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Nonlinear Regressions with Integrated Time Series

  • Joon Y. Park

    ()

  • Peter C. B. Phillips

An asymptotic thoery is developed for nonlinear regression with integrated processes. The models allow for nonlinear effects from unit root time series and theory covers integrable, asymptotically homeogeneous and explosive functions. Sufficient conditions for weak consistency are given and a limit distribution theory is provided. The rates of convergence depend on the properties of the nonlinear regression function, and are shown to be as slow as n^(1/4) for integrable functions, to be generally polynomial in n^(1/2) for homogeneous functions, and to be path dependent in the case of explosive functions. For regressions with integrable or explosive functions, the limiting distribution theory is mixed normal with mixing variates that depend on the sojourn time of the limiting Brownian motion of the integrated process.

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File URL: http://econ.snu.ac.kr/~ecores/activity/paper/no6.pdf
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Paper provided by Institute of Economic Research, Seoul National University in its series Working Paper Series with number no6.

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Date of creation: Mar 1999
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Handle: RePEc:snu:ioerwp:no6
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  1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  2. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  3. 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.
  4. Andrews, Donald W K & McDermott, C John, 1995. "Nonlinear Econometric Models with Deterministically Trending Variables," Review of Economic Studies, Wiley Blackwell, vol. 62(3), pages 343-60, July.
  5. 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.
  6. repec:cup:etheor:v:11:y:1995:i:5:p:888-911 is not listed on IDEAS
  7. 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.
  8. Saikkonen, Pentti, 1995. "Problems with the Asymptotic Theory of Maximum Likelihood Estimation in Integrated and Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 11(05), pages 888-911, October.
  9. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  10. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  11. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  12. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  13. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  14. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
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