Articles | Volume 21, issue 11
https://doi.org/10.5194/cp-21-1981-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/cp-21-1981-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Estimating breakpoints in the Cenozoic Era: an econometric approach
Mikkel Bennedsen
Department of Economics and Business Economics, Aarhus University, Aarhus, Denmark
Aarhus Center for Econometrics, Aarhus University, Aarhus, Denmark
Center for Research in Energy: Economics and Markets (CoRE), Aarhus University, Aarhus, Denmark
Eric Hillebrand
Department of Economics and Business Economics, Aarhus University, Aarhus, Denmark
Center for Research in Energy: Economics and Markets (CoRE), Aarhus University, Aarhus, Denmark
Siem Jan Koopman
Department of Econometrics and Data Science, Vrije Universiteit Amsterdam, Amsterdam, the Netherlands
Tinbergen Institute, Amsterdam, the Netherlands
Department of Economics and Business Economics, Aarhus University, Aarhus, Denmark
Center for Research in Energy: Economics and Markets (CoRE), Aarhus University, Aarhus, Denmark
Rachel Lupien
Department of Geoscience, Aarhus University, Aarhus, Denmark
Cited articles
Andrews, D. W. K.: Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation, Econometrica, 59, 817–858, https://doi.org/10.2307/2938229, 1991. a
Andrews, D. W. K. and Monahan, J. C.: An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator, Econometrica, 60, 953–966, https://doi.org/10.2307/2951574, 1992. a
Bagniewski, W., Ghil, M., and Rousseau, D. D.: Automatic detection of abrupt transitions in paleoclimate records, Chaos, 31, 113129, https://doi.org/10.1063/5.0062543, 2021. a
Bai, J. and Perron, P.: Multiple Structural Change Models: A Simulation Analysis, 212–238, Cambridge University Press, https://doi.org/10.1017/CBO9781139164863.010, 2006. a
Barker, S., Lisiecki, L. E., Knorr, G., Nuber, S., and Tzedakis, P. C.: Distinct roles for precession, obliquity, and eccentricity in Pleistocene 100-kyr glacial cycles, Science, 387, eadp3491, https://doi.org/10.1126/science.adp3491, 2025. a
Bennedsen, M., Hillebrand, E., Koopman, S. J., and Larsen, K. B.: Continuous-time state-space methods for delta-O-18 and delta-C-13, arXiv [preprint], https://doi.org/10.48550/arXiv.2404.05401, 2024. a
Berends, C. J., Köhler, P., Lourens, L. J., and van de Wal, R. S. W.: On the Cause of the Mid-Pleistocene Transition, Reviews of Geophysics, 59, https://doi.org/10.1029/2020RG000727, 2021. a
Boettner, C., Klinghammer, G., Boers, N., Westerhold, T., and Marwan, N.: Early-warning signals for Cenozoic climate transitions, Quaternary Science Reviews, 270, 107177, https://doi.org/10.1016/j.quascirev.2021.107177, 2021. a
Bohaty, S. M. and Zachos, J. C.: Significant Southern Ocean warming event in the late middle Eocene, Geology, 31, 1017–1020, https://doi.org/10.1130/G19800.1, 2003. a
Burke, K. D., Williams, J. W., Chandler, M. A., Haywood, A. M., Lunt, D. J., and Otto-Bliesner, B. L.: Pliocene and Eocene provide best analogs for near-future climates, P. Natl. Acad. Sci. USA, 115, 13288–13293, https://doi.org/10.1073/pnas.1809600115, 2018. a
Caballero, R. and Huber, M.: State-dependent climate sensitivity in past warm climates and its implications for future climate projections, P. Natl. Acad. Sci. USA, 110, 14162–14167, https://doi.org/10.1073/pnas.1303365110, 2013. a
