误差分位数的默示有效估计与\ 自回归时间序列的预测区间

误差分位数的默示有效估计与\ 自回归时间序列的预测区间
基于误差分布的核平滑估计与Yule-Walker方法计算的残差,本文提出了一个全新的自回归时间序列AR(p)误差分位数估计量。 ¥2元

摘要:
基于误差分布的核平滑估计与Yule-Walker方法计算的残差,本文提出了一个全新的自回归时间序列AR(p)误差分位数估计量。在特定假设条件下,本文证明了此估计量默示有效于真正误差的分位数,因此它具有与后者相同的渐近正态分布。利用此估计量, 本文构造出了AR(p) 的预测区间,并证明了它能够渐近达到事先规定的置信水平。大量数据模拟研究验证了文章的理论结果,并应用到一例实际数据中进行分析研究。

关键词:
AR(p);窗宽;核函数;残差
XU Hui1,, YANG Li-Jian2,*, HÄRDLE Wolfgang K.3,*


1、Center for Advanced Statistics and Econometrics Research,;       2、Center for Statistical Science and Department of industrial Engineering,;       3、C.A.S.E.–Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Unter den Linden 610099 Berlin, Germany;  )

Abstract:
An estimator is proposed for the quantile of autoregressive time serieserror distribution, based on kernel smoothing of Yule-Walker residuals. Itis proved under mild assumptions that the quantile estimator is oracallyefficient as the infeasible sample quantile estimator based on unobservederrors, and thus follows the same asymptotic normal distribution. Predictioninterval for future observation is constructed using the estimated quantilesand shown to possess asymptotically the prescribed confidence level.Simulation examples support the asymptotic theory and an application to realdata example is provided for illustration.

Keywords:
AR(p); Bandwidth; Kernel; Residual
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