Forecasting of Sunspot Time Series Using a Hybridization of ARIMA, ETS and SVM Methods

Solar activity directly influences the heliospheric environment and lives on the Earth. Sunspot number (SN) is one of the most crucial and commonly predicted solar activity indices. The prediction of SN time series is a challenging problem owing to its non-stationary, non-Gaussian and nonlinear nature. Therefore, improving the forecasting accuracy of SN time series is an important and challenging task. Motivated from this, in this paper, we have proposed a hybridization of the autoregressive integrated moving average (ARIMA); exponential smoothing with error, trend and seasonality (ETS); and support vector machine (SVM) to predict monthly and yearly SN time series. In this method, first ARIMA, ETS and SVM with linear kernel function are applied to the SN time series and the maximum of forecasts are determined to obtain the forecasts on linear component. Then the residual series is obtained by subtracting the forecasts on linear component from SN time series. The residual series is considered as nonlinear and modeled using SVM with Gaussian kernel function. Then the forecasts on linear component are added with the forecasts on nonlinear component to obtain the final forecasts. To evaluate the efficiency of the proposed method, three constituent models, one of the most popular deep learning models long short-term memory (LSTM), four hybrid methods, four ensemble methods are considered. Furthermore, two horizons, monthly and yearly sunspot time series are considered to evaluate the robustness of the proposed method. Results indicate the statistical superiority of the proposed methods over different horizons considering different accuracy measures.