A Study On Robustness And Sensitivity Base On ARMA Model

A variety of abnormal values may occur in a time series dataset that can, for example, be due to the break-out of socio-economic events and/or natural disasters for which many of them may never recur. This kind of abnormality is particularly reflected on the macro-economic dataset of our country with peculiar economic structure.In literature, there are two often-used methods to cope with the problem of inconsistency between real data and theoretical model. The first one concentrates on figuring out those abnormal values based on the model at hand, i. e. diagnostics of statistics. The second one puts main attention to the development of method that makes the statistical inference robust to insignificant alteration of the existing model.In this paper, the performance of the ARMA model was assessed from a robust point of view. Firstly, the fundamentals of the ARMA model and methods for stabilizing the model were reviewed. We also demonstrated the sensitiveness of traditional parameter estimation to potential abnormal values, and show the robustness of improved model by a way of simulation. Secondly, model-based diagonal approaches for identifying abnormal values, including pattern and estimation of the abnormal values and built-up process of these diagonal statistics, were introduced and simulated. Finally, by means of analyzing the retums of Shanghai security market, we conclude that the introduced diagonal approach in the paper may work as an efficient way to tackle the abnormal values which is in fact on the basis of the robust estimation of stabilized ARMA model.