基于MCMC方法的ARFIMA模型贝叶斯分析及实证研究

Bayesian Analysis of ARFIMA Model Based on MCMC Method and Its Empirical Study

在经济领域中,时间序列具有序列相关和长记忆等特征,用考虑了时间序列短记忆性和长记忆的ARFIMA来模型分析研究经济时间序列有利于提高拟合及预测的精度。近几十年来对ARFIMA模型参数估计和分数差分算子阶数d的研究越来越多,该模型的应用也越来越广泛。基于贝叶斯方法在参数估计中的优越性,本文结合众多应用此方法的文献所得到的后验分布特点,提出了合理的先验分布,考虑到计算难度,采用MCMC方法对模型的参数进行估计,最后应用我国过去几十年的GDP数据进行实证分析,得到了ARFIMA模型参数的后验分布图、均值、方差及95%的置信区间。

In economic field, time series have serial correlation long memory and other characteristics. Using ARFIMA model which have consider the short memory and long memory of time series to study economic time series can improve the precision of fitting and prediction. In recent decades, there are too many researches on parameters estimate, especially on the parameter, and this model had implicated in many field. Bayesian approach using in parameters estimation have a lot of advantages. Base on the parameter characteristics reference in other papers, reasonable prior distribution have bring out in this paper. Considering is difficult to calculation, the MCMC method will be used to calculate the posterior distribution of the parameters. Finally, I do an empirical study on China＇s GDP data over the past few decades, and get the ARFIMA model＇s parameters posteriors distribution, variance and 95% confidence interval.