The functional central limit theorem and weak convergence to stochastic integrals I: weakly dependent processes
De Jong, Robert M.
Michigan State University; Cardiff University (now at University of Exeter)
Cambridge University Press
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.
Pre-print; version dated May 1999
Econometric Theory, Vol. 16 (5) October 2000, pp 621-642