基于小波分析与贝叶斯估计的组合统计建模  

Statistical modeling based on the combination of wavelet analysis and Bayesian estimation

作　　者：林静[1] 唐国强[1] 覃良文 LIN Jing TANG Guo- qiang QIN Liang-wen(College of Science,Guilin University of Technology, Guilin 541006, China)

机构地区：[1]桂林理工大学理学院,广西桂林541004

出　　处：《桂林理工大学学报》2017年第1期217-222,共6页Journal of Guilin University of Technology

基　　金：国家自然科学基金项目(41101136);国家社会科学基金项目(13CJY075);广西财经学院数量经济学重点实验室项目(2014);广西空间信息与测绘重点实验室项目(15-140-07-33)

摘　　要：小波分解方法可以实现时间序列的分解。利用小波分析分解出趋势项序列与周期项序列,分别对两部分序列建立ARMA模型进行预测,并重构序列。为了降低估计效率的代价,本文引入MCMC方法对趋势项和周期项序列建立的ARMA模型参数进行估计,得出自回归系数与剩余项(趋势项序列减去自回归项的预测值),并利用OLS方法对剩余项重新估计,最后重组序列。利用样本外数据进行预测分析,我国铁路货运量数据的实证分析结果表明,小波分析的引入可提高预测效果,基于小波分析与MCMC-OLS估计组合方法与其他方法相比,预测效果更好。The method of wavelet decomposition can decompose time series. First, with the help of the wavelet a-nalysis, the original sequence can decompose term sequence and cycle sequence. The two-part series on ARMAmodel are established to predict the reconstructed sequence. In order to reduce the estimated cost efficiency, thisarticle uses MCMC method to estimate the parameters of the ARMA model by which term sequence and cycle se-quence are set up. However, we can get the regression coefficients and residual term （ trend series minus the au-toregressive） ,and use the OLS method to estimate the residual term. Finally, the series are restructured. Thispaper uses the sample data in forecast and analysis. By railway freight volume data of our country, the empiricalanalysis results show that introducing wavelet analysis can improve the prediction effect, and the method of combi-ning wavelet analysis with MCMC-OLS estimation has better prediction effect than other methods.

关 键 词：小波分析 贝叶斯估计 ARMA模型 MCMC方法 

分 类 号：O212.8[理学—概率论与数理统计]