An Enhanced GM(1,1) Grey Prediction Approach with Error Term μ(k)

The aim of this paper is to improve the GM(1,1) predictive model that has been originally developed by Deng in 1982. It is a non-statistic prediction model with very few original data, there has been applied in different fields. However, from the original grey predictive model, we find two problems, (1) applying the GM(1,1) model to predict maybe obtained the result of decreasing trend, this result violate hypothesis of exponential increase trend, (2) the first point of original data is different with 1st point of predictive value that both exist an error term. Therefore, we improved the problem of decreasing trend and provide a newly modified model. Moreover, we proposed an enhanced GM(1,1) grey prediction approach that adopted modified error terms for each original data point mapping into each predictive point to fit the actual value. Meanwhile, in this paper, we applying this enhanced model to predict electricity demand, and comparison with Deng's prediction model, the analyzed results demonstrate the usefulness of this study.