Clark, P. U., Archer, D., Pollard, D., Blum, J. D., Rial, J. A., Brovkin, V., Mix, A. C., Pisias, N. G., and Roy, M.: The middle Pleistocene transition: characteristics, mechanisms, and implications for long-term changes in atmospheric pCO2, Quat. Sci. Rev., 25, 3150–3184, https://doi.org/10.1016/j.quascirev.2006.07.008, 2006. a
Coxall, H. K., Wilson, P. A., Pälike, H., Lear, C. H., and Backman, J.: Rapid stepwise onset of Antarctic glaciation and deeper calcite compensation in the Pacific Ocean, Nature, 433, 53–57, https://doi.org/10.1038/nature03135, 2005. a
Crowley, T. J. and Hyde, W. T.: Transient nature of late Pleistocene climate variability, Nature, 456, 226–230, https://doi.org/10.1038/nature07365, 2008. a
Dansgaard, W., Johnsen, S., Clausen, H., Dahl-Jensen, D., Gundestrup, N., Hammer, C., Hvidberg, C., Steffensen, J., Sveinbjörnsdottir, A., Jouzel, J., and GC, B.: Evidence of general instability of past climate from a 250-kyr ice-core record, Nature, 364, 218–220, https://doi.org/10.1038/364218a0, 1993. a
Davidson, J., Stephenson, D., and Turasie, A.: Time series modeling of paleoclimate data, Environmetrics, 27, https://doi.org/10.1002/env.2373, 2015. a
Dickey, D. and Fuller, W.: Distribution of the Estimators for Autoregressive Time Series With a Unit Root, Journal of the American Statistical Association, 74, https://doi.org/10.2307/2286348, 1979. a
Elderfield, H., Ferretti, P., Greaves, M., Crowhurst, S., McCave, I. N., Hodell, D., and Piotrowski, A. M.: Evolution of ocean temperature and ice volume through the mid-Pleistocene climate transition, Science, 337, 704–709, https://doi.org/10.1126/science.1221294, 2012. a
Epstein, S., Buchsbaum, R., Lowenstam, H., and Urey, H. C.: Carbonate-Water Isotopic Temperature Scale, GSA Bulletin, 62, 417–426, https://doi.org/10.1130/0016-7606(1951)62[417:CITS]2.0.CO;2, 1951. a
Fischer, M. L., Munz, P. M., Asrat, A., Foerster, V., Kaboth-Bahr, S., Marwan, N., Schaebitz, F., Schwanghart, W., and Trauth, M. H.: Spatio-temporal variations of climate along possible African–Arabian routes of H. sapiens expansion, Quaternary Science Advances, 14, 100174, https://doi.org/10.1016/j.qsa.2024.100174, 2024. a
Fleitmann, D., Burns, S. J., Mudelsee, M., Neff, U., Kramers, J., Mangini, A., and Matter, A.: Holocene Forcing of the Indian Monsoon Recorded in a Stalagmite from Southern Oman, Science, 300, 1737–1739, https://doi.org/10.1126/science.1083130, 2003. a
Flower, B. P. and Kennett, J. P.: The middle Miocene climatic transition: East Antarctic ice sheet development, deep ocean circulation and global carbon cycling, Palaeogeography, Palaeoclimatology, Palaeoecology, 108, 537–555, https://doi.org/10.1016/0031-0182(94)90251-8, 1994. a, b
Franke, J. G. and Donner, R. V.: Correlating paleoclimate time series: Sources of uncertainty and potential pitfalls, Quaternary Science Reviews, 212, 69–79, https://doi.org/10.1016/j.quascirev.2019.03.017, 2019. a
Garcia, R. and Perron, P.: An Analysis of the Real Interest Rate under Regime Shifts, Rev. Econ. Stat., 78, 111–125, https://doi.org/10.2307/2109851, 1996. a
Goswami, B., Boers, N., Rheinwalt, A., Marwan, N., Heitzig, J., Breitenbach, S., and Kurths, J.: Abrupt transitions in time series with uncertainties, Nature Communications, 9, https://doi.org/10.1038/s41467-017-02456-6, 2018. a, b
