Quantitative Forecasting of Sunspot Numbers: Statistical Methods and Deep Learning Models

¹ St. Xavier’s College (Autonomous), Kolkata
² Universität Heidelberg, Germany

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Published online: 29 May 2026

Abstract

Forecasting sunspot numbers is fundamental for understanding solar variability and its implications for space weather. However, most existing studies predominantly rely on Total Sunspot Number (TSN), thereby neglecting hemispheric asymmetry and limiting their ability to capture the full spatiotemporal complexity of solar activity. In addition, conventional statistical models such as ARIMA/SARIMA and TBATS, as well as shallow machine learning approaches (e.g., SVM, Random Forest, and simple ANN/MLP), suffer from inherent limitations including linear assumptions, poor handling of non-stationarity, limited capability in modeling long-range temporal dependencies, and sensitivity to noise and abrupt fluctuations.

To address these challenges, this study proposes a unified comparative framework for sunspot forecasting using Daily Sunspot Number (DSN) and Hemispheric Sunspot Number (HSN). Classical time-series models (TBATS and SARIMA) are employed to capture trend and seasonal structures, while deep learning models, such as a feedforward Artificial Neural Network MLPRegressor (ANN-MLPR) and a hybrid Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM) model are employed to address nonlinear and sequential dependencies.

The results of this study establish the hybrid CNN-LSTM model as a robust solution for sunspot number forecasting, offering significant improvements over traditional and single-model methodologies in capturing the complex dynamics of sunspot activity.