Hostname: page-component-7dd5485656-pnlb5 Total loading time: 0.001 Render date: 2025-10-31T04:02:23.763Z Has data issue: false hasContentIssue false
  • English
  • Français

NONPARAMETRIC COINTEGRATING REGRESSION WITH NNH ERRORS

Published online by Cambridge University Press:  06 July 2012

Qiying Wang  and
Ying Xiang Rachel Wang
Qiying Wang*
Affiliation:
The University of Sydney
Ying Xiang Rachel Wang
Affiliation:
The University of Sydney
*
*Address correspondence to Qiying Wang, School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia; e-mail: qiying.wang@sydney.edu.au.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper studies a nonlinear cointegrating regression model with nonlinear nonstationary heteroskedastic error processes. We establish uniform consistency for the conventional kernel estimate of the unknown regression function and develop atwo-stage approach for the estimation of the heterogeneity generating function.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 29 , Issue 1 , February 2013 , pp. 1 - 27
Copyright
Copyright © Cambridge University Press 2012 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

The authors thank the co-editor Professor Saikkonen and two referees for helpful comments on the original version. The main idea of this paper greatly benefited from discussions with Professor Phillips when the first author visited Singapore Management University in April 2009. Wang acknowledges partial research support from the Australian Research Council.

References

REFERENCES

Bandi, F. (2004) On Persistence and Nonparametric Estimation (with an Application to Stock Return Predictability). Manuscript, University of Chicago.Google Scholar
Berman, S.M. (1969) Local times and sample function properties of stationary Gaussian processes. Transactions of the American Mathematical Society 137, 277–299.Google Scholar
Borodin, A.N. & Ibragimov, I.A. (1995) Limit Theorems for Functionals of Random Walks. Proceedings of the Steklov Institute of Mathematics, vol. 195. American Mathematical Society.Google Scholar
Cai, Z., Li, Q., & Park, J.Y. (2009) Functional-coefficient models for nonstationary time series data. Journal of Econometrics 148, 101–113.CrossRefGoogle Scholar
Chan, N.H. & Wei, C.Z. (1987) Asymptotic inference for nearly nonstationary AR (1) rocess. Annals of Statistics 15, 1050–1063.Google Scholar
Chen, J., Li, D., & Zhang, L. (2010) Robust estimation in nonlinear cointegrating model. Journal of Multivariate Analysis 101, 707–717.CrossRefGoogle Scholar
Choi, I. & Saikkonen, P. (2004) Testing linearity in cointegrating smooth transition regressions. Econometrics Journal 7, 341–365.CrossRefGoogle Scholar
Choi, I. & Saikkonen, P. (2010) Tests for nonlinear cointegration. Econometric Theory, 26, 682–709.CrossRefGoogle Scholar
Chung, H. & Park, J.Y. (2007) Nonstationary nonlinear heteroskedasticity in regression. Journal of Econometrics 137, 230–259.CrossRefGoogle Scholar
Csörgö, M. & Révész, P. (1981) Strong Approximations in Probability and Statistics. Probability and Mathematical Statistics. Academic Press.Google Scholar
de la Pena, V.H. (1999) A general class of exponential inequalities for martingales and ratios. Annals of Probability 27, 537–564.Google Scholar
Fan, J. & Gijbels, I. (1996) Local Polynomial Modeling and Its Applications. Chapman & Hall.Google Scholar
Gao, J., King, M., Lu, Z., & Tjøstheim, D. (2009a) Nonparametric specification testing for nonlinear time series with nonstationarity. Econometric Theory 25, 1869–1892.Google Scholar
Gao, J., King, M., Lu, Z., & Tjøstheim, D. (2009b) Specification testing in nonlinear and nonstationary time series autoregression. Annals of Statistics 37, 3893–3928.CrossRefGoogle Scholar
