What question did this study set out to answer?

The aim is to improve sunspot number forecasting by addressing limitations in existing statistical and machine learning models.

June 3, 2026

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

Key Points

The aim is to improve sunspot number forecasting by addressing limitations in existing statistical and machine learning models.
Classical time-series models like TBATS and SARIMA were used to analyze trend and seasonal structures.
Deep learning models including feedforward ANN-MLPR and CNN-LSTM were applied to capture nonlinear and sequential dependencies in sunspot data.
A unified framework compared these methods using Daily Sunspot Number (DSN) and Hemispheric Sunspot Number (HSN).
The hybrid CNN-LSTM model significantly outperformed traditional time-series and simple machine learning models in forecasting accuracy.
Improvements in capturing complex dynamics of solar activity were observed with deep learning approaches compared to classical models.
The study highlights the limitations of conventional models in handling non-stationarity and long-range dependencies.

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.

Bookmark

Cite This Study

Singha et al. (Fri,) studied this question.

synapsesocial.com/papers/6a1fc730dee9eb8c0dce80ea https://doi.org/https://doi.org/10.1051/epjconf/202637001029/pdf

Bookmark