Journal of Applied Mathematics and Decision Sciences
Volume 6 (2002), Issue 4, Pages 255-269

Asymptotics for general nonstationary fractionally integrated processes without prehistoric influence

Qiying Wang,1 Yan-Xia Lin,2 and Chandra Gulati2

1CMA, School of Mathematical Science, The Australian National University, 0200, ACT, Australia
2School of Mathematics and Applied Statistics, University of Wollongong, Wollongong 2522, NSW, Australia

Copyright © 2002 Qiying Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper derives a functional limit theorem for general nonstationary fractionally integrated processes having no influence from prehistory. Asymptotic distributions of sample autocovariances and sample autocorrelations based on these processes are also investigated. The problem arises naturally in discussing fractionally integrated processes when the processes starts at a given initial date.