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WEAK CONVERGENCE OF NONLINEAR TRANSFORMATIONS OF INTEGRATED PROCESSES: THE MULTIVARIATE CASE

Published online by Cambridge University Press:  01 October 2009

Norbert Christopeit
Norbert Christopeit*
Affiliation:
University of Bonn
*
*Address correspondence to Norbert Christopeit, Institute of Econometrics, Department of Economics, University of Bonn, Adenauerallee 24-42, D-53113 Bonn, Germany; e-mail: christopeit@uni-bonn.de.
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Abstract

We consider weak convergence of sample averages of nonlinearly transformed stochastic triangular arrays satisfying a functional invariance principle. A fundamental paradigm for such processes is constituted by integrated processes. The results obtained are extensions of recent work in the literature to the multivariate and non-Gaussian case. As admissible nonlinear transformation, a new class of functionals (so-called locally p-integrable functions) is introduced that adapts the concept of locally integrable functions in Pötscher (2004, Econometric Theory 20, 1–22) to the multidimensional setting.

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Type
ARTICLES
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Econometric Theory , Volume 25 , Issue 5 , October 2009 , pp. 1180 - 1207
Copyright
Copyright © Cambridge University Press 2009

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