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NONPARAMETRIC TRANSFORMATION REGRESSION WITH NONSTATIONARY DATA

Published online by Cambridge University Press:  10 October 2014

Oliver Linton*
Affiliation:
University of Cambridge
Qiying Wang
Affiliation:
University of Sydney
*
*Address correspondence to Oliver Linton, Faculty of Economics, University of Cambridge, Austin Robinson Building, Sidgwick Avenue, Cambridge CB3 9DD, United Kingdom; e-mail: obl20@cam.ac.uk.
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Abstract

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We examine a kernel regression estimator for time series that takes account of the error correlation structure as proposed by Xiao et al. (2003, Journal of the American Statistical Association 98, 980–992). We show that this method continues to improve estimation in the case where the regressor is a unit root or a near unit root process.

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ARTICLES
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Copyright © Cambridge University Press 2014 

References

Cai, Z., Li, Q., & Park, J.Y. (2009) Functional-coefficient models for nonstationary time series data. Journal of Econometrics 148, 101113.CrossRefGoogle Scholar
Chan, N. & Wang, Q. (2014) Uniform convergence for Nadaraya-Watson estimators with non-stationary data. Econometric Theory 30, 11101133.CrossRefGoogle Scholar
Chan, N.H. & Wei, C.Z. (1987) Asymptotic inference for nearly nonstationary AR(1) process. Annals of Statistics 15, 10501063.CrossRefGoogle Scholar
Csörgö, M. & Révész, P. (1981) Strong Approximations in Probability and Statistics. Probability and Mathematical Statistics. Academic Press, Inc.Google Scholar
Engle, R.F. & Granger, C.W.J. (1987) Cointegration and error correction: Representation, estimation, and testing. Econometrica 55, 251276.CrossRefGoogle Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and Its Application. Probability and Mathematical Statistics. Academic Press, Inc.Google Scholar
Johansen, S. (1988) Statistical analysis of cointegrating vectors. Journal of Economic Dynamics and Control 12, 231254.CrossRefGoogle Scholar
Karlsen, H.A. & Tjøstheim, D. (2001) Nonparametric estimation in null recurrent time series. Annals of Statistics 29, 372416.Google Scholar
Karlsen, H.A., Myklebust, T., & Tjøstheim, D. (2007) Nonparametric estimation in a nonlinear cointegration model. Annals of Statistics 35, 252299.CrossRefGoogle Scholar
Linton, O.B. & Mammen, E. (2008) Nonparametric transformation to white noise. Journal of Econometrics 141, 241264.CrossRefGoogle Scholar
Liu, W., Chan, N., & Wang, Q. (2014) Uniform approximation to local time with applications in non-linear co-integrating regression. Preprint, School of Mathematics and Statistics, The University of Sydney. Available on http://www.maths.usyd.edu.au/u/pubs/publist/preprints/2014/liu-18.pdf.
Phillips, P.C.B. (1987) Towards a unified asymptotic theory for autoregression. Biometrika 74, 535547.CrossRefGoogle Scholar
Phillips, P.C.B. (1991) Optimal inference in cointegrated systems. Econometrica 59(2), 283306.CrossRefGoogle Scholar
Phillips, P.C.B. & Park, J.Y. (1998) Nonstationary Density Estimation and Kernel Autoregression. Cowles Foundation Discussion paper no. 1181.
Revuz, D. & Yor, M. (1994) Continuous Martingales and Brownian Motion. Fundamental Principles of Mathematical Sciences 293. Springer-Verlag.Google Scholar
Schienle, M. (2008) Nonparametric nonstationary regression. Unpublished Ph.D. thesis, University of Mannheim.
Stock, J.H. (1987) Asymptotic properties of least squares estimators of cointegration vectors. Econometrica 55, 10351056.CrossRefGoogle Scholar
Wang, Q. (2014) Martingale limit theorem revisited and nonlinear cointegrating regression. Econometric Theory 30, 509535.CrossRefGoogle Scholar
Wang, Q. & Phillips, P.C.B. (2009a) Asymptotic theory for local time density estimation and nonparametric cointegrating regression. Econometric Theory 25, 710738.CrossRefGoogle Scholar
Wang, Q. & Phillips, P.C.B. (2009b) Structural nonparametric cointegrating regression. Econometrica 77, 19011948.Google Scholar
Wang, Q. & Phillips, P.C.B. (2011) Asymptotic theory for zero energy functionals with nonparametric regression applications. Econometric Theory 27, 235259.CrossRefGoogle Scholar
Wang, Q. & Phillips, P.C.B. (2012) A specification test for nonlinear nonstationary models. Annals of Statistics 40, 727758.CrossRefGoogle Scholar
Xiao, Z., Linton, O., Carroll, R.J., & Mammen, E. (2003) More efficient local polynomial estimation in nonparametric regression with autocorrelated errors. Journal of the American Statistical Association 98, 980992.CrossRefGoogle Scholar
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