This study proposes a novel hybrid forecasting approach designed explicitly for long-horizon financial time series. It incorporates LMD (Local Mean Decomposition), SD (Signal Decomposition), and sophisticated machine learning methods. The framework for the NASDAQ Composite Index begins by decomposing the original time series into stochastic and deterministic components using the LMD approach. This method effectively separates linear and nonlinear signal structures. The stochastic components are modeled using ARIMA to represent linear temporal dynamics, while the deterministic components are projected using cutting-edge machine learning methods, including XGBoost, Random Forest (RF), Artificial Neural Networks (ANNs), and Support Vector Machines (SVMs). This study employs various statistical metrics to evaluate the predictive ability across both short-term noise and long-term trends, including Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Directional Statistic (DS). Furthermore, the Diebold–Mariano test is used to determine the statistical significance of any forecast improvements. Empirical results demonstrate that the hybrid LMD–ARIMA–SD–XGBoost model consistently outperforms alternative configurations in terms of prediction accuracy and directional consistency. These findings demonstrate the advantages of integrating decomposition-based signal filtering with ensemble machine learning to improve the robustness and generalizability of long-term forecasting. This study presents a scalable and adaptive approach for modeling complex, nonlinear, and high-dimensional time series, thereby contributing to the enhancement of intelligent forecasting systems in the economic and financial sectors. As far as the authors are aware, this is the first study to combine XGBoost and LMD in a hybrid decomposition framework for forecasting long-horizon stock indexes.
Nasir et al. (2025) studied this question.