Outlier Minging In ARIMAX Based On Gibbs Sampling

Outlier mining can be used in two sides. In conventional concept, outlier was often presumed to be noise or useless data and was removed in analysis. At present, with the development of modern information and technology, there are a lot of data about time series that contain much commercial information. Lon-Mu Liu etc (2001) illustrated an illustration using fast-food restaurant franchise data, which considered the commercial value in outlier data indeed. In purpose of estimating parameter, some important work was done by Box and Tiao Abraham(1972), Chang and Tiao(1983), Muculloch Tsay(1994)in outlier mining. And they mainly concerned AR or ARMA model.The autoregressive moving average with exogenous variable (ARIMAX) model is more complete than AR or ARMA model. It is widely used in finance, economy, aerography and signal management. Lei Guo and D. Huang(1989), Xinjei Fan and Nicholas H. Younan(1991), Hong-Tzer Yang and Chao-Ming Huang(1997) did a lot in parameter estimation about ARMAX model. But they didn't concern on outlier mining.Based on the former work, in this paper, the motivation is mining the value of outliers based on ARIMAX models with AO outliers. First, we introduce ARIMAX model and its system identification. Secondly, we introduce outliers. Then we propose Gibbs sampling methods to mine outlier in the view of Bayesian. At last, simulation is done by computer, we acquire better result.