Yule-Walker估计法的敏感性分析及其稳健改进
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摘要
时间序列自回归AR模型的Yule-Walker估计法在建模过程中易受离群值的影响,导致计算结果与实际不相符。针对这一现象,基于均值和方差的稳健组合估计量构建了稳健自相关函数,得到了时序AR模型的稳健Yule-Walker估计算法,以克服离群值的影响。并对此方法进行了模拟与金融数据实证检验,模拟和实证检验均表明:当时序数据中不存在离群值时,传统估计方法与稳健估计方法得到的结果基本保持一致;当数据中存在离群值时,运用传统估计方法得到的结果出现较大变化,而运用稳健估计方法得到的结果基本不变。这说明相对于传统估计方法,稳健估计方法能有效抵抗离群值的影响,具有良好的抗干扰性和高抗差性。
The Yule-Walker estimation method for AR model of time series were easily be interfered by outliers when modeling,which will lead to the outcome of modeling deviates from the fact.In reaction to the phenomenon,this paper constructs robust autocorrelation function based on robust combination estimator of mean and variance,and then the robust algorithm of Yule-Walker for AR model was formation to avoid the disturbance from outliers.Also we made the digital simulation and financial data empirical test on the basis of robust algorithm of autocorrelation function.We found that the results of the traditional estimate method and the robust estimate method were basically the same when there were no outliers in the data;the results from the traditional estimate method changed considerably,while robust estimate method remained consistent when there were outliers in the data.This comparison showed that the robust estimate method,which had good anti-interference and high reliability,could efficiently avoid the disturbance from the outliers.
The Yule-Walker estimation method for AR model of time series were easily be interfered by outliers when modeling,which will lead to the outcome of modeling deviates from the fact.In reaction to the phenomenon,this paper constructs robust autocorrelation function based on robust combination estimator of mean and variance,and then the robust algorithm of Yule-Walker for AR model was formation to avoid the disturbance from outliers.Also we made the digital simulation and financial data empirical test on the basis of robust algorithm of autocorrelation function.We found that the results of the traditional estimate method and the robust estimate method were basically the same when there were no outliers in the data;the results from the traditional estimate method changed considerably,while robust estimate method remained consistent when there were outliers in the data.This comparison showed that the robust estimate method,which had good anti-interference and high reliability,could efficiently avoid the disturbance from the outliers.
引文
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[5] 王志坚,王斌会.稳健改进的AO型异常点检测法在金融时序中的应用[J].数理统计与管理,2016,35(2).
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[13] Muler N,Pena D,Yohai V J.Robust Estimation for ARMA Models[J].Annals of Statistics,2009,37(2).
[14] 王志坚.稳健AR模型的构建及其在金融时序中的应用[J].统计与信息论坛,2017(5).
[15] 袁海静.稳健回归模型的非迭代抽样算法与计数时间序列模型的统计推断[D].济南:山东大学,2018.
[2] Chareka P,Matarise F,Turner R.A Test for Additive Outliers Applicable to Long-memory Time Series[J].Journal of Economic Dynamics and Control,2006,30(4).
[3] Louni H.Outlier Detection in ARMA Models[J].Journal of Time Series Analysis,2008,29(6).
[4] Nare H,Maposa D,Lesaoana M.A Method for Detection and Correction of Outliers in Time Series Data[J].African Journal of Business Management,2012,6(22).
[5] 王志坚,王斌会.稳健改进的AO型异常点检测法在金融时序中的应用[J].数理统计与管理,2016,35(2).
[6] Martin R D.Robust Estimation for Time Series Autoregression[D].New York:Academic Press,1979.
[7] Martin R D.Robust Estimation of Autoregressive Models[M].New York:Institute of Mathematical Statistics,1980:228-254.
[8] Martin R D.Robust Methods for Time Series[M].New York:Academic Press,1981:683-759.
[9] Martin R D,Yohai V J.Robustness in Time Series and Estimating ARMA Models[J].Handbook of Statistics,1985,5(85).
[10] Martin R D,Yohai V J.Influence Functionals for Time Series[J].The Annals of Statistics,1986,14(3).
[11] Maddala G S,Yin Y.Outliers,Unit Roots and Robust Estimation of Nonstationary Time Series[J].Handbook of Statistics,1997,15(97).
[12] Luna X D,Genton M G.Robust Simulation-based Estimation of ARMA Models[J].Journal of Computational & Graphical Statistics,2001,10(2).
[13] Muler N,Pena D,Yohai V J.Robust Estimation for ARMA Models[J].Annals of Statistics,2009,37(2).
[14] 王志坚.稳健AR模型的构建及其在金融时序中的应用[J].统计与信息论坛,2017(5).
[15] 袁海静.稳健回归模型的非迭代抽样算法与计数时间序列模型的统计推断[D].济南:山东大学,2018.
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