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NONLINEAR FUNCTIONS AND CONVERGENCE TO BROWNIAN MOTION: BEYOND THE CONTINUOUS MAPPING THEOREM

Published online by Cambridge University Press:  05 March 2004

Benedikt M. Pötscher
Benedikt M. Pötscher
Affiliation:
University of Vienna
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Abstract

Weak convergence results for sample averages of nonlinear functions of (discrete-time) stochastic processes satisfying a functional central limit theorem (e.g., integrated processes) are given. These results substantially extend recent work by Park and Phillips (1999, Econometric Theory 15, 269–298) and de Jong (2002, working paper), in that a much wider class of functions is covered. For example, some of the results hold for the class of all locally integrable functions, thus avoiding any of the various regularity conditions imposed on the functions in Park and Phillips (1999) or de Jong (2002).I thank Robert de Jong for drawing my attention to this problem and Hannes Leeb for helpful comments. This paper was presented at the Econometric Society European Meeting 2002 in Venice.

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 1 , February 2004 , pp. 1 - 22
Copyright
© 2004 Cambridge University Press

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References

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