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A note on the invertibility of nonlinear ARMA models

By Kung-Sik Chan and Howell Tong


We review the concepts of local and global invertibility for a nonlinear auto-regressive moving-average (NLARMA) model. Under very general conditions, a local invertibility analysis of an NLARMA model shows the generic dichotomy that the innovation reconstruction errors either diminish geometrically fast or grow geometrically fast. We derive a simple sufficient condition for an NLARMA model to be locally invertible. The invertibility of the polynomial MA models is revisited. Moreover, we show that the threshold MA models may be globally invertible even though some component MA models are non-invertible. One novelty of our approach is its cross-fertilization with dynamical systems

Topics: HA Statistics, QA Mathematics
Publisher: Elsevier
Year: 2010
DOI identifier: 10.1016/j.jspi.2010.04.036
OAI identifier:
Provided by: LSE Research Online
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