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.
Information
Published: 1 January 2006
First available in Project Euclid: 28 November 2007
zbMATH: 1268.60045
MathSciNet: MR2409061
Digital Object Identifier: 10.1214/074921706000000572
Subjects:
Primary:
60F17
Secondary:
62M10
Keywords:
fractional integration
,
long memory
,
nonlinear time series
,
weak convergence
Rights: Copyright © 2006, Institute of Mathematical Statistics
