Invariance principles for fractionally integrated nonlinear processes

Details Invariance principles for fractionally integrated nonlinear processes Invariance principles for fractionally integrated nonlinear processes

2006-08-09

arxiv.org/abs/math/0608223v2

IMS Lecture Notes--Monograph Series 2006, Vol. 50, 20-30

Mathematics

Probability

Published at http://dx.doi.org/10.1214/074921706000000572 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000572

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.

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