Model detection for grey forecasting model with polynomial term

Abstract

A grey forecasting model with polynomial term which includes the traditional grey model (GM (1)), the nonhomogeneous grey model (NGM(1,1,k)) and the integer order grey model with a time power term (GM(1,1,t)) as special cases is considered. In grey forecasting model with polynomial term, we need to balance the costs and benefits of using higher order term. The novel method of model detection to identify which orders of polynomial term are significant is proposed. Simulation studies prove the proposed methods can identify the true model and have good prediction performances. An empirical example about annual health expenditure in China is used to illustrate the accuracy of proposed method.