Fractional stochastic configuration networks-based nonstationary time series prediction and confidence interval estimation

Time series prediction is an important topic in the field of data analytics for real industrial production. However, the time series from real system usually has strong nonstationarity, which affects the generalization ability of the prediction model. An improved forecasting technique, named as fractional stochastic configura-tion networks (FSCN), is proposed for the prediction of nonstationary time series. FSCN is built on the basis of traditional stochastic configuration network by introducing fractional differential operator. The fractional differential technique avoids the challenge of infinite variance caused by modeling nonstationary series and the over-difference problem caused by traditional integer order difference. First, several data analysis methods are introduced to find the tendency, periodicity and probability density distribution characteristics hidden in the raw industrial data. Hurst exponent is calculated to determine the order of fractional difference to eliminate the nonstationarity of the raw data. Then FSCN network is constructed to model and forecast the sequential data. An explicit prediction uncertainty is derived to provide the confidence interval for the FSCN prediction. The proposed method is tested on a nonstationary time series benchmark dataset and a real cooling system. The experiment result demonstrates that it has a good potential prediction performance compared with several traditional prediction methods.