随机误差序列自相关的贝叶斯诊断及其单位根检验

Bayesian Diagnosis for Autocorrelation of Random Error Series and Its Unit Root Test

在线性模型Y=Xβ+U中,通常假定随机误差向量U的各分量相互独立、方差相同,而且均服从正态分布.但在利用时间序列数据和横截面数据的模型中,前一期的误差一般与后一期的误差相关,误差项并不满足独立性要求,此时OLS估计不再是最佳线性无偏估计.根据贝叶斯定理,通过自相关系数的条件后验分布,研究了自相关系数的统计推断问题,包括点估计、区间估计、自相关的统计诊断和单位根的统计检验.

In the linear regression model, Y=Xβ+U, it is usually assumed that the elements of the error term U have constant variance, are nonrelated, and are normally distributed. However, in the models established with both the data of time series and that of crosssection, each error is usually correlated with the one preceding it, and thus U doesn't satisfy the condition of independence.In the paper, the authors first dicuss the distribution of an autocorrelation coefficient for the given β when the errors in a linear regression model follow a firstorder autoregressive process, then develop a general methodology to make statistical inferences on the coefficient in terms of the Bayesian theorem, including its point estimation, interval estimation and relative statistical tests, and finally give an example to show how to use this procedure.