COVID-19. As a result, this study represents a significant step in evaluating the performance of time series models used in Ecological Footprint forecasting and understanding how they respond, particularly to unexpected events. The obtained results provide valuable insights for researchers in model selection and development. When examining studies that forecast EF in the literature, it is observed that both a limited number of models are used, and the evaluation of model performances is based on the training set. [PERSON] et al. [7] evaluated the dataset for the years 1999\(-\)2018 for training and assessed only ARIMA and GM based on the fitting performance criterion. [PERSON] [9] only used the ARIMA-LSTM model. The model's performance was tested on the training set, and MAE and RMSE values were displayed on the graph.