Electronic Journal of Statistics

Kernel estimates of nonparametric functional autoregression models and their bootstrap approximation

Tingyi Zhu and Dimitris N. Politis

Full-text: Open access

Abstract

This paper considers a nonparametric functional autoregression model of order one. Existing contributions addressing the problem of functional time series prediction have focused on the linear model and literatures are rather lacking in the context of nonlinear functional time series. In our nonparametric setting, we define the functional version of kernel estimator for the autoregressive operator and develop its asymptotic theory under the assumption of a strong mixing condition on the sample. The results are general in the sense that high-order autoregression can be naturally written as a first-order AR model. In addition, a component-wise bootstrap procedure is proposed that can be used for estimating the distribution of the kernel estimation and its asymptotic validity is theoretically justified. The bootstrap procedure is implemented to construct prediction regions that achieve good coverage rate. A supporting simulation study is presented in the end to illustrate the theoretical advances in the paper.

Article information

Source
Electron. J. Statist. Volume 11, Number 2 (2017), 2876-2906.

Dates
Received: October 2016
First available in Project Euclid: 8 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1502157625

Digital Object Identifier
doi:10.1214/17-EJS1303

Zentralblatt MATH identifier
1373.62170

Subjects
Primary: 62G08: Nonparametric regression 62G09: Resampling methods 37M10: Time series analysis 60G25: Prediction theory [See also 62M20]

Keywords
Functional time series nonparametric autoregression $\alpha$-mixing regression-type bootstrap prediction region

Rights
Creative Commons Attribution 4.0 International License.

Citation

Zhu, Tingyi; Politis, Dimitris N. Kernel estimates of nonparametric functional autoregression models and their bootstrap approximation. Electron. J. Statist. 11 (2017), no. 2, 2876--2906. doi:10.1214/17-EJS1303. https://projecteuclid.org/euclid.ejs/1502157625


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