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A WILD BOOTSTRAP FOR DEPENDENT DATA

Published online by Cambridge University Press:  17 November 2021

Ulrich Hounyo
Ulrich Hounyo*
Affiliation:
University at Albany, SUNY and CREATES
*
Address correspondence to Ulrich Hounyo, Department of Economics, University at Albany, SUNY, Hudson Building (bldg. 25), room 103, 1400 Washington Ave, Albany, New York, NY 12222, USA; e-mail: khounyo@albany.edu.
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Abstract

This paper introduces a novel wild bootstrap for dependent data (WBDD) as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on dependent heterogeneous data. The consistency of the bootstrap variance estimator for smooth function of the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first-order asymptotic validity of the WBDD in distribution approximation is established when data are assumed to satisfy a near epoch dependent condition and under the framework of the smooth function model. The WBDD offers a viable alternative to the existing non parametric bootstrap methods for dependent data. It preserves the second-order correctness property of blockwise bootstrap (provided we choose the external random variables appropriately), for stationary time series and smooth functions of the mean. This desirable property of any bootstrap method is not known for extant wild-based bootstrap methods for dependent data. Simulation studies illustrate the finite-sample performance of the WBDD.

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Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 2 , April 2023 , pp. 264 - 289
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

I wish to thank editor Peter C. B. Phillips, co-editor Giuseppe Cavaliere and four anonymous referees for helpful comments and suggestions. This manuscript subsumes a previous working paper entitled “The wild tapered block bootstrap”. Financial support from CREATES, Center for Research in Econometric Analysis of Time Series (DNRF78), funded by the Danish National Research Foundation, is gratefully acknowledged.

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