Hansen, J., Sato, M., Russell, G., and Kharecha, P.: Climate Sensitivity, Sea Level and Atmospheric Carbon Dioxide, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371, https://doi.org/10.1098/rsta.2012.0294, 2013. a
Harper, D. T., Hönisch, B., Bowen, G. J., Zeebe, R. E., Haynes, L. L., Penman, D. E., and Zachos, J. C.: Long- and short-term coupling of sea surface temperature and atmospheric CO2 during the late Paleocene and early Eocene, P. Natl. Acad. Sci. USA, 121, e2318779121, https://doi.org/10.1073/pnas.2318779121, 2024. a
Henehan, M. J., Edgar, K. M., Foster, G. L., Penman, D. E., Hull, P. M., Greenop, R., Anagnostou, E., and Pearson, P. N.: Revisiting the Middle Eocene Climatic Optimum “Carbon Cycle Conundrum” With New Estimates of Atmospheric pCO2 From Boron Isotopes, Paleoceanography and Paleoclimatology, 35, e2019PA003713, https://doi.org/10.1029/2019PA003713, 2020. a, b
Hönisch, B., Royer, D. L., Breecker, D. O., et al.: Toward a Cenozoic history of atmospheric CO2, Science, 382, eadi5177, https://doi.org/10.1126/science.adi5177, 2023. a, b
James, A., Emile-Geay, J., Malik, N., and Khider, D.: Detecting Paleoclimate Transitions With Laplacian Eigenmaps of Recurrence Matrices (LERM), Paleoceanography and Paleoclimatology, 39, e2023PA004700, https://doi.org/10.1029/2023PA004700, 2024. a
Kejriwal, M., Perron, P., and Zhou, J.: Wald tests for detecting multiple structural changes in persistence, Econometric Theory, 29, 289–323, https://doi.org/10.1017/S0266466612000357, 2013. a
Keyes, N. D. B., Giorgini, L. T., and Wettlaufer, J. S.: Stochastic paleoclimatology: Modeling the EPICA ice core climate records, Chaos, 33, 093132, https://doi.org/10.1063/5.0128814, 2023. a
Killick, R., Fearnhead, P., and Eckley, I. A.: Optimal Detection of Changepoints With a Linear Computational Cost, Journal of the American Statistical Association, 107, 1590–1598, https://doi.org/10.1080/01621459.2012.737745, 2012. a
Kunz, T., Dolman, A. M., and Laepple, T.: A spectral approach to estimating the timescale-dependent uncertainty of paleoclimate records – Part 1: Theoretical concept, Clim. Past, 16, 1469–1492, https://doi.org/10.5194/cp-16-1469-2020, 2020. a
Kurozumi, E. and Tuvaandorj, P.: Model selection criteria in multivariate models with multiple structural changes, Journal of Econometrics, 164, 218–238, https://doi.org/10.1016/j.jeconom.2011.04.003, 2011. a
Laskar, J., Robutel, P., Joutel, F., Gastineau, M., Correia, A. C. M., and Levrard, B.: A long-term numerical solution for the insolation quantities of the Earth, Astronomy & Astrophysics, 428, 261–285, https://doi.org/10.1051/0004-6361:20041335, 2004. a
Liang, J., Wang, Y., Zhang, S., Huang, C., Xu, E., and Zhang, Z.: Astronomical Forcing of late oligocene to early Miocene Paleoclimate: A case study from the Northern South China Sea, Palaeogeography, Palaeoclimatology, Palaeoecology, 673, 113007, https://doi.org/10.1016/j.palaeo.2025.113007, 2025. a
Lisiecki, L. E. and Raymo, M. E.: A Pliocene-Pleistocene stack of 57 globally distributed benthic δ18O records, Paleoceanography, 20, PA1003, https://doi.org/10.1029/2004PA001071, 2005. a, b, c
