Institute of Mathematical Statistics Lecture Notes - Monograph Series

Invariance principles for fractionally integrated nonlinear processes

Wei Biao Wu and Xiaofeng Shao

Full-text: Open access

Abstract

We obtain invariance principles for a wide class of fractionally integrated nonlinear processes. The limiting distributions are shown to be fractional Brownian motions. Under very mild conditions, we extend earlier ones on long memory linear processes to a more general setting. The invariance principles are applied to the popular R/S and KPSS tests.

Chapter information

Source
Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page, eds., Recent Developments in Nonparametric Inference and Probability: Festschrift for Michael Woodroofe (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 20-30

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196284050

Digital Object Identifier
doi:10.1214/074921706000000572

Mathematical Reviews number (MathSciNet)
MR2409061

Zentralblatt MATH identifier
1268.60045

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
fractional integration long memory nonlinear time series weak convergence

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

Wu, Wei Biao; Shao, Xiaofeng. Invariance principles for fractionally integrated nonlinear processes. Recent Developments in Nonparametric Inference and Probability, 20--30, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000572. https://projecteuclid.org/euclid.lnms/1196284050


Export citation