In this paper, we propose a new prediction analysis model which combines the first order one variable Grey differential equation Model (abbreviated as GM(1,1) model) from grey system theory and time series Autoregressive Integrated Moving Average (ARIMA) model from statistics theory. We abbreviate the combined GM(1,1) ARIMA model as ARGM(1,1) model. This combined model takes the advantage of high predictable power of GM(1,1) model and at the same time takes the advantage of the prediction power of ARIMA model. For prediction accuracy improvements, three-points average model is further applied to ARGM(1,1) model. We call the improved version as 3P-ARGM(1,1) model. In addition, Markov chain model from stochastic process theory to enhance the prediction power of 3P-ARGM(1,1) model. The generated model is called as M3P-ARGM(1,1) model. As an illustrative example, we use the statistical data recording the number of China's fixed telephone subscribers from 1989 to 2004 for a validation of the effectiveness of the M3P-ARGM(1,1) model. (Contains 4 tables and 3 figures.)