GM(1;  1) Model;  after-effect incentives;  IGM(1;  1) Model;  gray system;  Step

In order to make the modeling of the after-effect excitation step sequence more effective and concise, based on the general GM(1,1) model modeling method, the recursive method is used to determine the step point of the post-excitation step data sequence and its subsequent points, and the gray system prediction IGM (1,1) model of the after-effect excitation step data sequence is established. It has been verified that the fitting accuracy of this method is high, and the parameter estimation is simple, which is convenient and practical, and can replace the modeling method of post-excitation step data series in the above literature. Finally, applying this method, a national urban residential market demand model is established, and the market is predicted and analyzed.