GM(1,1) Cosine Self-Memory model and its application

In view of the self-memory feature of system and some characteristic of real time series, we propose a hybrid model-GM(1, 1) Cosine Self-Memory (GMCSM), in order to meet the need of practical application. In this model, we take GM (1, 1) Cosine model as dynamic kernel, deduce the difference-integral equation in Hilbert space, and give the parameter identification by least squares method As the application, we use the GMCSM model to fit and forecast the net income of rural households in China, the result shows that the new model has higher accuracy than GM (1, 1) and GM (1, 1) Cosine, GM (1, 1) Self-Memory (GMSM), and GM (1, 1, t(2)) Self-Memory (GM (1, 1, t(2)) SM) models both in the simulation phase and the forecast period So, the GMCSM model has significance for enriching and perfecting the grey prediction model system as well as extending its application scope.