Liu, J., Wu, S., and Zidek, J. V.: On Segmented Multivariate Regressions, Statistica Sinica, 7, 497–525, 1997. a
Livina, V. N., Kwasniok, F., and Lenton, T. M.: Potential analysis reveals changing number of climate states during the last 60 kyr, Clim. Past, 6, 77–82, https://doi.org/10.5194/cp-6-77-2010, 2010. a, b
Lund, R. and Shi, X.: Changepoint Methods in Climatology, CHANCE, 36, 4–8, https://doi.org/10.1080/09332480.2023.2203643, 2023. a
Marwan, N.: Challenges and perspectives in recurrence analyses of event time series, Frontiers in Applied Mathematics and Statistics, 9, https://doi.org/10.3389/fams.2023.1129105, 2023. a
Marwan, N., Carmen Romano, M., Thiel, M., and Kurths, J.: Recurrence plots for the analysis of complex systems, Physics Reports, 438, 237–329, https://doi.org/10.1016/j.physrep.2006.11.001, 2007. a
Marwan, N., Donges, J. F., Donner, R. V., and Eroglu, D.: Nonlinear time series analysis of palaeoclimate proxy records, Quaternary Science Reviews, 274, 107245, https://doi.org/10.1016/j.quascirev.2021.107245, 2021. a, b, c
McClymont, E. L., Ho, S. L., Ford, H. L., Bailey, I., Berke, M. A., Bolton, C. T., De Schepper, S., Grant, G. R., Groeneveld, J., Inglis, G. N., Karas, C., Patterson, M. O., Swann, G. E. A., Thirumalai, K., White, S. M., Alonso-Garcia, M., Anand, P., Hoogakker, B. A. A., Littler, K., Petrick, B. F., Risebrobakken, B., Abell, J. T., Crocker, A. J., de Graaf, F., Feakins, S. J., Hargreaves, J. C., Jones, C. L., Markowska, M., Ratnayake, A. S., Stepanek, C., and Tangunan, D.: Climate Evolution Through the Onset and Intensification of Northern Hemisphere Glaciation, Reviews of Geophysics, 61, e2022RG000793, https://doi.org/10.1029/2022RG000793, 2023. a
McInerney, F. A. and Wing, S. L.: The Paleocene-Eocene Thermal Maximum: A Perturbation of Carbon Cycle, Climate, and Biosphere with Implications for the Future, Annual Review of Earth and Planetary Sciences, 39, 489–516, https://doi.org/10.1146/annurev-earth-040610-133431, 2011. a
Miller, K. G., Browning, J. V., Schmelz, W. J., Kopp, R. E., Mountain, G. S., and Wright, J. D.: Cenozoic sea-level and cryospheric evolution from deep-sea geochemical and continental margin records, Science Advances, 6, eaaz1346, https://doi.org/10.1126/sciadv.aaz1346, 2020. a, b
Mudelsee, M.: Ramp function regression: a tool for quantifying climate transitions, Computers & Geosciences, 26, 293–307, https://doi.org/10.1016/S0098-3004(99)00141-7, 2000. a
Mudelsee, M.: Climate Time Series Analysis: Classical Statistical and Bootstrap Methods, vol. 51 of Atmospheric and Oceanographic Sciences Library, Springer, Cham, Heidelberg, New York, Dordrecht, London, 2nd edn., ISBN 978-3-319-04449-1, https://doi.org/10.1007/978-3-319-04450-7, 2014. a
Mudelsee, M. and Raymo, M. E.: Slow dynamics of the Northern Hemisphere Glaciation, Paleoceanography, 20, PA4022, https://doi.org/10.1029/2005PA001153, 2005. a
Mudelsee, M., Bickert, T., Lear, C. H., and Lohmann, G.: Cenozoic climate changes: A review based on time series analysis of marine benthic δ18O records, Reviews of Geophysics, 52, 333–374, https://doi.org/10.1002/2013RG000440, 2014. a, b, c, d
Nguyen, L., Yamamoto, Y., and Perron, P.: mbreaks: Estimation and Inference for Structural Breaks in Linear Regression Models, r package version 1.0.0, Econometrica, 66, 47–78, https://doi.org/10.2307/2998540, 2023. a, b, c, d
