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Nonparametric cointegrating regression with endogeneity and long memory

Nonparametric cointegrating regression with endogeneity and long memory
Nonparametric cointegrating regression with endogeneity and long memory
This paper explores nonparametric estimation, inference, and specification testing in a nonlinear cointegrating regression model where the structural equation errors are serially dependent and where the regressor is endogenous and may be driven by long memory innovations. Generalizing earlier results of Wang and Phillips (2009a,b, Econometric Theory 25, 710–738, Econometrica 77, 1901–1948), the conventional nonparametric local level kernel estimator is shown to be consistent and asymptotically (mixed) normal in these cases, thereby opening up inference by conventional nonparametric methods to a wide class of potentially nonlinear cointegrated relations. New results on the consistency of parametric estimates in nonlinear cointegrating regressions are provided, extending earlier research on parametric nonlinear regression and providing primitive conditions for parametric model testing. A model specification test is studied and confirmed to provide a valid mechanism for testing parametric specifications that is robust to endogeneity. But under long memory innovations the test is not pivotal, its convergence rate is parameter dependent, and its limit theory involves the local time of fractional Brownian motion. Simulation results show good performance for the nonparametric kernel estimates in cases of strong endogeneity and long memory, whereas the specification test is shown to be sensitive to the presence of long memory innovations, as predicted by asymptotic theory.
0266-4666
359-401
Wang, Qiying
383180c7-4d60-4bb7-aa21-d4f9bc86ea81
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Wang, Qiying
383180c7-4d60-4bb7-aa21-d4f9bc86ea81
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243

Wang, Qiying and Phillips, Peter C.B. (2016) Nonparametric cointegrating regression with endogeneity and long memory. Econometric Theory, 32 (02), 359-401. (doi:10.1017/S0266466614000917).

Record type: Article

Abstract

This paper explores nonparametric estimation, inference, and specification testing in a nonlinear cointegrating regression model where the structural equation errors are serially dependent and where the regressor is endogenous and may be driven by long memory innovations. Generalizing earlier results of Wang and Phillips (2009a,b, Econometric Theory 25, 710–738, Econometrica 77, 1901–1948), the conventional nonparametric local level kernel estimator is shown to be consistent and asymptotically (mixed) normal in these cases, thereby opening up inference by conventional nonparametric methods to a wide class of potentially nonlinear cointegrated relations. New results on the consistency of parametric estimates in nonlinear cointegrating regressions are provided, extending earlier research on parametric nonlinear regression and providing primitive conditions for parametric model testing. A model specification test is studied and confirmed to provide a valid mechanism for testing parametric specifications that is robust to endogeneity. But under long memory innovations the test is not pivotal, its convergence rate is parameter dependent, and its limit theory involves the local time of fractional Brownian motion. Simulation results show good performance for the nonparametric kernel estimates in cases of strong endogeneity and long memory, whereas the specification test is shown to be sensitive to the presence of long memory innovations, as predicted by asymptotic theory.

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More information

e-pub ahead of print date: 18 December 2014
Published date: 1 April 2016
Organisations: Economics

Identifiers

Local EPrints ID: 410825
URI: http://eprints.soton.ac.uk/id/eprint/410825
ISSN: 0266-4666
PURE UUID: 74453f2a-724a-42ec-acf6-fb0325efaab6
ORCID for Peter C.B. Phillips: ORCID iD orcid.org/0000-0003-2341-0451

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Date deposited: 09 Jun 2017 09:42
Last modified: 15 Mar 2024 12:45

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Author: Qiying Wang

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