自回归模型阶数的Bayes判据

The Bayesan Criterion for the Orders of AR Models of Time Series

本文在假定自回归模型的阶数k是有已知上界M的离散随机变数且有一定先验概率P_k,k=1,2,…,M的前提下,对一般损失函数L(k,d)给出模型阶数估计量k的Bnyes判据: 并证明按∧(k)=min∧(d)所确定的估计量k是有一致性的估计. 本文概括了文献[1]和[2],使后两者成为本文的特殊情形.此外,对三种具体的损失函数W_1(n)=n,W_2(n)=n^4和W_3(n)-1n(1+n),进行了模型阶数估计量k的模似计算.

This paper discusses the problem of determining the order of AR models of time series on the basis of Bayesan estimation theory in case that a priori distribution for the order is proposed. For a general loss function we give the Bayesan criterion as follows: Let satisfy the following equation Then we prove that the estimator is a consistent estimator.