Oerlemans, J.: Correcting the Cenozoic δ18O deep-sea temperature record for Antarctic ice volume, Palaeogeography, Palaeoclimatology, Palaeoecology, 208, 195–205, https://doi.org/10.1016/j.palaeo.2004.03.004, 2004. a
Pisias, N. G. and Moore, T. C.: The Evolution of the Pleistocene Climate: A Time Series Approach, Earth and Planetary Science Letters, 52, 450–458, https://doi.org/10.1016/0012-821X(81)90197-7, 1981. a
Polissar, P. J., Rose, C., Uno, K. T., Phelps, S. R., and deMenocal, P.: Synchronous rise of African C4 ecosystems 10 million years ago in the absence of aridification, Nature Geoscience, 12, 657–660, https://doi.org/10.1038/s41561-019-0399-2, 2019. a, b
Reeves, J., Chen, J., Wang, X. L., Lund, R., and Lu, Q.: A Review and Comparison of Changepoint Detection Techniques for Climate Data, Journal of Applied Meteorology and Climatology, 46, 900–915, https://doi.org/10.1175/JAM2493.1, 2007. a
Rousseau, D.-D., Bagniewski, W., and Lucarini, V.: A Punctuated Equilibrium Analysis of the Climate Evolution of Cenozoic Exhibits a Hierarchy of Abrupt Transitions, Scientific Reports, 13, 11290, https://doi.org/10.1038/s41598-023-38454-6, 2023. a, b, c
Ruggieri, E.: A Bayesian approach to detecting change points in climatic records, International Journal of Climatology, 33, 520–528, https://doi.org/10.1002/joc.3447, 2013. a
Schütz, N. and Holschneider, M.: Detection of trend changes in time series using Bayesian inference, Physical Review E, 83, 041131, https://doi.org/10.1103/PhysRevE.84.021120, 2011. a
Shackleton, N.: Oxygen Isotope Analyses and Pleistocene Temperatures Re-assessed, Nature, 215, 15–17, https://doi.org/10.1038/215015a0, 1967. a
Spray, J. F., Bohaty, S. M., Davies, A., Bailey, I., Romans, B. W., Cooper, M. J., Milton, J. A., and Wilson, P. A.: North Atlantic Evidence for a Unipolar Icehouse Climate State at the Eocene-Oligocene Transition, Paleoceanography and Paleoclimatology, 34, 1124–1138, https://doi.org/10.1029/2019PA003563, 2019. a
Steffen, W., Rockström, J., Richardson, K., Lenton, T., Folke, C., Liverman, D., Summerhayes, C., Barnosky, A., Cornell, S., Crucifix, M., Donges, J., Fetzer, I., Lade, S., Scheffer, M., and Schellnhuber, H.: Trajectories of the Earth System in the Anthropocene, P. Natl. Acad. Sci. USA, 115, 201810141, https://doi.org/10.1073/pnas.1810141115, 2018. a
Strömberg, C. A. E.: Evolution of Grasses and Grassland Ecosystems, Annual Review of Earth and Planetary Sciences, 39, 517–544, https://doi.org/10.1146/annurev-earth-040809-152402, 2011. a
Telford, R., Heegaard, E., and Birks, H.: All age–depth models are wrong: but how badly?, Quaternary Science Reviews, 23, 1–5, https://doi.org/10.1016/j.quascirev.2003.11.003, 2004. a
Tierney, J. E., Poulsen, C. J., Montañez, I. P., Bhattacharya, T., Feng, R., Ford, H. L., Hönisch, B., Inglis, G. N., Petersen, S. V., Sagoo, N., Tabor, C. R., Thirumalai, K., Zhu, J., Burls, N. J., Foster, G. L., Goddéris, Y., Huber, B. T., Ivany, L. C., Turner, S. K., Lunt, D. J., McElwain, J. C., Mills, B. J. W., Otto-Bliesner, B. L., Ridgwell, A., and Zhang, Y. G.: Past climates inform our future, Science, 370, eaay3701, https://doi.org/10.1126/science.aay3701, 2020. a
