Modelling directionality for paleoclimatic time series
The ice core time series from Vostok Station in Antarctica and the North Greenland Ice Core Project have seasonal variation corresponding to the Milankovitch cycles. After removing these cycles, and interpolating to equal time intervals, stationary time series models are fitted. The series show clea...
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Australian Mathematical Society
2016
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Australian Mathematical Society (AustMS): E-Journals |
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Directional time series reversibility ice cores threshold autoregressive models penalised least squares 62M10 |
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Directional time series reversibility ice cores threshold autoregressive models penalised least squares 62M10 Mansor, Mahayaudin M. Mohd. Isa, Farah L. Green, David A. Metcalfe, Andrew V. Modelling directionality for paleoclimatic time series |
topic_facet |
Directional time series reversibility ice cores threshold autoregressive models penalised least squares 62M10 |
description |
The ice core time series from Vostok Station in Antarctica and the North Greenland Ice Core Project have seasonal variation corresponding to the Milankovitch cycles. After removing these cycles, and interpolating to equal time intervals, stationary time series models are fitted. The series show clear directionality and this feature is modelled by either non-Gaussian errors or non-linear time series models. Threshold autoregressive models are fitted by penalized least squares and compared with non-threshold autoregressive models. Since both ice core time series are reasonably modelled as first order autoregressive series with parameters close to one, directionality will arise from non-symmetric error distributions. However, two regime threshold autoregressive models, of order one and two for Greenland and Vostok, respectively, give an improved match to the observed directionality and a reduced sum of squared residuals. Realizations from the threshold autoregressive models are noticeably different from the non-threshold models. Since the non-threshold models are a restricted case of the threshold models, and the threshold models are a better fit to the observed time series, threshold models should provide more realistic realizations. References C. Chatfield. The Analysis of Time Series: An Introduction. CRC Press, 2004. https://www.crcpress.com/The-Analysis-of-Time-Series-An-Introduction-Sixth-Edition/Chatfield/p/book/9781584883173 A. J. Lawrance. Directionality and reversibility in time series. Int. Stat. Rev. 59(1):67–79, 1991. doi:10.2307/1403575 M. M. Mansor, M. E. Glonek, D. A. Green and A. V. Metcalfe. Threshold autoregressive models for directional time series. In I. Rojas and H. Pomares (Eds.), Time Series Analysis and Forecasting Selected Contributions from the ITISE Conference (ITISE 2015). pp. 13–25, 2016. doi:10.1007/978-3-319-28725-6 M. M. Mansor, M. E. Glonek, D. A. Green and A. V. Metcalfe. Modelling directionality in stationary geophysical time series. International work-conference on Time Series (ITISE 2015). http://www.researchgate.net/publication/281835075 M. M. Mansor, D. A. Green and A. V. Metcalfe. Modelling and simulation of directional financial time series. Proceedings of the 21st International Congress on Modelling and Simulation (MODSIM 2015), pp. 1022–1028, 2015. http://www.mssanz.org.au/modsim2015/E4/mansor.pdf M. M. Mansor, D. A. Green and A. V. Metcalfe. Directionality and volatility in electroencephalogram time series. Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS 2016), AIP Conf. Proc. 1739:020080, 2016. doi:10.1063/1.4952560 North Greenland Ice Core Project members. High-resolution record of Northern Hemisphere climate extending into the last interglacial period. Nature, 431:147–151, 2004. doi:10.1038/nature02805 J. R. Petit, J. Jouzel, D. Raynaud, N. I. Barkov, J.-M. Barnola, I. Basile, M. Bender, J. Chappellaz, M. Davis, G. Delaygue, M. Delmotte, V. M. Kotlyakov, M. Legrand, V. Y. Lipenkov, C. Lorius, L. Pepin, C. Ritz, E. Saltzman and M. Stievenard. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature, 399:429–436, 1999. doi:10.1038/20859 S. Soubeyrand, C. E. Morris and E. K. Bigg. Analysis of fragmented time directionality in time series to elucidate feedbacks in climate data. Environ. Modell. Softw. 61:78–86, 2014. doi:10.1016/j.envsoft.2014.07.003 |
format |
Article in Journal/Newspaper |
author |
Mansor, Mahayaudin M. Mohd. Isa, Farah L. Green, David A. Metcalfe, Andrew V. |
author_facet |
Mansor, Mahayaudin M. Mohd. Isa, Farah L. Green, David A. Metcalfe, Andrew V. |
author_sort |
Mansor, Mahayaudin M. |
title |
Modelling directionality for paleoclimatic time series |
title_short |
Modelling directionality for paleoclimatic time series |
title_full |
Modelling directionality for paleoclimatic time series |
title_fullStr |
Modelling directionality for paleoclimatic time series |
title_full_unstemmed |
Modelling directionality for paleoclimatic time series |
title_sort |
modelling directionality for paleoclimatic time series |
publisher |
Australian Mathematical Society |
publishDate |
2016 |
url |
https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10415 |
long_lat |
ENVELOPE(-50.517,-50.517,63.183,63.183) ENVELOPE(-164.000,-164.000,-78.500,-78.500) ENVELOPE(162.350,162.350,-72.467,-72.467) ENVELOPE(-66.942,-66.942,-67.976,-67.976) ENVELOPE(-63.950,-63.950,-64.817,-64.817) ENVELOPE(106.837,106.837,-78.464,-78.464) |
geographic |
Greenland Itise Lawrance Lorius Metcalfe Rojas Vostok Station |
geographic_facet |
