EMD and LSTM Hybrid Deep Learning Model for Predicting Sunspot Number Time Series with a Cyclic Pattern

The prediction of a time series such as climate indices and the sunspot number (SSN) with long-term oscillatory behaviors has been a challenging task due to the complex combination of oscillations. Frequency extraction algorithms have been developed to separate a time series into different oscillation components according to frequency, such as empirical model decomposition (EMD) and wavelet analysis. In the current study, the deep learning long short-term memory (LSTM) model was employed to predict the oscillation components extracted using EMD. The SSN series was modeled with the hybrid EMD-LSTM model. The simulation study results indicate that the LSTM model reproduces the smooth cyclic pattern of the sine function, and only a few hidden units are needed to model it. The EMD-LSTM model achieves better performance than does the LSTM model for mid-range SSN predictions while the LSTM achieves better performance within the first few time lags. However, the cyclic prediction of the SSN requires mid-range lags; thus, the superior performance of the EMD-LSTM model for these lags cannot be ignored. Furthermore, the remaining components from the significant EMD signals can be modeled to reveal the variability (or uncertainty) in the prediction. The summed residual is fitted by k-nearest neighbor resampling. The final SSN prediction results show that the EMD-LSTM model predicts a later and larger SSN for Solar Cycle 25 than does the LSTM model. Overall, the results lead to the conclusion that the EMD-LSTM model might be a suitable alternative for modeling complex sunspot time series with cyclic patterns.