Fractional invariance principle

The paper presents a central limit theorem and an allied invariance theorem related to what Marinucci and Robinson [Journal of Statistics, Planning and Inference (1999) Vol. 21, pp. 111-122] termed type II fractional Brownian motion. To widen the applicability, their independent and identically distributed (i.i.d.) assumption for the innovation process is relaxed, allowing it to be mildly conditionally heteroscedastic and requiring the Martingale-difference property only asymptotically. Additionally, the paper presents, for contrast, the weak convergence of the conventional partial sum process in a related set-up.