Greenland Itise Lawrance Lorius Metcalfe Rojas Vostok Station |
genre |
Antarc* Antarctica Greenland Greenland ice core Greenland Ice core Project ice core North Greenland North Greenland Ice Core Project |
genre_facet |
Antarc* Antarctica Greenland Greenland ice core Greenland Ice core Project ice core North Greenland North Greenland Ice Core Project |
op_source |
ANZIAM Journal; Vol. 57 (2015); C66--C81 1445-8810 |
op_relation |
https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10415/1950 https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10415/1952 https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10415 |
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Copyright (c) 2016 AMPAI |
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ANZIAM Journal |
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66 |
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1766264277827584000 |
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ftaustralianmsoj:oai:journal.austms.org.au:article/10415 2023-05-15T13:56:42+02:00 Modelling directionality for paleoclimatic time series Mansor, Mahayaudin M. Mohd. Isa, Farah L. Green, David A. Metcalfe, Andrew V. 2016-06-17 application/pdf text/plain https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10415 eng eng Australian Mathematical Society https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10415/1950 https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10415/1952 https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10415 Copyright (c) 2016 AMPAI ANZIAM Journal; Vol. 57 (2015); C66--C81 1445-8810 Directional time series reversibility ice cores threshold autoregressive models penalised least squares 62M10 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Peer reviewed conference article 2016 ftaustralianmsoj 2022-02-28T12:00:46Z The ice core time series from Vostok Station in Antarctica and the North Greenland Ice Core Project have seasonal variation corresponding to the Milankovitch cycles. After removing these cycles, and interpolating to equal time intervals, stationary time series models are fitted. The series show clear directionality and this feature is modelled by either non-Gaussian errors or non-linear time series models. Threshold autoregressive models are fitted by penalized least squares and compared with non-threshold autoregressive models. Since both ice core time series are reasonably modelled as first order autoregressive series with parameters close to one, directionality will arise from non-symmetric error distributions. However, two regime threshold autoregressive models, of order one and two for Greenland and Vostok, respectively, give an improved match to the observed directionality and a reduced sum of squared residuals. Realizations from the threshold autoregressive models are noticeably different from the non-threshold models. Since the non-threshold models are a restricted case of the threshold models, and the threshold models are a better fit to the observed time series, threshold models should provide more realistic realizations. References C. Chatfield. The Analysis of Time Series: An Introduction. CRC Press, 2004. https://www.crcpress.com/The-Analysis-of-Time-Series-An-Introduction-Sixth-Edition/Chatfield/p/book/9781584883173 A. J. Lawrance. Directionality and reversibility in time series. Int. Stat. Rev. 59(1):67–79, 1991. doi:10.2307/1403575 M. M. Mansor, M. E. Glonek, D. A. Green and A. V. Metcalfe. Threshold autoregressive models for directional time series. In I. Rojas and H. Pomares (Eds.), Time Series Analysis and Forecasting Selected Contributions from the ITISE Conference (ITISE 2015). pp. 13–25, 2016. doi:10.1007/978-3-319-28725-6 M. M. Mansor, M. E. Glonek, D. A. Green and A. V. Metcalfe. Modelling directionality in stationary geophysical time series. International work-conference on Time Series (ITISE 2015). http://www.researchgate.net/publication/281835075 M. M. Mansor, D. A. Green and A. V. Metcalfe. Modelling and simulation of directional financial time series. Proceedings of the 21st International Congress on Modelling and Simulation (MODSIM 2015), pp. 1022–1028, 2015. http://www.mssanz.org.au/modsim2015/E4/mansor.pdf M. M. Mansor, D. A. Green and A. V. Metcalfe. Directionality and volatility in electroencephalogram time series. Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS 2016), AIP Conf. Proc. 1739:020080, 2016. doi:10.1063/1.4952560 North Greenland Ice Core Project members. High-resolution record of Northern Hemisphere climate extending into the last interglacial period. Nature, 431:147–151, 2004. doi:10.1038/nature02805 J. R. Petit, J. Jouzel, D. Raynaud, N. I. Barkov, J.-M. Barnola, I. Basile, M. Bender, J. Chappellaz, M. Davis, G. Delaygue, M. Delmotte, V. M. Kotlyakov, M. Legrand, V. Y. Lipenkov, C. Lorius, L. Pepin, C. Ritz, E. Saltzman and M. Stievenard. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature, 399:429–436, 1999. doi:10.1038/20859 S. Soubeyrand, C. E. Morris and E. K. Bigg. Analysis of fragmented time directionality in time series to elucidate feedbacks in climate data. Environ. Modell. Softw. 61:78–86, 2014. doi:10.1016/j.envsoft.2014.07.003 Article in Journal/Newspaper Antarc* Antarctica Greenland Greenland ice core Greenland Ice core Project ice core North Greenland North Greenland Ice Core Project Australian Mathematical Society (AustMS): E-Journals Greenland Itise ENVELOPE(-50.517,-50.517,63.183,63.183) Lawrance ENVELOPE(-164.000,-164.000,-78.500,-78.500) Lorius ENVELOPE(162.350,162.350,-72.467,-72.467) Metcalfe ENVELOPE(-66.942,-66.942,-67.976,-67.976) Rojas ENVELOPE(-63.950,-63.950,-64.817,-64.817) Vostok Station ENVELOPE(106.837,106.837,-78.464,-78.464) ANZIAM Journal 57 66 |