Asymptotics for Nonlinear Transformations of Integrated Time Series

Peter Phillips and Joon Park

No 1182, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: An asymptotic theory for stochastic processes generated from nonlinear transformations of nonstationary integrated time series is developed. Various nonlinear functions of integrated series such as ARIMA time series are studied, and the asymptotic distributions of sample moments of such functions are obtained and analyzed. The transformations considered in the paper include a variety of functions that are used in practical nonlinear statistical analysis. It is shown that their asymptotic theory is quite different from that of integrated processes and stationary time series. When the transformation function is exponentially explosive, for instance, the convergence rate of sample functions is path-dependent. In particular, the convergence rate depends not only on the size of the sample, but also on the realized sample path. Some brief applications of these asymptotics are given to illustrate the effects of nonlinearly transformed integrated processes on regression. The methods developed in the paper are useful in a project of greater scope concerned with the development of a general theory of nonlinear regression for nonstationary time series.

Keywords: Additive functionals of Brownian motion; Brownian motion; integrated process; local time; nonlinear transformation; occupation time; regression asymptotics (search for similar items in EconPapers)
Pages: 27 pages
Date: 1998-06
Note: CFP 980.
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Citations: View citations in EconPapers (10)

Published in Econometric Theory (1999), 15: 260-298

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Journal Article: ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES (1999)
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