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Semiparametric Estimation in Multivariate Nonstationary Time Series Models

  • Jiti Gao

    ()

  • Peter C.B. Phillips

A system of multivariate semiparametric nonlinear time series models is studied with possible dependence structures and nonstationarities in the parametric and nonparametric components. The parametric regressors may be endogenous while the nonparametric regressors are assumed to be strictly exogenous. The parametric regressors may be stationary or nonstationary and the nonparametric regressors are nonstationary integrated time series. Semiparametric least squares (SLS) estimation is considered and its asymptotic properties are derived. Due to endogeneity in the parametric regressors, SLS is not consistent for the parametric component and a semiparametric instrumental variable (SIV) method is proposed instead. Under certain regularity conditions, the SIV estimator of the parametric component is shown to have a limiting normal distribution. The rate of convergence in the parametric component depends on the properties of the regressors. The conventional √n rate may apply even when nonstationarity is involved in both sets of regressors.

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File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp17-11.pdf
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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 17/11.

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Length: 44 pages
Date of creation: 05 Sep 2011
Date of revision:
Handle: RePEc:msh:ebswps:2011-17
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  1. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September.
  2. Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413.
  3. Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
  4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  5. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
  6. Qiying Wang & Peter C.B. Phillips, 2008. "Structural Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1657, Cowles Foundation for Research in Economics, Yale University.
  7. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  8. Phillips, Peter C.B., 2009. "Local Limit Theory And Spurious Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1466-1497, December.
  9. Whitney Newey & James Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-16, Massachusetts Institute of Technology (MIT), Department of Economics.
  10. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  11. FLORENS, Jean-Pierre & JOHANNES, Jan & VAN BELLEGEM, Sébastien, 2006. "Instrumental regression in partially linear models," CORE Discussion Papers 2006025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation for Research in Economics, Yale University.
  13. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
  14. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  15. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  16. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
  17. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
  18. Qiying Wang & Peter C.B. Phillips, 2006. "Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1594, Cowles Foundation for Research in Economics, Yale University.
  19. P tscher, Benedikt M., 2004. "Nonlinear Functions And Convergence To Brownian Motion: Beyond The Continuous Mapping Theorem," Econometric Theory, Cambridge University Press, vol. 20(01), pages 1-22, February.
  20. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(03), pages 726-748, June.
  21. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  22. P. Jeganathan, 2008. "Limit Theorems for Functionals of Sums that Converge to Fractional Brownian and Stable Motions," Cowles Foundation Discussion Papers 1649, Cowles Foundation for Research in Economics, Yale University.
  23. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers 811R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1987.
  24. Gao, Jiti & King, Maxwell & Lu, Zudi & Tjøstheim, Dag, 2009. "Nonparametric Specification Testing For Nonlinear Time Series With Nonstationarity," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1869-1892, December.
  25. Berkes, Istv n & Horv th, Lajos, 2006. "Convergence Of Integral Functionals Of Stochastic Processes," Econometric Theory, Cambridge University Press, vol. 22(02), pages 304-322, April.
  26. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
  27. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  28. Jia Chen & Jiti Gao & Degui Li, 2009. "Semiparametric Regression Estimation in Null Recurrent Nonlinear Time Series," School of Economics Working Papers 2009-02, University of Adelaide, School of Economics.
  29. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-92, November.
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