Comment on: Threshold autoregressions with a unit root
Comment on: Threshold autoregressions with a unit root
In this paper we revisit the results in Caner and Hansen (2001), where the authors obtained novel limiting distributions of Wald type test statistics for testing for the presence of threshold nonlinearities in autoregressive models containing unit roots. Using the same framework, we obtain a new formulation of the limiting distribution of the Wald statistic for testing for threshold effects, correcting an expression that appeared in the main theorem presented by Caner and Hansen. Subsequently, we show that under a particular scenario that excludes stationary regressors such as lagged dependent variables and despite the presence of a unit root, this same limiting random variable takes a familiar form that is free of nuisance parameters and already tabulated in the literature, thus removing the need to use bootstrap based inferences. This is a novel and unusual occurrence in this literature on testing for the presence of nonlinear dynamics.
threshold autoregressive models, unit roots, nonlinear time series
1207-1217
Pitarakis, Jean-Yves
ee5519ae-9c0f-4d79-8a3a-c25db105bd51
9 September 2008
Pitarakis, Jean-Yves
ee5519ae-9c0f-4d79-8a3a-c25db105bd51
Pitarakis, Jean-Yves
(2008)
Comment on: Threshold autoregressions with a unit root.
Econometrica, 76 (5), .
(doi:10.3982/ECTA6979).
Abstract
In this paper we revisit the results in Caner and Hansen (2001), where the authors obtained novel limiting distributions of Wald type test statistics for testing for the presence of threshold nonlinearities in autoregressive models containing unit roots. Using the same framework, we obtain a new formulation of the limiting distribution of the Wald statistic for testing for threshold effects, correcting an expression that appeared in the main theorem presented by Caner and Hansen. Subsequently, we show that under a particular scenario that excludes stationary regressors such as lagged dependent variables and despite the presence of a unit root, this same limiting random variable takes a familiar form that is free of nuisance parameters and already tabulated in the literature, thus removing the need to use bootstrap based inferences. This is a novel and unusual occurrence in this literature on testing for the presence of nonlinear dynamics.
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e-pub ahead of print date: 9 September 2008
Published date: 9 September 2008
Keywords:
threshold autoregressive models, unit roots, nonlinear time series
Organisations:
Economics
Identifiers
Local EPrints ID: 156073
URI: http://eprints.soton.ac.uk/id/eprint/156073
ISSN: 0012-9682
PURE UUID: 4d3701c6-bbc0-4e13-8c15-7baba6caa2e4
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Date deposited: 01 Jun 2010 08:53
Last modified: 14 Mar 2024 02:48
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