Abstract: The idea and method of weight vector group of kernel clustering have been combined with the central moving average model and grey system prediction model in response to the problems existing in the traditional moving average formula. A grey-weighted central moving average model was proposed in this paper. In the modeling process of the grey-weighted center moving average model, the number of moving average terms should be determined first, and the weight vector should be set according to the rules of weight setting for each component of the weight vector group of kernel clustering. Next, the weighted center moving average formula can be used to calculate the moving average simulation value, and the simulation errors were analyzed. Then, the grey system prediction model is applied to obtain a set of predicted values for the studied time series data. Finally, based on actual data and the predicted values of the grey system model, the required predicted values are calculated using the weighted center moving average formula. The new model can effectively solve the problem of serious lag in the simulation and prediction results of the simple moving average formula and the weighted moving average formula and also overcome the shortcomings of the center moving average model and the weighted center moving average model, which cannot be used to predict future changes due to the need for data on both sides of the "center" yt during calculation. From the simulation and prediction results of China's invention patent authorization volume, it can be seen that the new model has obvious advantages. 

Key words: Grey System, Moving Average Method, Kernel Clustering Weight Vector Group, Weighted Central Moving Average, Grey Forecasting Model, Authorized Volume of Patent for Invention in China