Performance of the Autoregressive Method in Long-Term Prediction of Sunspot Number

Abstract

Abstract:The autoregressive method provides a univariate procedure to predict the future sunspot number (SSN) based on past record. The strength of this method lies in the possibility that from past data it yields the SSN in the future as a function of time. On the other hand, its major limitation comes from the intrinsic complexity of solar magnetic activity that may deviate from the linear stationary process assumption that is the basis of the autoregressive model. By analyzing the residual errors produced by the method, we have obtained the following conclusions: (1) the optimal duration of the past time for the forecast is found to be 8.5 years; (2) the standard error increases with prediction horizon and the errors are mostly systematic ones resulting from the incompleteness of the autoregressive model; (3) there is a tendency that the predicted value is underestimated in the activity rising phase, while it is overestimated in the declining phase; (5) the model prediction of a new Solar Cycle is fairly good when it is similar to the previous one, but is bad when the new cycle is much different from the previous one; (6) a reasonably good prediction of a new cycle can be made using the AR model 1.5 years after the start of the cycle. In addition, we predict the next cycle (Solar Cycle 25) will reach the peak in 2024 at the activity level similar to the current cycle.

The Sunspot Number Forecasting Using a Hybridization Model of EMD, LSTM and Attention Mechanism

“…At present, the frequent forecasting algorithms for sunspot number are mainly divided into two categories: statistical methods and machine learning. In statistical stage, exponential smoothing [4], Kalman filter [5] and auto-regression (AR) [6]. The AR is a basic method [7] and some improved methods have been proposed, such as auto-regressive moving average (ARMA) [8], auto-regressive integrated moving average (ARIMA) [9,10] and other forms [11,12], which have widely applied to time series forecasting in different fields [10,12,13].…”