A New Type of Model Validity Used in Linear Combining Forecasting Model - Zhao Zhang (Journal of Mathematics)
When combining numerous individual forecasting models linearly, it is common to construct a measure of model validity based on AD(Absolute Deviation=yi−y^i) or APE(Absolute Percentage Error=yi−y^i/yi×100%). Specifically, we generally construct model validity by using the mean and the standard deviation of AD or APE. The model validity resulting from this approach will serve as the basis for assigning weights, and then the weights will be used to combine multiple individual models into a linear combining forecasting model (LCFM).However, the drawback of using AD or APE alone is that they do not consider the varying importance between recent errors and long-term errors. To address this limitation, this article reconstructs a new type of model validity (New Model Validity). The sliding average of fitting accuracy and the standard deviation of fitting accuracy are the two components of this New Model Validity, and the sliding average of fitting accuracy enhances the importance of recent errors by incorporating a smoothing coefficient. Thus when applying this New Model Validity to construct a LCFM, the individual model will be assigned a higher weight if its fitting accuracy are more accurate in the recent period. Through proof, it is shown that as long as appropriate weights are obtained, the LCFM remains superior to each individual model under this New Model Validity. Therefore, it is feasible to attempt to improve the forecasting performance of the LCFM by using this New Model Validity.