贝叶斯型的时变系数回归模型

Bayesian nonstationary regression model

提出了具有时变系数的回归模型及其模型识别和参数估计的贝叶斯方 法．在此模型中对于时变回归系数的变动，应用了高斯型概率差分方程式作 为约束条件，称之为高斯型平滑性事先分布．模型中的超参数（ｈｙｐｅｒｐａｒａｍｅ－ ｔｅｒ）的估计，采用了最大似然估计法．模型的识别（差分次数的决定）应用了 Ａｋａｉｋｅ的最小 ＡＢＩＣ法．给出了模型估计的算法及其应用例子．最后，讨论了 平滑性事先分布中参数的最优估计的意义．

Bayesian nonstationary regression model with time varying coefficients is introduced for inferring dynamic relationship between two time series. Smoothness prior in the form of a Gaussian stochastic difference equation is imposed on the time varying regression coefficients. The estimates of hyperparameters in the model and the best order of difference equation are determined by maximizing marginal likelihood of the hyperparameters and using the minimum ABIC (Akaike' s Bayesian Information Criterion) procedure. An algorithm for estimation of the model and its application to the analysis of dynamic dependence of steel consumption on GNP for various countries are given.