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OPTIMAL BANDWIDTH SELECTION IN NONLINEAR COINTEGRATING REGRESSION

Published online by Cambridge University Press:  14 December 2020

Qiying Wang  and
Peter C. B. Phillips
Qiying Wang
Affiliation:
School of Mathematics and Statistics, University of Sydney
Peter C. B. Phillips*
Affiliation:
Yale University University of Auckland University of Southampton Singapore Management University
*
Address correspondence to Peter C. B. Phillips, Yale University, New Haven, CT, USA; e-mail: peter.phillips@yale.edu.
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Abstract

We study optimal bandwidth selection in nonparametric cointegrating regression where the regressor is a stochastic trend process driven by short or long memory innovations. Unlike stationary regression, the optimal bandwidth is found to be a random sequence which depends on the sojourn time of the process. All random sequences $h_{n}$ that lie within a wide band of rates as the sample size $n\rightarrow \infty $ have the property that local level and local linear kernel estimates are asymptotically normal, which enables inference and conveniently corresponds to limit theory in the stationary regression case. This finding reinforces the distinctive flexibility of data-based nonparametric regression procedures for nonstationary nonparametric regression. The present results are obtained under exogenous regressor conditions, which are restrictive but which enable flexible data-based methods of practical implementation in nonparametric predictive regressions within that environment.

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Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 6: SPECIAL ISSUE IN HONOR OF BENEDIKT M PÖTSCHER , December 2023 , pp. 1325 - 1337
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

The authors thank the Guest Co-Editor, Professor Ingmar Prucha, and one referee for helpful comments on the original manuscript, which have led to many improvements. Wang acknowledges research support from the Australian Research Council and Phillips acknowledges research support from the NSF under Grant No. SES 18-50860 and the Kelly Fund at the University of Auckland.

References

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