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Transformation cost spectrum for irregularly sampled time series

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Abstract

Irregularly sampled time series analysis is a common problem in various disciplines. Since conventional methods are not directly applicable to irregularly sampled time series, a common interpolation approach is used; however, this causes data distortion and consequently biases further analyses. We propose a method that yields a regularly sampled time series spectrum of costs with minimum information loss. Each time series in this spectrum is a stationary series and acts as a difference filter. The transformation costs approach derives the differences between consecutive and arbitrarily sized segments. After obtaining regular sampling, recurrence plot analysis is performed to distinguish regime transitions. The approach is applied to a prototypical model to validate its performance and to different palaeoclimate proxy data sets located around Africa to identify critical climate transition periods during the last 5 million years and their characteristic properties.

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Data Availability

This manuscript has associated data in a data repository. [Authors’ comment:TACTS code library for the analysis can be accessed via https://doi.org/10.5281/zenodo.6038896. The proxies are published/available data sets. Requests for the TACTS of proxies can be sent to celik.ozdes@khas.edu.tr.]

References

  1. O. Anderson, RAIRO-Oper. Res. 11, 3 (1977)

    Article  Google Scholar 

  2. J. Friedman, T. Hastie, R. Tibshirani et al., The Elements of Statistical Learning, Springer Series in Statistics, vol. 1 (Springer, New York, 2001)

    MATH  Google Scholar 

  3. V.N. Livina, T.M. Lenton, Geophys. Res. Lett. 34, L03712 (2007)

    Article  ADS  Google Scholar 

  4. L.L. Trulla, A. Giuliani, J.P. Zbilut, C.L. Webber Jr., Phys. Lett. A 223, 255 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  5. M. Small, Complex networks from time series: capturing dynamics. In: 2013 IEEE International Symposium on Circuits and Systems (ISCAS) (IEEE, 2013), pp. 2509–2512

  6. N. Marwan, J.F. Donges, R.V. Donner, D. Eroglu, Quatern. Sci. Rev. 274, 107245 (2021)

    Article  Google Scholar 

  7. D. Eroglu, N. Marwan, S. Prasad, J. Kurths, Nonlinear Process. Geophys. 21, 1085 (2014)

    Article  ADS  Google Scholar 

  8. K. Rehfeld, N. Marwan, S.F.M. Breitenbach, J. Kurths, Clim. Dyn. 41, 3 (2013)

    Article  Google Scholar 

  9. D. Eroglu, F.H. McRobie, I. Ozken, T. Stemler, K.H. Wyrwoll, S.F. Breitenbach, N. Marwan, J. Kurths, Nat. Commun. 7, 1 (2016)

    Google Scholar 

  10. K. Rehfeld, N. Marwan, J. Heitzig, J. Kurths, Nonlinear Process. Geophys. 18, 389 (2011)

    Article  ADS  Google Scholar 

  11. K. Rehfeld, J. Kurths, Clim. Past 10, 107 (2014)

    Article  Google Scholar 

  12. I. Ozken, D. Eroglu, T. Stemler, N. Marwan, G.B. Bagci, J. Kurths, Phys. Rev. E 91, 062911 (2015)

    Article  ADS  Google Scholar 

  13. I. Ozken, D. Eroglu, S.F.M. Breitenbach, N. Marwan, L. Tan, U. Tirnakli, J. Kurths, Phys. Rev. E 98, 052215 (2018)

    Article  ADS  Google Scholar 

  14. N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438, 237 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  15. J.D. Victor, K.P. Purpura, Netw. Comput. Neural Syst. 8, 127 (1997)

    Article  Google Scholar 

  16. S. Suzuki, Y. Hirata, K. Aihara, Int. J. Bifurc. Chaos 20, 3699 (2010)

    Article  Google Scholar 

  17. T. Braun, C.N. Fernandez, D. Eroglu, A. Hartland, S.F. Breitenbach, N. Marwan, arXiv:2112.04843 (arXiv preprint) (2021)

  18. M. Priestley, J. Time Ser. Anal. 17, 85 (1996)

    Article  MathSciNet  Google Scholar 

  19. H. Kantz, Phys. Lett. A 185, 77 (1994)

    Article  ADS  Google Scholar 

  20. S.M. Pincus, Proc. Natl. Acad. Sci. 88, 2297 (1991)

    Article  ADS  Google Scholar 

  21. L. Lacasa, B. Luque, F. Ballesteros, J. Luque, J.C. Nuno, Proc. Natl. Acad. Sci. 105, 4972 (2008)

    Article  ADS  Google Scholar 

  22. J.P. Eckmann, S. Oliffson Kamphorst, D. Ruelle, Europhys. Lett. 4, 973 (1987)

    Article  ADS  Google Scholar 

  23. Y. Hirata, K. Aihara, Phys. Rev. E 81, 016203 (2010)

    Article  ADS  Google Scholar 

  24. D. Eroglu, T.K.D. Peron, N. Marwan, F.A. Rodrigues, L.D.F. Costa, M. Sebek, I.Z. Kiss, J. Kurths, Phys. Rev. E 90, 042919 (2014)

