Journal of Applied Mathematics and Decision Sciences 
Volume 6 (2002), Issue 4, Pages 255-269
doi:10.1155/S1173912602000184

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

Abstract

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.