Grey optimized models and their existence theorem

Based on ideal absolute errors and relative errors, a new grey model‐GM^p(1,1) model is presented. The existence problem of its solution is also solved based on a few conditions. Then, MGM^p(1,n) model is presented. These optimized models GM^p(1,n) and MGM^p(1,n) have good anti‐noise property to absolute and relative errors. Examples illustrate that they have very good fitting and forecasting results.