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Nonlinear Regressions with Integrated Time Series

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Author Info
Joon Y. Park (School of Economics, Seoul National University)
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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Abstract

An asymptotic theory is developed for nonlinear regression with integrated processes. The models allow for nonlinear effects from unit root time series and therefore deal with the case of parametric nonlinear cointegration. The theory covers integrable, asymptotically homogeneous and explosive functions. Sufficient conditions for weak consistency are given and a limit distribution theory is provided. In general, the limit theory is mixed normal with mixing variates that depend on the sojourn time of the limiting Brownian motion of the integrated process. 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.

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File URL: http://cowles.econ.yale.edu/P/cd/d11b/d1190.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1190.

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Length: 63 pages
Date of creation: Aug 1998
Date of revision:
Publication status: Published in Econometrica (2001), 69(1): 117-161
Handle: RePEc:cwl:cwldpp:1190

Note: CFP 1016.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Functionals of Brownian motion; Brownian motion; integrated process; local time; mixed normal limit theory; nonlinear transformations; nonparametric density estimation; occupation time; nonlinear regression;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  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!]
    Other versions:
  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)
    Other versions:
  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)
    Other versions:
  8. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March. [Downloadable!] (restricted)
    Other versions:
  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!]
    Other versions:
  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)
    Other versions:
  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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