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Description
Accurate forecasting of space weather disturbances is of critical importance, as geomagnetic storms and solar activity can significantly impact satellite communications, navigation systems, aviation, and power grids. Reliable prediction of these phenomena is therefore essential for safeguarding critical infrastructures and ensuring operational resilience. This study introduces a hybrid forecasting methodology that combines two classical time series models, ARMA-ARMAX, to improve the prediction of key space weather indices.
Unlike the current trend of seeking increasingly complex or computationally intensive approaches, our work emphasizes the potential of using well-established models in a smarter way. The proposed hybrid scheme leverages the strengths of both techniques: ARMA’s ability to capture autoregressive and moving average dependencies, and ARMAX’s capacity to incorporate exogenous variables that drive sudden variations. The hybrid model is constructed through a staged estimation process, in which the forecasts of one model are integrated into the other, leading to an iterative refinement that reduces residual errors and enhances predictive skill.
Historical datasets of geomagnetic indices were employed to evaluate the performance of the models.
training individual ARMA and ARMAX models,
constructing the hybrid framework by combining their respective forecasts,
and benchmarking the performance using error metrics such as mean squared error and mean absolute error.
The results demonstrate that the hybrid model consistently outperforms both standalone ARMA and ARMAX approaches. The inclusion of exogenous drivers improves responsiveness to abrupt events, while the interaction with the autoregressive structure minimizes residual variance. As a result, the hybrid approach achieves significantly improved short-term forecasting accuracy without requiring high computational cost or overly complex algorithms.
To further validate the methodology, we investigated the relationship between the predicted geomagnetic indices and solar wind parameters. The experimental results confirmed a strong statistical correlation, especially when exogenous variables representing solar wind speed were incorporated into the ARMAX component of the hybrid scheme. This demonstrates not only the statistical soundness of the model but also its physical relevance. Moreover, although ARMA and ARMAX are traditionally considered linear, the hybrid configuration exhibits the ability to capture certain nonlinear behaviors present in the data, providing a more realistic representation of space weather dynamics.
The contribution of this work is twofold. First, it provides a practical and computationally efficient technique for operational space weather forecasting, suitable even for environments with limited resources. Second, it highlights the value of optimizing classical time series models, offering an alternative to the continual pursuit of increasingly complicated methods. By extracting more predictive power from existing statistical tools, the hybrid scheme illustrates that simplicity, when used intelligently, can rival or even surpass complexity.
In conclusion, the hybrid ARMA–ARMAX framework can deliver more accurate and robust forecasts of space weather indices than either model alone. The findings underscore the importance of smart model design rather than escalating complexity, providing a transparent and reliable solution for operational forecasting. Future work will focus on expanding the dataset, exploring additional exogenous variables, and comparing the hybrid scheme against modern machine learning techniques, while preserving the efficiency and interpretability of classical statistical models.
