Premium
Fractional Invariance Principle
Author(s) -
Hosoya Yuzo
Publication year - 2005
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2004.00411.x
Subject(s) - mathematics , invariance principle , pure mathematics , epistemology , philosophy
. 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.