Synergistic sunspot forecasting: a fusion of time series analysis and machine learning

In this article, we conduct nonlinear time series analysis and utilise machine learning (ML) techniques for predicting and forecasting daily sunspot data sets. Additionally, we review available time series and ML techniques to provide a comprehensive overview. For time series analysis, the variations in the persistence of sunspot data sets were confirmed through Hurst exponent with various time lengths. Moreover, the fast Fourier transform was performed. For the ML approach, prediction and forecasting of sunspot data sets are performed with various simple ML algorithms. Recurrent neural networks (RNN), long–short time memories (LSTM) and gated recurrent unit (GRU) algorithms were used for the prediction. A discussion of the significant outcomes of the sunspot predictions made using the aforementioned algorithms is presented. With the use of these sunspot data sets, several statistical metrics, including R-squared, mean average error (MAE), etc., are examined. Further, the sunspot data forecast was done for more than eight solar cycles with the help of different forecasting algorithms (e.g., neural basis expansion analysis for time series (N-BEATS), neural hierarchical interpolation for the time series (NHITS), etc.). A summary of the sunspot predictions using several ML techniques in an effort to determine the most effective methodology is discussed.