Gao, J., Li, D., & Tjøstheim, D. (2009) Uniform Consistency for Nonparametric Estimates in Null Recurrent Time Series. Working Paper series 0085, University of Adelaide, School of Economics.CrossRefGoogle Scholar
Granger, C.W.J. & Teräsvirta, T. (1993) Modelling Nonlinear Economic Relationships. Oxford University Press.Google Scholar
Guerre, E. (2004) Design-Adaptive Pointwise Nonparametric Regression Estimation for Recurrent Markov Time Series. CREST Working paper 2004–22.Google Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and Its Application, Probability and Mathematical Statistics. Academic Press.Google Scholar
Han, H. & Park, J.Y. (2008) Time series properties of ARCH processes with persistent covariates. Journal of Econometrics 146, 275–292.CrossRefGoogle Scholar
Han, H. & Zhang, S. (2009) Nonstationary Semiparametric ARCH Model and Nonparametric Cointegrating Volatility Model. Working paper, National University of Singapore.Google Scholar
Hansen, B.E. (1995) Regression with nonstationary volatility. Econometrica 63, 1113–1132.CrossRefGoogle Scholar
Hansen, B.E. (2008) Uniform convergence rate for kernel estimation with dependent data. Econometric Theory 24, 726–748.CrossRefGoogle Scholar
Harvey, A.C. & Robinson, P.M. (1988) Efficient estimation of nonstationary time series regression. Journal of Time Series Analysis 9, 201–214.CrossRefGoogle Scholar
Karlsen, H.A., Myklebust, T., & Tjøstheim, D. (2007) Nonparametric estimation in a nonlinear cointegration model. Annals of Statistics 35, 252–259.Google Scholar
Karlsen, H.A. & Tjøstheim, D. (2001) Nonparametric estimation in null recurrent time series. Annals of Statistics 29, 372–416.Google Scholar
Kasparis, I. & Phillips, P.C.B. (2009) Dynamic Misspecification in Nonparametric Cointegrating Regression. Cowles Foundation Discussion paper 1700.CrossRefGoogle Scholar
Kim, C.S. & Park, J.Y. (2010) Cointegrating regressions with time heterogeneity. Econometric Review 29, 397–438.CrossRefGoogle Scholar
Kristensen, D. (2009) Uniform convergence rates of kernel estimators with heterogenous dependent data. Econometric Theory 25, 1433–1445.CrossRefGoogle Scholar
Lukács, E. (1970) Characteristic Functions. Hafner Publishing.Google Scholar
Marmer, V. (2008) Nonlinearity, nonstationarity, and spurious forecasts. Journal of Econometrics 142, 1–27.CrossRefGoogle Scholar
Park, J.Y. (2002) Nonstationary nonlinear heteroskedasticity. Journal of Econometrics 110, 383–415.Google Scholar
Park, J.Y. & Hahn, S.B. (1999) Cointegrating regressions with time varying coefficients. Econometric Theory 15, 664–703.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. (1987) Towards a unified asymptotic theory for autoregression. Biometrika 74,535–547.CrossRefGoogle Scholar
Phillips, P.C.B. (1988) Regression theory for near-integrated time series. Econometrica 56, 1021–1044.CrossRefGoogle Scholar
Phillips, P.C.B. & Park, J.Y. (1998) Nonstationary Density Estimation and Kernel Autoregression. Cowles Foundation Discussion paper 1181.Google Scholar
Quintos, C.E. & Phillips, P.C.B. (1993) Parameter constancy in cointegrating regressions. Empirical Economics 18, 675–706.CrossRefGoogle Scholar
Robinson, P.M. (1987) Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form. Econometrica 55, 875–891.CrossRefGoogle Scholar
Schienle, M. (2008) Nonparametric nonstationary regression. Ph.D. dissertation, University of Mannheim.Google Scholar
Sun, Y., Cai, Z., & Li, Q. (2008) Consistent Nonparametric Test on Parametric Smooth Coefficient Model with Nonstationary Data. Manuscript, University of Toronto.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.CrossRefGoogle 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.CrossRefGoogle Scholar
Xiao, Z. (2009) Functional-coefficient cointegration models. Journal of Econometrics 152, 81–92.CrossRefGoogle Scholar