COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1190 Nonlinear Regressions with Integrated Time Series Joon Y. Park and Peter C. B. Phillips August 1998 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 n1/4 for integrable functions, to be generally polynomial in n1/2 for homogeneous functions, and to be path dependent in the case of explosive functions. Key words and phrases: Functionals of Brownian motion, Brownian motion, integrated process, local time, mixed normal limit theory, nonlinear transformations, nonparametric density estimation, occupation time, nonlinear regression. |
