AR模型阶数依平方损失函数下的Bayes估计

THE BAYESAN ESTIMATOR OF THE ORDERS OF AR MODELS OF TIME SERIES WITH A SQUARED-ERROR LOSS FUNCTION

本文在假定模型阶数K有已知上界、并为离散随机变量,且具有一定的先验概率函数的情况下,讨论了在平方损失下AR模型阶数的Bayes估计,并证明了所给的估计量是有一致性的估计。

This paper discusses the problem of determinining the orders of AR models of time series on the basis of the Bayesian estimation theory. Suppose that a general prior distribution for the order and a general family of prior distribution for the paramaters are proposed. With respect to a squared-error loss function, we give the Bayesian estimator for the orders of AR models, denoted by ■, ■={sum from k=1 to M(KP_(k^(e^(η(K)/2)))/sum from K=1 to M(P_(k^(e^(η(K)/2)))} Where η(K)=-(T-K-1)10g■_k^2-log|■_K^(k)|+21ogG((T-K-1)/2)+Klogπ, and we prove that the estimated order K is a consistent estimator.