"Convergence to stochastic integrals with non-linear integrands"

Carlos Caceres and Bent Nielsen
Department of Economics, University of Oxford

Abstract:
In this paper we present a general result concerning the
convergence to stochastic integrals with non-linear integrands.
The key finding represents a generalization of Chan and Wei's
(1988) Theorem 2.4. and that of Ibragimov and Phillips' (2004)
Theorem 8.2. This result is necessary for analysing the asymptotic
properties of mis-specification tests, when applied to a unit root
process, for which Wooldridge (1999) mentioned that the exiting
results in the literature were not sufficient.