基于贝叶斯估计的中国人均GDP之时序模型

The Times Series Model of China's GDP Per Capita Based on Bayesian Estimation

本文应用SAS软件对1952-2009年的中国人均GDP建立时间序列模型并对2010-2013年的中国人均GDP进行了预测;在此基础上建立了以时间序列模型得到的参数信息作为先验信息的两种贝叶斯修匀模型与算法。由此所得的参数贝叶斯估计及预测,能充分利用样本信息和参数的先验信息,因而具有更小的方差或平方误差,估计参数更科学。为了检验该方法对先验分布的灵敏性,我们做了基于两种先验分布的模拟预测。将预测结果与传统时间序列预测相比,发现单一正态观测值、方差已知的先验分布的贝叶斯模型得到的预测值更准确,而基于先验分布为指数分布的贝叶斯模型的预测误差较大,预测效果差。

A time series model of China＇s GDP per capital from 1952 to 2009 is get and thus thework of forecasting future values is done for 2010 to 2013 with SAS software. This paper presents aBayesian approach to time series model for GDP per capital, in which the parameters are estimated withtraditional time series model as prior information. Then, we obtain Bayesian estimation of parametersand forecast future values. It takes advantage of the sample information and the prior information ofthe model. Thus, the estimates have smaller variance and can gain more scientific results than thoseget by traditional time series forecasting method. Because of sensitivity of the prior distribution, twosimulations based on different prior distributions are made. The result shows that the proposed modelwith variance known and normal distribution have more accurate prediction than traditional single timeseries model. However, prediction error of Bayesian model with exponential distribution is larger, so theprediction result is poor.