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THE FUNCTIONAL CENTRAL LIMIT THEOREM AND WEAK CONVERGENCE TO STOCHASTIC INTEGRALS I

Weakly Dependent Processes

Published online by Cambridge University Press:  05 October 2000

Robert M. de Jong
Affiliation:
Michigan State University
James Davidson
Affiliation:
Cardiff University

Abstract

This paper gives new conditions for the functional central limit theorem, and weak convergence of stochastic integrals, for near-epoch-dependent functions of mixing processes. These results have fundamental applications in the theory of unit root testing and cointegrating regressions. The conditions given improve on existing results in the literature in terms of the amount of dependence and heterogeneity permitted, and in particular, these appear to be the first such theorems in which virtually the same assumptions are sufficient for both modes of convergence.

Type
Research Article
Copyright
© 2000 Cambridge University Press

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