Latent Variable Nonparametric Cointegrating Regression

29 Pages Posted: 20 Sep 2017 Last revised: 16 Mar 2018

See all articles by Qiying Wang

Qiying Wang

University of Sydney

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Ioannis Kasparis

University of Cyprus - Department of Economics

Date Written: September 16, 2017

Abstract

This paper 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 regressions arise naturally in linear and nonlinear regressions where the regressor suffers from measurement error or where the true regressor is a latent variable. The model considered allows for endogenous regressors as the latent variable and proxy variables that cointegrate asymptotically with the true latent variable. Such a framework includes correctly specified systems as well as misspecified models in which the actual regressor serves as a proxy variable for the true regressor. The system is therefore intermediate between nonlinear nonparametric cointegrating regression (Wang and Phillips, 2009a, 2009b) and completely misspecified nonparametric regressions in which the relationship is entirely spurious (Phillips, 2009). The asymptotic results relate to recent work on dynamic misspecification in nonparametric nonstationary systems by Kasparis and Phillips (2012) and Duffy (2014). 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.

Keywords: Cointegrating regression, Kernel regression, Latent variable, Local time, Misspecification, Nonlinear nonparametric nonstationary regression

JEL Classification: C23

Suggested Citation

Wang, Qiying and Phillips, Peter C. B. and Kasparis, Ioannis, Latent Variable Nonparametric Cointegrating Regression (September 16, 2017). Cowles Foundation Discussion Paper No. 2111, Available at SSRN: https://ssrn.com/abstract=3039420 or http://dx.doi.org/10.2139/ssrn.3039420

Qiying Wang

University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand
+64 9 373 7599 x7596 (Phone)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3695 (Phone)
203-432-5429 (Fax)

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

Ioannis Kasparis

University of Cyprus - Department of Economics ( email )

75 Kallipoleos Street
P.O. Box 20537
1678 Nicosia
Cyprus

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