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ADAPTATION FOR NONPARAMETRIC ESTIMATORS OF LOCALLY STATIONARY PROCESSES

Published online by Cambridge University Press:  07 November 2022

Rainer Dahlhaus  and
Stefan Richter
Rainer Dahlhaus*
Affiliation:
Heidelberg University
Stefan Richter
Affiliation:
Heidelberg University
*
Address correspondence to Rainer Dahlhaus, Institut für Angewandte Mathematik, Heidelberg University, Im Neuenheimer Feld 205, Heidelberg, Germany; e-mail: dahlhaus@statlab.uni-heidelberg.de.
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Abstract

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Two adaptive bandwidth selection methods for minimizing the mean squared error of nonparametric estimators in locally stationary processes are proposed. We investigate a cross-validation approach and a method based on contrast minimization and derive asymptotic properties of both methods. The results are applicable for different statistics under a general setting of local stationarity including nonlinear processes. At the same time, we deepen the general framework for local stationarity based on stationary approximations. For example, a general Bernstein inequality is derived for such processes. The properties of the bandwidth selection methods are also investigated in several simulation studies.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 6: SPECIAL ISSUE IN HONOR OF BENEDIKT M PÖTSCHER , December 2023 , pp. 1123 - 1153
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - SA
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (https://creativecommons.org/licenses/by-nc-sa/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is included and the original work is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

We are very grateful to two referees whose comments helped to improve the paper significantly.

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