Electronic Journal of Statistics

Some properties of the autoregressive-aided block bootstrap

Tobias Niebuhr, Jens-Peter Kreiss, and Efstathios Paparoditis

Full-text: Open access

Abstract

We investigate properties of a hybrid bootstrap procedure for general, strictly stationary sequences, called the autoregressive-aided block bootstrap which combines a parametric autoregressive bootstrap with a nonparametric moving block bootstrap. The autoregressive-aided block bootstrap consists of two main steps, namely an autoregressive model fit and an ensuing (moving) block resampling of residuals. The linear parametric model-fit prewhitenes the time series so that the dependence structure of the remaining residuals gets closer to that of a white noise sequence, while the moving block bootstrap applied to these residuals captures nonlinear features that are not taken into account by the linear autoregressive fit. We establish validity of the autoregressive-aided block bootstrap for the important class of statistics known as generalized means which includes many commonly used statistics in time series analysis as special cases. Numerical investigations show that the hybrid bootstrap procedure considered in this paper performs quite well, it behaves as good as or it outperforms in many cases the ordinary moving block bootstrap and it is robust against mis-specifications of the autoregressive order, a substantial advantage over the autoregressive bootstrap.

Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 725-751.

Dates
Received: April 2016
First available in Project Euclid: 8 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1488964115

Digital Object Identifier
doi:10.1214/17-EJS1239

Mathematical Reviews number (MathSciNet)
MR3620734

Zentralblatt MATH identifier
1362.62062

Subjects
Primary: 62F40: Bootstrap, jackknife and other resampling methods 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62P20: Applications to economics [See also 91Bxx] 91B84: Economic time series analysis [See also 62M10]

Keywords
Block bootstrap weak ARMA CARMA low-frequency observations

Rights
Creative Commons Attribution 4.0 International License.

Citation

Niebuhr, Tobias; Kreiss, Jens-Peter; Paparoditis, Efstathios. Some properties of the autoregressive-aided block bootstrap. Electron. J. Statist. 11 (2017), no. 1, 725--751. doi:10.1214/17-EJS1239. https://projecteuclid.org/euclid.ejs/1488964115


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