Rm. De Jong et J. Davidson, The functional central limit theorem and weak convergence to stochastic integrals I - Weakly dependent processes, ECONOMET TH, 16(5), 2000, pp. 621-642
This paper gives new conditions for the functional central limit theorem, a
nd weak convergence of stochastic integrals, for near-epoch-dependent funct
ions of mixing processes. These results have fundamental applications in th
e 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.