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A note on the invertibility of nonlinear ARMA models

Chan, Kung-Sik and Tong, Howell (2010) A note on the invertibility of nonlinear ARMA models. Journal of Statistical Planning and Inference, 140 (12). pp. 3709-3714. ISSN 0378-3758

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Identification Number: 10.1016/j.jspi.2010.04.036


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.

Item Type: Article
Official URL:
Additional Information: © 2010 Elsevier B.V.
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Sets: Departments > Statistics
Date Deposited: 19 Oct 2010 15:31
Last Modified: 20 Jul 2021 00:50

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