Enhancing Solar Cycle 25 and 26 Forecasting with Vipin-Deep-Decomposed-Recomposed Rolling-window (vD2R2w) Model on Sunspot Number Observations

Effective predicting sunspot numbers (SSN) is the complex task of studying space weather, solar activity, satellite communication, and Earth’s climate. Developing a reliable SSN forecasting model is difficult because SSN time series exhibit complex patterns, nonlinearity, and nonstationarity characteristics. The state-of-the-art shows that deep-learning models often need help capturing SSN data’s intricate dynamics and long-term dependencies. The SSN time series’ decomposed trend and seasonal and residual characteristics may provide better information on long-term dependencies and associated dynamics for effective learning. In this research, the vipin-deep-decomposed-recomposed rolling-window (vD2R2w) models have been proposed with a combination of time-series decomposition, deep-learning models, and a rolling-window method to predict the SSN accurately. The proposed vD2R2w models have been evaluated over four datasets and consistently outperform traditional deep-learning models. The model improves the performance in terms of RMSE, MAPE, and $R^2$ $R^{2}$ over the datasets as SSN_Daily: 84.18% (RMSE), 10.38% (MAPE), and 3.504% ( $R^2$ $R^{2}$ ); SSN_Monthly: 39.5% (RMSE), 26.06% (MAPE), and 7.258% ( $R^2$ $R^{2}$ ); SSN_MonthlyMean: 178.32% (RMSE), 54.83% (MAPE), and 1.56% ( $R^2$ $R^{2}$ ); and SSN_Yearly: 6.06% (RMSE), 10.36% (MAPE), and 1.366% ( $R^2$ $R^{2}$ ). Further, the superiority of the vD2R2w models is validated through AIC & BIC, Diebold Mariano test, and Friedman ranking statistical tests. Additionally, the vD2R2w model has forecasted the peak value of Solar Cycles (SC) and time, i.e., SC25: 127.16 (± 6.83) in 2025 and SC26: 191.71 (± 43.37) in 2035. The analysis of proposed model performances and statistical validation over various measures with four SSNs have concluded that the vD2R2w model outperforms the traditional models and is a reliable framework for SSN time series forecasting. Implementing the proposed model may benefit domains such as space-weather monitoring, satellite communication planning, and solar energy forecasting that rely on accurate SSN predictions.