Comparison of Classical Arima Forecasting Methods to the Machine Learning LSTM Method: a Case Study on DAX® 50 ESG Index

Background. Traditional econometric models like ARIMA, while foundational for time series forecasting, often rely on assumptions of linearity and stationarity. These models can fall short in capturing the complex, nonlinear dynamics frequently present in financial markets. This has led to the adoption of machine learning methods like Long Short-Term Memory (LSTM) networks, which are specifically designed to recognize long-term dependencies in sequential data, offering a potential advantage in modeling volatile financial time series. Aim. This study compares the predictive performance of a classical econometric model (ARIMA) with a deep learning approach (LSTM) in the context of stock index forecasting using the DAX 50 ESG index from 2020 to 2024. Methods. An autoregressive integrated moving average (ARIMA) model is compared against a long short-term memory (LSTM) neural network. The models are evaluated using both a static train-test split and a more rigorous expanding window forecast scheme. Predictive accuracy is measured by standard error metrics (MAE, RMSE, MAPE) and the Diebold-Mariano test. Results. The empirical results show that the LSTM model achieves lower forecast errors than the best-fitting ARIMA model in both evaluation frameworks. In the expanding window scenario (repeated retraining), the LSTM maintains a statistically significant, though modest, forecasting advantage over the ARIMA model. Originality/Value. The findings suggest that while the LSTM's ability to capture nonlinear patterns offers a forecasting edge, the improvement is incremental in a highly liquid and efficient market. This case study highlights the potential of deep learning methods in finance but also reinforces he notion that strong market efficiency can limit the forecasting benefits of such complex models.