ARMA过程平稳性的贝叶斯检验

Bayesian test for stationary of ARMA process

根据贝叶斯原理,分别讨论了在误差项的方差σ2已知与未知两种情况下,AR(1)过程和ARMA(1,1)过程平稳性的检验问题,对于AR(1)过程,在误差项的方差σ2已知与未知两种情况下该过程回归系数的后验分布分别为正态分布和t分布,而ARMA(1,1)过程在σ2已知的前提下其回归系数的后验分布为t分布.并由此得到其最大后验密度(HPD)置信区间.以近30年来中国国民生产总值(GGNP)和价格指数(PI)的统计数据为实例进行实证分析,研究了以价格指数校正后的中国对数的国民生产总值序列ln(GGNP/PI)的平稳性,所得的结果与增广的迪基富勒检验(ADF检验)相同.

By means of Bayesian principle, we discussed the test for stationary of AR(1) process and (ARMA(1),1) process when the variance of error term is known or unknown. For the AR(1) process, under the above conditions, the posterior distribution of the regression parameters are normal distribution and student distribution respectively, while for the ARMA(1,1) process, when the variance of error term is known, the posterior distribution of its regression parameters is student distribution. What ever cases we can deduce the confidence interval of high posterior density (HPD). To illustrate the application of our method, we analyzed the stationary of series made by the ln{G_(GNP)/P_I} (G_(GNP) indicates gross national product for China, P_I indicates price index for China). We got the same results as augmented Dickey-Fuller test does.