The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form integral_{0}^{1}WdW, where W(r) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA processes the...

We prove a central limit theorem for products of centered i.i.d. r.v.'s taking values on nilpotent, graded, simply connected Lie groups. The main tool is given by weak approximation results for SDEs.