    Article  ADS  Google Scholar 

  25. Y. Hirata, K. Aihara, Phys. A 391, 760 (2012)

    Article  Google Scholar 

  26. G. Zimatore, L. Falcioni, M.C. Gallotta, V. Bonavolontà, M. Campanella, M. De Spirito, L. Guidetti, C. Baldari, PLoS One 16, e0249504 (2021)

    Article  Google Scholar 

  27. J. Wu, X. Zhou, Y. Peng, X. Zhao, Phys. A 585, 126439 (2022)

  28. S. Proksch, M. Reeves, M. Spivey, R. Balasubramaniam, Sci. Rep. 12, 1 (2022)

    Article  Google Scholar 

  29. G. Baranowski-Pinto, V. Profeta, M. Newson, H. Whitehouse, D. Xygalatas, Sci. Rep. 12, 1 (2022)

  30. H. Poincaré, Acta Math. 13, 1 (1890)

    Google Scholar 

  31. P.M. Addo, M. Billio, D. Guegan, N. Am. J. Econ. Financ. 26, 416 (2013)

    Article  Google Scholar 

  32. N. Marwan, D. Eroglu, I. Ozken, T. Stemler, K.H. Wyrwoll, J. Kurths, in Advances in Nonlinear Geosciences. ed. by A.A. Tsonis (Springer, Cham, 2018), pp. 357–368. (ISBN 978-3-319-58895-7)

  33. P.B. Demenocal, Science 270, 53 (1995)

    Article  ADS  Google Scholar 

  34. M.H. Trauth, J.C. Larrasoana, M. Mudelsee, Quatern. Sci. Rev. 28, 399 (2009)

    Article  ADS  Google Scholar 

  35. A.C. Ravelo, D.H. Andreasen, M. Lyle, A.O. Lyle, M.W. Wara, Nature 429, 263 (2004)

    Article  ADS  Google Scholar 

  36. R. Tiedemann, M. Sarnthein, N.J. Shackleton, Paleoceanography 9, 619 (1994)

    Article  ADS  Google Scholar 

  37. L.E. Lisiecki, M.E. Raymo, Paleoceanography 20, 20 (2005)

    Google Scholar 

  38. N. Shackleton, M. Hall, D. Pate, 15. Pliocene stable isotope stratigraphy of Site 846. In: Proceedings of Ocean Drill. Program Sci. Results (1995), Vol. 138, pp. 337–355

  39. P.U. Clark, D. Archer, D. Pollard, J.D. Blum, J.A. Rial, V. Brovkin, A.C. Mix, N.G. Pisias, M. Roy, Quatern. Sci. Rev. 25, 3150 (2006)

  40. T.D. Herbert, L.C. Peterson, K.T. Lawrence, Z. Liu, Science 328, 1530 (2010)

    Article  ADS  Google Scholar 

  41. L.J. Lourens, A. Antonarakou, F. Hilgen, A. Van Hoof, C. Vergnaud-Grazzini, W. Zachariasse, Paleoceanography 11, 391 (1996)

    Article  ADS  Google Scholar 

  42. J. Larrasoaña, A. Roberts, E. Rohling, M. Winklhofer, R. Wehausen, Clim. Dyn. 21, 689 (2003)

    Article  Google Scholar 

  43. B.D. Peter, Earth Planet. Sci. Lett. 220, 3 (2004)

  44. N. Marwan, S. Schinkel, J. Kurths, Europhys. Lett. 101, 20007 (2013)

    Article  ADS  Google Scholar 

  45. N.H. Packard, J.P. Crutchfield, J.D. Farmer, R.S. Shaw, Phys. Rev. Lett. 45, 712 (1980)

    Article  ADS  Google Scholar 

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Acknowledgements

We thank Norbert Marwan and Sebastian F. M. Breitenbach for enlightening discussions. Financial support from TUBITAK is acknowledged (Grant No. 118C236). D.E. was supported by the BAGEP Award of the Science Academy.

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Authors and Affiliations

  1. Faculty of Engineering and Natural Sciences, Kadir Has University, 34083, Istanbul, Turkey

    Celik Ozdes & Deniz Eroglu

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  1. Celik Ozdes
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  2. Deniz Eroglu
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Correspondence to Celik Ozdes.

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Ozdes, C., Eroglu, D. Transformation cost spectrum for irregularly sampled time series. Eur. Phys. J. Spec. Top. 232, 35–46 (2023). https://doi.org/10.1140/epjs/s11734-022-00512-x

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