The functional central limit theorem and weak convergence to stochastic integrals II: fractionally integrated processes
De Jong, Robert M.
Cardiff University (now at University of Exeter); Michigan State University
Cambridge University Press
This paper derives a functional central limit theorem for the partial sums of fractionally integrated processes, otherwise known as I(d) processes for |d| < 1/2. Such processes have long memory, and the limit distribution is the so-called fractional Brownian motion, having correlated increments even asymptotically. The underlying shock variables may themselves exhibit quite general weak dependence by being near-epoch-dependent functions of mixing processes. Several weak convergence results for stochastic integrals having fractional integrands and weakly dependent integrators are also obtained. Taken together, these results permit I(p + d) integrands for any integer p [greater-than-or-equal] 1.
Pre-print; verson dated May 1999. Addendum clarifies the proof of Theorem 3.1.
Econometric Theory 16, 5 (2000) 643-666