The validity of bootstrap testing for threshold autoregression
We consider bootstrap-based testing for threshold effects in non-linear threshold autoregressive (TAR) models. It is well-known that classic tests based on asymptotic theory tend to be biased in case of small, or even moderate sample sizes, especially when the estimated parameters indicate non-stati...
Published in: | Journal of Econometrics |
---|---|
Main Authors: | , , |
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
2023
|
Subjects: | |
Online Access: | https://hdl.handle.net/11585/913284 https://doi.org/10.1016/j.jeconom.2023.01.004 |
id |
ftunibolognairis:oai:cris.unibo.it:11585/913284 |
---|---|
record_format |
openpolar |
spelling |
ftunibolognairis:oai:cris.unibo.it:11585/913284 2024-04-14T08:12:27+00:00 The validity of bootstrap testing for threshold autoregression Giannerini, Simone Goracci, Greta Rahbek, Anders Giannerini, Simone Goracci, Greta Rahbek, Anders 2023 ELETTRONICO https://hdl.handle.net/11585/913284 https://doi.org/10.1016/j.jeconom.2023.01.004 eng eng volume:2023 issue:January firstpage:1 lastpage:24 numberofpages:24 journal:JOURNAL OF ECONOMETRICS https://hdl.handle.net/11585/913284 doi:10.1016/j.jeconom.2023.01.004 info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85147225387 info:eu-repo/semantics/openAccess Bootstrap test Threshold autoregressive models Law of large numbers Heteroskedasticity Greenland ice sheet info:eu-repo/semantics/article 2023 ftunibolognairis https://doi.org/10.1016/j.jeconom.2023.01.004 2024-03-21T17:04:58Z We consider bootstrap-based testing for threshold effects in non-linear threshold autoregressive (TAR) models. It is well-known that classic tests based on asymptotic theory tend to be biased in case of small, or even moderate sample sizes, especially when the estimated parameters indicate non-stationarity, or in presence of heteroskedasticity, as often witnessed in the analysis of financial or climate data. To address the issue we propose a supremum Lagrange Multiplier test statistic (sLM), where the null hypothesis specifies a linear autoregressive (AR) model against the alternative of a TAR model. We consider both the classical recursive residual i.i.d. bootstrap (sLMi) and a wild bootstrap (sLMw), applied to the sLM statistic, and establish their validity under the null hypothesis. The framework is new, and requires the proof of non-standard results for bootstrap analysis in time series models; this includes a uniform bootstrap law of large numbers and a bootstrap functional central limit theorem. The Monte Carlo evidence shows that the bootstrap tests have correct empirical size even for small samples; the wild bootstrap version (sLMw) is also robust against the presence of heteroskedasticity. Moreover, there is no loss of empirical power when compared to the asymptotic test and the size of the tests is not affected if the order of the tested model is selected through AIC. Finally, we use our results to analyse the time series of the Greenland ice sheet mass balance. We find a significant threshold effect and an appropriate specification that manages to reproduce the main nonlinear features of the series, such as the asymmetric seasonal cycle, the main periodicities and the multimodality of the probability density function. Article in Journal/Newspaper Greenland Ice Sheet IRIS Università degli Studi di Bologna (CRIS - Current Research Information System) Greenland Lagrange ENVELOPE(-62.597,-62.597,-64.529,-64.529) Journal of Econometrics 105379 |
institution |
Open Polar |
collection |
IRIS Università degli Studi di Bologna (CRIS - Current Research Information System) |
op_collection_id |
ftunibolognairis |
language |
English |
topic |
Bootstrap test Threshold autoregressive models Law of large numbers Heteroskedasticity Greenland ice sheet |
spellingShingle |
Bootstrap test Threshold autoregressive models Law of large numbers Heteroskedasticity Greenland ice sheet Giannerini, Simone Goracci, Greta Rahbek, Anders The validity of bootstrap testing for threshold autoregression |
topic_facet |
Bootstrap test Threshold autoregressive models Law of large numbers Heteroskedasticity Greenland ice sheet |
description |
We consider bootstrap-based testing for threshold effects in non-linear threshold autoregressive (TAR) models. It is well-known that classic tests based on asymptotic theory tend to be biased in case of small, or even moderate sample sizes, especially when the estimated parameters indicate non-stationarity, or in presence of heteroskedasticity, as often witnessed in the analysis of financial or climate data. To address the issue we propose a supremum Lagrange Multiplier test statistic (sLM), where the null hypothesis specifies a linear autoregressive (AR) model against the alternative of a TAR model. We consider both the classical recursive residual i.i.d. bootstrap (sLMi) and a wild bootstrap (sLMw), applied to the sLM statistic, and establish their validity under the null hypothesis. The framework is new, and requires the proof of non-standard results for bootstrap analysis in time series models; this includes a uniform bootstrap law of large numbers and a bootstrap functional central limit theorem. The Monte Carlo evidence shows that the bootstrap tests have correct empirical size even for small samples; the wild bootstrap version (sLMw) is also robust against the presence of heteroskedasticity. Moreover, there is no loss of empirical power when compared to the asymptotic test and the size of the tests is not affected if the order of the tested model is selected through AIC. Finally, we use our results to analyse the time series of the Greenland ice sheet mass balance. We find a significant threshold effect and an appropriate specification that manages to reproduce the main nonlinear features of the series, such as the asymmetric seasonal cycle, the main periodicities and the multimodality of the probability density function. |
author2 |
Giannerini, Simone Goracci, Greta Rahbek, Anders |
format |
Article in Journal/Newspaper |
author |
Giannerini, Simone Goracci, Greta Rahbek, Anders |
author_facet |
Giannerini, Simone Goracci, Greta Rahbek, Anders |
author_sort |
Giannerini, Simone |
title |
The validity of bootstrap testing for threshold autoregression |
title_short |
The validity of bootstrap testing for threshold autoregression |
title_full |
The validity of bootstrap testing for threshold autoregression |
title_fullStr |
The validity of bootstrap testing for threshold autoregression |
title_full_unstemmed |
The validity of bootstrap testing for threshold autoregression |
title_sort |
validity of bootstrap testing for threshold autoregression |
publishDate |
2023 |
url |
https://hdl.handle.net/11585/913284 https://doi.org/10.1016/j.jeconom.2023.01.004 |
long_lat |
ENVELOPE(-62.597,-62.597,-64.529,-64.529) |
geographic |
Greenland Lagrange |
geographic_facet |
Greenland Lagrange |
genre |
Greenland Ice Sheet |
genre_facet |
Greenland Ice Sheet |
op_relation |
volume:2023 issue:January firstpage:1 lastpage:24 numberofpages:24 journal:JOURNAL OF ECONOMETRICS https://hdl.handle.net/11585/913284 doi:10.1016/j.jeconom.2023.01.004 info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85147225387 |
op_rights |
info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.1016/j.jeconom.2023.01.004 |
container_title |
Journal of Econometrics |
container_start_page |
105379 |
_version_ |
1796310249376841728 |