One-Step Prediction for GM(1,1) with a Sliding Data Window

Most studies on grey models (GMs) focus on modeling and optimizing the construction and parameters of GMs, but not on the data and one-step prediction. Generally, GM(1,1) ignores the function of new data and is employed for multistep prediction. In multistep prediction, the worse the prediction precision, the larger the number of prediction steps will be. From the viewpoint of a sliding data window, the current one-step prediction will correspond to the past nth step prediction that was done by the fixed data window. In addition, the value of the first step prediction, sliding over time, is widely used in practice and is expected to be very accurate. Therefore, the sliding data window removes the old data and uses the new data. This is introduced to improve the past nth step prediction precision that corresponds to the current one-step prediction precision. Through the example of forecasts of Chinese energy consumption, the prediction precision can be enhanced effectively.