A note on the invertibility of nonlinear ARMA models

Kung-Sik Chan; Howell Tong

doi:10.1016/j.jspi.2010.04.036

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A note on the invertibility of nonlinear ARMA models

Journal article

Peer reviewed

A note on the invertibility of nonlinear ARMA models

Kung-Sik Chan and Howell Tong

Journal of statistical planning and inference, Vol.140(12), pp.3709-3714

2010

DOI: 10.1016/j.jspi.2010.04.036

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Abstract

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.

Subadditive ergodic theory

Nonlinear time series

Polynomial MA model

Threshold MA model

Dynamical system

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Details

Title: Subtitle: A note on the invertibility of nonlinear ARMA models
Creators: Kung-Sik Chan - Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, IA 52242, USA
Howell Tong - Department of Statistics, London School of Economics, London WC2A 2AE, UK
Resource Type: Journal article
Publication Details: Journal of statistical planning and inference, Vol.140(12), pp.3709-3714
DOI: 10.1016/j.jspi.2010.04.036
ISSN: 0378-3758
eISSN: 1873-1171
Publisher: Elsevier B.V
Language: English
Date published: 2010
Academic Unit: Statistics and Actuarial Science; Radiology
Record Identifier: 9983985966902771

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