An Ensemble Multivariate Multiscale Framework for Prediction of Long‐Term Solar Activity With Nonstationary Oscillations

Solar activity is usually characterized by different indices from different perspectives, which are commonly interconnected and contain nonstationary oscillations (NSOs). Given the significant influence of solar activity on space weather, the Earth and humans, it is of great significance to predict solar activity for better understanding not only solar dynamics but also geomagnetic activity and space weather. Because of the time‐varying phase and modulus of NSOs, accurate prediction of long‐term solar activity is a challenging task. For this task, we propose an ensemble multivariate multiscale framework taking advantage of the fast and adaptive multivariate empirical mode decomposition, ensemble multivariate nonstationary oscillation resampling, and the time lag effect. We first simultaneously obtain the decomposed components at aligned scales. At each scale, we iteratively predict the target component by integrating its connection with relevant factors, considering error propagation in the iterative prediction and the time lag due to delivery of the impact of specific factors to the target series. Then we sum the predictions at all scales to produce the final long‐term prediction. A simulation experiment using the Rössler system is performed to evaluate and verify the effectiveness of our proposed framework. The method is then applied to produce long‐term predictions of sunspot number and solar flux, which are two important indices of solar activity. The results indicate our proposed framework has similar prediction performance with longer lead time relative to the official model. These numerical results support the feasibility and applicability of the framework in empirical data analysis.