Oracally efficient estimation of innovation quantile andprediction bounds for autoregressive time series

XU Hui; YANG Li-Jian; HÄRDLE Wolfgang K.

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Oracally efficient estimation of innovation quantile andprediction bounds for autoregressive time series

XU Hui 1,YANG Li-Jian 2 * #,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

*Correspondence author

#Submitted by

Subject:

Funding: United States National Science Foundation award DMS（No.1007594）, National Natural Science Foundation of China（No.11371272）, Jiangsu Specially-Appointed Professor Program（No.SR10700111）, Jiangsu Province Key-Discipline Program (Statistics)（No.ZY107002, ZY107992）, Research Fund for the Doctoral Program of Higher Education of China（No.20133201110002）

Opened online:13 January 2017

Accepted by: none

Citation: XU Hui,YANG Li-Jian,HÄRDLE Wolfgang K..Oracally efficient estimation of innovation quantile andprediction bounds for autoregressive time series[OL]. [13 January 2017] http://en.paper.edu.cn/en_releasepaper/content/4716925

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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