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NONPARAMETRIC COINTEGRATING REGRESSION WITH ENDOGENEITY AND LONG MEMORY

Published online by Cambridge University Press:  18 December 2014

Qiying Wang  and
Peter C. B. Phillips
Qiying Wang*
Affiliation:
The University of Sydney
Peter C. B. Phillips
Affiliation:
Yale University, University of Auckland, University of Southampton, and Singapore Management University
*
*Address correspondence to Qiying Wang, School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia; e-mail: [email protected].
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Abstract

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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.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 2 , April 2016 , pp. 359 - 401
Copyright
Copyright © Cambridge University Press 2014 

References

REFERENCES

Andrews, D.W.K. & Sun, Y. (2004) Adaptive local polynomial Whittle estimation of long-range dependence. Econometrica 72, 569–614.Google Scholar
Berkes, I. & Horváth, L. (2006) Convergence of integral functionals of stochastic processes. Econometric Theory 22, 304–322.Google Scholar
Cai, Z., Li, Q., & Park, J.Y. (2009) Functional-coefficient models for nonstationary time series data. Journal of Econometrics 148, 101–113.Google Scholar
Chan, N. & Wang, Q. (2014a) Uniform convergence for nonparametric estimators with non-stationary data. Econometric Theory 30, 1110–1133.Google Scholar
Chan, N. & Wang, Q. (2014b) Nonlinear regression with nonstationary time series. Journal of Econometrics, in Press.Google Scholar
Chang, Y., Park, J.Y., & Phillips, P.C.B. (2001) Nonlinear econometric models with cointegrated and deterministically trending regressors. Econometrics Journal 4, 1–36.CrossRefGoogle Scholar
Chen, X., Liao, Z., & Sun, Y. (2014) Sieve inference on possibly misspecified semi-nonparametric time series models. Journal of Econometrics 178, 639–658.CrossRefGoogle Scholar
Duffy, J. (2013) Uniform convergence rates on a maximal domain for structural nonparametric cointegrating regression. Unpublished paper, Yale University.Google Scholar
Fan, J. & Gijbels, I. (1996) Local Polynomial Modeling and its Applications. Chapman and Hall.Google Scholar
Gao, J., Tjøstheim, D., & Yin, J. (2012) Model Specification Between Parametric and Nonparametric Cointegration. Working paper.Google Scholar
Gao, J., K., Maxwell, Lu, Z., & Tjøstheim, D. (2009) Speci.cation testing in nonlinear and nonstationary time series autoregression. Annals of Statistics 37, 3893–3928.CrossRefGoogle Scholar
Geman, D. & Horowitz, J. (1980) Occupation densities. Annals of Probability 8, 1–67.CrossRefGoogle Scholar
Härdle, W. & Mammen, E. (1993) Comparing nonparametric versus parametric regression fits. Annals of Statistics 21, 1926–1947.CrossRefGoogle Scholar
Horowitz, J.L. & Spokoiny, V.G. (2001) An adaptive rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69, 599–631.Google Scholar
Karlsen, H.A., Myklebust, T., & Tjostheim, D. (2007) Nonparametric estimation in a nonlinear cointegration model. Annals of Statistics 35, 252–299.Google Scholar
Kasparis, I., Andreou, E., & Phillips, P.C.B. (2014) Nonparametric predictive regression. Journal of Econometrics. Forthcoming.Google Scholar
Kiefer, N.M. & Vogelsang, N.J. (2005) A new asymptotic theory for heteroskedasticity-autocorrelation robust tests. Econometric Theory 21, 1130–1164.CrossRefGoogle Scholar
Park, J.Y. (2014) Nonstationary nonlinearity: A survey on Peter Phillips’s contributions with a new perspective. Econometric Theory 30, 894–922.Google Scholar
Park, J.Y. & Phillips, P.C.B. (1999) Asymptotics for nonlinear transformation of integrated time series, Econometric Theory 15, 269–298.Google Scholar
Park, J.Y. & Phillips, P.C.B. (2001) Nonlinear regressions with integrated time series. Econometrica 69, 117–161.Google Scholar
Phillips, P.C.B. (2005) HAC estimation by automated regression. Econometric Theory 21, 116–142.CrossRefGoogle Scholar
Shimotsu, K. & Phillips, P.C.B. (2005) Exact local Whittle estimation of fractional integration. Annals of Statistics 33(4), 1890–1933.CrossRefGoogle Scholar
Sun, Y. (2011) Robust trend inference with series variance estimator and testing-optimal smoothing parameter. Journal of Econometrics 164, 345–366.Google Scholar
Sun, Y. (2014) Let’s fix it: Fixed-b asymptotics versus small-b asymptotics in heteroskedasticity and autocorrelation robust inference. Journal of Econometrics 178, 659–677.CrossRefGoogle Scholar
Wang, Q. (2014) Martingale limit theorems revisited and non-linear cointegrating regression. Econometric Theory 30, 509–535.Google Scholar
Wang, Q., Lin, Y.X., & Gulati, C.M. (2003) Asymptotics for general fractionally integrated processes with applications to unit root tests. Econometric Theory 19, 143–164.Google Scholar
Wang, Q. & Phillips, P.C.B. (2009a) Asymptotic theory for local time density estimation and nonparametric cointegrating regression. Econometric Theory 25, 710–738.Google Scholar
Wang, Q. & Phillips, P.C.B. (2009b) Structural nonparametric cointegrating regression. Econometrica 77, 1901–1948.Google Scholar
Wang, Q. & Phillips, P.C.B. (2011) Asymptotic theory for zero energy functionals with nonparametric regression applications. Econometric Theory 27, 235–259.Google Scholar
Wang, Q. & Phillips, P.C.B. (2012) A specification test for nonlinear nonstationary models. Annals of Statistics 40, 727–758.Google Scholar
Wooldridge, J.M. (1994) Estimation and inference for dependent processes. Handbook of econometrics 4, 2639–2738.Google Scholar