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Nonlinear Regressions with Integrated Time Series

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Author Info
Joon Y. Park ()
Peter C. B. Phillips

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Abstract

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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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. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation, Yale University. [Downloadable!]
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  2. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  3. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation, Yale University. [Downloadable!]
  4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  5. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  6. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  7. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December. [Downloadable!] (restricted)
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  8. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March. [Downloadable!] (restricted)
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  9. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers 811R, Cowles Foundation, Yale University, revised Aug 1987. [Downloadable!]
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  10. Andrews, Donald W K & McDermott, C John, 1995. "Nonlinear Econometric Models with Deterministically Trending Variables," Review of Economic Studies, Blackwell Publishing, vol. 62(3), pages 343-60, July. [Downloadable!] (restricted)
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  11. 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. [Downloadable!]
  12. 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. [Downloadable!] (restricted)
  13. repec:cup:etheor:v:11:y:1995:i:5:p:888-911 is not listed on IDEAS
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