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NONLINEAR COINTEGRATING POWER FUNCTION REGRESSION WITH ENDOGENEITY

Published online by Cambridge University Press:  26 January 2021

Zhishui Hu ,
Peter C.B. Phillips  and
Qiying Wang
Zhishui Hu
Affiliation:
University of Science and Technology of China
Peter C.B. Phillips
Affiliation:
Yale University The University of Auckland University of Southampton Singapore Management University
Qiying Wang*
Affiliation:
The University of Sydney
*
Address correspondence to Qiying Wang, School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia; e-mail: qiying.wang@sydney.edu.au.
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Abstract

This paper develops an asymptotic theory for nonlinear cointegrating power function regression. The framework extends earlier work on the deterministic trend case and allows for both endogeneity and heteroskedasticity, which makes the models and inferential methods relevant to many empirical economic and financial applications, including predictive regression. A new test for linear cointegration against nonlinear departures is developed based on a simple linearized pseudo-model that is very convenient for practical implementation and has standard normal limit theory in the strictly exogenous regressor case. Accompanying the asymptotic theory of nonlinear regression, the paper establishes some new results on weak convergence to stochastic integrals that go beyond the usual semimartingale structure and considerably extend existing limit theory, complementing other recent findings on stochastic integral asymptotics. The paper also provides a general framework for extremum estimation limit theory that encompasses stochastically nonstationary time series and should be of wide applicability.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 6 , December 2021 , pp. 1173 - 1213
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

The authors thank the Co-Editor, Pentti Saikkonen, and two referees for helpful comments on the original manuscript, which have led to many improvements. Hu acknowledges research support from NSFC (No. 11671373); Wang acknowledges research support from the Australian Research Council; Phillips acknowledges research support from the NSF under Grant No. 18-50860 and the Kelly Fund at The University of Auckland.

References

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