Time Series Forecasting Model for Sunspot Number

Chaos plays a prominent role in nonlinear systems like energy, finance, and weather. In these systems, a changing parameter to time yields a chaotic time series that contains a lot of system information. This information helps to analyze and understand the behavior of the chaotic system. However, traditional methods of investigating these chaotic time series have low prediction accuracy. Recently, various researchers have got interested in applying machine learning models for these time series. Accordingly, this study has developed two machine learning models using LSTM and NAR neural networks to forecast monthly smoothed sunspot number time series. Further, Adam and Levenberg-Marquardt algorithms are utilized for LSTM and NAR neural networks during the training process. Besides, mean square error and
$\mathrm{R}^{2}$
are used to assess the proposed models' performance. The simulation results demonstrated that the developed prediction models have successfully predicted the sunspot number.