Institute of Mathematical Statistics Lecture Notes - Monograph Series

Invariance principles for fractionally integrated nonlinear processes

Wei Biao Wu and Xiaofeng Shao

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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

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

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

fractional integration long memory nonlinear time series weak convergence

Copyright © 2006, Institute of Mathematical Statistics


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.

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