A GM(1,1)–Markov chain combined model with an application to predict the number of Chinese international airlines

In this paper, we propose a new dynamic analysis model which combines the first-order one-variable grey differential equation model (abbreviated as GM(1,1) model) from grey system theory and Markov chain model from stochastic process theory. We abbreviate the combined GM(1,1)–Markov chain (MC) model as MCGM(1,1) model. This combined model takes advantage of the high predictable power of GM(1,1) model and at the same time take advantage of the prediction power of Markov chain modelling on the discretized states based on the GM(1,1) modelling residual sequence. For prediction accuracy improvements, Taylor approximation is applied to MCGM(1,1) model. We call the improved version as T-MCGM(1,1) model. As an example, we use the statistical data of the number of Chinese international airlines from 1985 to 2003 for a validation of the effectiveness of the T-MCGM(1,1) model.