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Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression

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Abstract

We provide a new asymptotic theory for local time density estimation for a general class of functionals of integrated time series. This result provides a convenient basis for developing an asymptotic theory for nonparametric cointegrating regression and autoregression. Our treatment directly involves the density function of the processes under consideration and avoids Fourier integral representations and Markov process theory which have been used in earlier research on this type of problem. The approach provides results of wide applicability to important practical cases and involves rather simple derivations that should make the limit theory more accessible and useable in econometric applications. Our main result is applied to offer an alternative development of the asymptotic theory for non-parametric estimation of a non-linear cointegrating regression involving non-stationary time series. In place of the framework of null recurrent Markov chains as developed in recent work of Karlsen, Myklebust and Tjostheim (2007), the direct local time density argument used here more closely resembles conventional nonparametric arguments, making the conditions simpler and more easily verified.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1594.

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Length: 26 pages
Date of creation: Dec 2006
Date of revision:
Handle: RePEc:cwl:cwldpp:1594

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Brownian Local time; Cointegration; Integrated process; Local time density estimation; Nonlinear functionals; Nonparametric regression; Unit root;

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  1. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
  2. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
  3. Emmanuel Guerre, 2004. "Design-Adaptive Pointwise Nonparametric Regression Estimation for Recurrent Markov Time Series," Working Papers 2004-22, Centre de Recherche en Economie et Statistique.
  4. Wang, Qiying & Lin, Yan-Xia & Gulati, Chandra M., 2003. "Asymptotics For General Fractionally Integrated Processes With Applications To Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(01), pages 143-164, February.
  5. Peter C.B. Phillips, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation for Research in Economics, Yale University.
  6. 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.
  7. Joon Y. Park, 2004. "The Spatial Analysis of Time Series," Econometric Society 2004 North American Winter Meetings 595, Econometric Society.
  8. 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.
  9. Hannan, E. J., 1979. "The central limit theorem for time series regression," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 281-289, December.
  10. Ling Hu & Peter C.B. Phillips, 2002. "Nonstationary Discrete Choice," Cowles Foundation Discussion Papers 1364, Cowles Foundation for Research in Economics, Yale University.
  11. de Jong, Robert M., 2004. "Addendum To," Econometric Theory, Cambridge University Press, vol. 20(03), pages 627-635, June.
  12. Federico M. Bandi & Peter C.B. Phillips, 2001. "Fully Nonparametric Estimation of Scalar Diffusion Models," Cowles Foundation Discussion Papers 1332, Cowles Foundation for Research in Economics, Yale University.
  13. 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.
  14. Seung Hyun Hong & Peter C. B. Phillips, 2005. "Testing Linearity in Cointegrating Relations with an Application to Purchasing Power Parity," Cowles Foundation Discussion Papers 1541, Cowles Foundation for Research in Economics, Yale University.
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