1.Shanghai Polytechnic University;2.Shanghai Jiao Tong University
The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)
It is a traditional way to establish parameter estimation and simulation of unbiased grey models by the discrete time response function of whiten differential equation. A novel unbiased grey model based on high precise direct integration method is proposed without using the discrete time response function. The recurrence relation can be deduced by exponential matrix of the matrix differential equation,written by introducing some new variables, and the unbiased parameters can be derived. Then the simulated value is calculated by the high precise direct integration method, that can reduce rounding errors and improve precision. The validity and utility of the proposed model is proved by rigorous non-homogenous exponential sequence, approximate non-homogenous sequence, monotone sequences and the practical example of car ownership, and it can improve the precision of simulation and prediction.