Nonlinear Regressions with Integrated Time Series

TLDR: In this paper, an asymptotic theory for nonlinear regression with integrated processes is developed, and sufficient conditions for weak consistency are given and a limit distribution theory is provided, which is mixed normal with mixing variates that depend on the sojourn time of the limiting Brownian motion of the integrated process.

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 and asymptotically homogeneous 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, and to be generally polynomial in n 1/2 for homogeneous functions. For regressions with integrable 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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COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY
Box 2125, Yale Station
New Haven, Connecticut 06520
COWLES FOUNDATION DISCUSSION PAPER NO. 1190
Note: Cowles Foundation Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment.
Requests for single copies of a Paper will be filled by the
Cowles Foundation within the limits of the supply. References
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protect the tentative character of these papers.
NONLINEAR REGRESSIONS WITH INTEGRATED TIME SERIES
Joon Y. Park and Peter C. B. Phillips
August 1998

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