Research of resdiul error – particle swarm optimization gray model based on Markov in load forecasting

GM(1,1) forecasting model has the advantages of few sample data, simple principle, easy calculation, high prediction accuracy in short terms, examination, etc. It is extensively applied in the load forecasting However, it has its localization. The greater the gray level of data is, the lower the prediction precision is. Besides, it is not suitable for long term forecasting of economy to step backwards for years, which, to a certain extent, is caused by parameter alpha in the model. To solve the problem, vector thetas was introduced to set up residual error GM(1,1,thetas) model, which is solved by the use of particle swarm optimization (PSO) . Meanwhile equal dimension new information and Markov matrix are applied to estimate symbol of residual error forecast value when k >n. Case analysis shows that it effectively improves prediction accuracy in comparison with traditional forecasting methods. Application shows that the method has definite utility value.