Trauth, M. H.: MATLAB® Recipes for Earth Sciences, Springer Textbooks in Earth Sciences, Geography and Environment, Springer, access provided by Vrije Universiteit Amsterdam, https://doi.org/10.1007/978-3-031-57949-3, 2025. a, b
Trauth, M. H., Asrat, A., Berner, N., Bibie, F., Foerster, V., Grove, M., Kaboth-Bahr, S., Maslin, M. A., Mudelsee, M., and Schäbitz, F.: Northern Hemisphere Glaciation, African climate and human evolution, Quaternary Science Reviews, 268, 107095, https://doi.org/10.1016/j.quascirev.2021.107095, 2021. a
Trauth, M. H., Asrat, A., Fischer, M. L., Hopcroft, P. O., Foerster, V., Kaboth-Bahr, S., Kindermann, K., Lamb, H. F., Marwan, N., Maslin, M. A., Schaebitz, F., and Valdes, P. J.: Early warning signals of the termination of the African Humid Period(s), Nature Communications, 15, 3697, https://doi.org/10.1038/s41467-024-47921-1, 2024. a
Waelbroeck, C., Labeyrie, L., Michel, E., Duplessy, J. C., McManus, J. F., Lambeck, K., Balbon, E., and Labracherie, M.: Sea-level and deep water temperature changes derived from benthic foraminifera isotopic records, Quaternary Science Reviews, 21, 295–305, https://doi.org/10.1016/S0277-3791(01)00101-9, 2002. a
Westerhold, T., Röhl, U., Donner, B., and Zachos, J. C.: Global Extent of Early Eocene Hyperthermal Events: A New Pacific Benthic Foraminiferal Isotope Record From Shatsky Rise (ODP Site 1209), Paleoceanography and Paleoclimatology, 33, 626–642, https://doi.org/10.1029/2017PA003306, 2018. a
Westerhold, T., Marwan, N., Drury, A. J., Liebrand, D., Agnini, C., Anagnostou, E., Barnet, J. S. K., Bohaty, S. M., Vleeschouwer, D. D., Florindo, F., Frederichs, T., Hodell, D. A., Holbourn, A. E., Kroon, D., Lauretano, V., Littler, K., Lourens, L. J., Lyle, M., Pälike, H., Röhl, U., Tian, J., Wilkens, R. H., Wilson, P. A., and Zachos, J. C.: An astronomically dated record of Earth's climate and its predictability over the last 66 million years, Science, 369, 1383–1387, https://doi.org/10.1126/science.aba6853, 2020. a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, aa, ab, ac, ad, ae, af, ag, ah, ai, aj, ak, al, am, an, ao, ap, aq, ar, as, at, au, av, aw, ax
Yao, Y.-C.: Estimating the number of change-points via Schwarz' criterion, Statistics & Probability Letters, 6, 181–189, https://doi.org/10.1016/0167-7152(88)90118-6, 1988. a
Zachos, J., MO, P., Sloan, L., Thomas, E., and Billups, K.: Trends, Rhythms, and Aberrations in Global Climate 65 Ma to Present, Science (New York, N.Y.), 292, 686–93, https://doi.org/10.1126/science.1059412, 2001. a, b, c
Zachos, J. C., Dickens, G. R., and Zeebe, R. E.: An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics, Nature, 451, 279–283, https://doi.org/10.1038/nature06588, 2008. a
Short summary
This study presents a statistical approach for identifying transitions between climate states in the Cenozoic Era using a 67.1 million-year proxy record. Our results support transitions previously identified in the literature and provide statistical justification for additional ones. The approach enables construction of confidence intervals, offering measures of uncertainty. This adds to our understanding of the Cenozoic climate and provides a tool for analyzing other paleoclimate records.
This study presents a statistical approach for identifying transitions between climate states in...