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LATENT VARIABLE NONPARAMETRIC COINTEGRATING REGRESSION

Published online by Cambridge University Press:  23 March 2020

Qiying Wang
Affiliation:
The University of Sydney
Peter C.B. Phillips
Affiliation:
University of Auckland, Yale University, University of Southampton, Singapore Management University
Ioannis Kasparis
Affiliation:
University of Cyprus
Corresponding
E-mail address:

Abstract

This article studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspecified through the use of a proxy regressor in place of the true regressor. Such models occur in linear and nonlinear regressions where the regressor suffers from measurement error or where the true regressor is a latent or filtered variable as in mixed-data-sampling. The treatment allows for endogenous regressors as the latent variable and proxy variables that cointegrate asymptotically with the true latent variable, including correctly specified as well as misspecified systems, and is therefore intermediate between nonlinear nonparametric cointegrating regression and completely spurious nonparametric nonstationary regression. The results relate to recent work on dynamic misspecification in nonparametric nonstationary systems and the limit theory accommodates regressor variables with autoregressive roots that are local to unity and whose errors are driven by long memory and short memory innovations, thereby encompassing applications with a wide range of economic and financial time series. Some implications for forecasting under misspecification are also examined.

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ARTICLES
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© Cambridge University Press 2020

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Footnotes

The authors thank the Co-Editor, Rob Taylor, and two referees for helpful comments on the original manuscript, which have led to many improvements. Qiying Wang acknowledges research support from the Australian Research Council and Peter C.B. Phillips acknowledges research support from the Kelly Fund, University of Auckland.

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