This paper presents a comparative study on GM model with residual modification and ARMA model. First set up a grey GM(1, 1) prediction model based on the original a series of data. In order to improve the accuracy of prediction, re-establish GM(1, 1) prediction model for residual tails and revise original GM(1, 1) prediction model with error modification. Then, use series of ARMA(p, q) models for modeling in original sequence. By comparing parameters of the candidate models, finally select MA (2) as appropriate for the prediction model. At Last, through the comparison of a variety of parameters, study their respective advantages and disadvantages of these two kinds of predictive models in the network information system survival situation.