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

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 \hatK, \hatK=\left\\sum_K=1^n K P_I K e^\fracn(K)2 / \sum_K=1^n P_K e^\frac\eta(K)2\right\ Where η（K）=-（T-K-1）\log \hat\sigma_K^2-\log \left|\hat\Gamma_K^(K)\right|+21ogG（（T-K-1）/2）+Klogπ, and we prove that the estimated order \hatK is a consistent estimator.