时间序列的AR及ARMA模型的阶数的贝叶斯判据

<正> In this paper, we discuss the problem of determining the orders of AR（k） andARMA（p, q） models of time series on the basis of the Bayesian estimate theory. Ageneral prior distribution for the order and a general family of prior distribution forthe parameters are proposed. With respect to a particular loss-function, the criterionfor the order of AR（k）, denoted by η1（k）, and the approximate criterion for theorder of ARMA （p, q） are given. The consistency of the order K estimated by usingη1（k）is proved.Finally, the simulation comparisons between η1（k）, AIC（k） （Akaike,1976） and φ（k） （Hannan,1979） are made. The results show that η1（k） is superiorto AIC（k）.