Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using chatterjee’s correlation coefficient

This study revisits the cross-correlation between cosmic ray intensity (CRI) and solar activity (SA) by comparing traditional Pearson correlation with Chatterjee’s correlation coefficient. Traditional analyses using Pearson correlation are useful for identifying linear relationships and time lags. H...

Full description

Autores:: Sierra Porta, David

Tipo de recurso:

Fecha de publicación:: 2024

Institución:: Universidad Tecnológica de Bolívar

Repositorio:: Repositorio Institucional UTB

Idioma:: eng

id	UTB2_1525706ac1bdc618c0833b1937b643b8
oai_identifier_str	oai:repositorio.utb.edu.co:20.500.12585/12757
network_acronym_str	UTB2
network_name_str	Repositorio Institucional UTB
repository_id_str
dc.title.es_CO.fl_str_mv	Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using chatterjee’s correlation coefficient
title	Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using chatterjee’s correlation coefficient
spellingShingle	Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using chatterjee’s correlation coefficient Cosmic Rays Solar Activity Cross-Correlation Chatterjee’s correlation Pearson correlation Space Weather LEMB
title_short	Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using chatterjee’s correlation coefficient
title_full	Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using chatterjee’s correlation coefficient
title_fullStr	Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using chatterjee’s correlation coefficient
title_full_unstemmed	Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using chatterjee’s correlation coefficient
title_sort	Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using chatterjee’s correlation coefficient
dc.creator.fl_str_mv	Sierra Porta, David
dc.contributor.author.none.fl_str_mv	Sierra Porta, David
dc.subject.keywords.es_CO.fl_str_mv	Cosmic Rays Solar Activity Cross-Correlation Chatterjee’s correlation Pearson correlation Space Weather
topic	Cosmic Rays Solar Activity Cross-Correlation Chatterjee’s correlation Pearson correlation Space Weather LEMB
dc.subject.armarc.none.fl_str_mv	LEMB
description	This study revisits the cross-correlation between cosmic ray intensity (CRI) and solar activity (SA) by comparing traditional Pearson correlation with Chatterjee’s correlation coefficient. Traditional analyses using Pearson correlation are useful for identifying linear relationships and time lags. However, they may not fully capture more complex interactions in the data. Chatterjee’s correlation coefficient, while sensitive to different types of relationships, including nonlinear ones, provides a complementary perspective on the temporal relationships between CRI and SA. This approach broadens our understanding of potential dependencies, offering additional insights that may not be captured through Pearson correlation alone. The findings reveal that Chatterjee’s correlation complements Pearson’s insights by providing an alternative view of the relationship between cosmic ray intensity (CRI) and solar activity (SA). The results show that Chatterjee’s correlation coefficients are, on average, approximately 45-50% smaller than Pearson’s, which could reflect different sensitivities to the underlying data structure rather than solely indicating a nonlinear component. Additionally, the time lags identified using Chatterjee’s correlation are generally shorter and more consistent across different solar cycles compared to those obtained with Pearson’s correlation, suggesting that CCC may capture temporal patterns in a distinct manner. Further analysis using Dynamic Time Warping (DTW) and Mean Absolute Percentage Error (MAPE) metrics demonstrated that, in more than half of the scenarios considered, alignment based on Chatterjee’s time lags resulted in lower errors and better alignment of the series compared to Pearson’s lags. This indicates that Chatterjee’s method is particularly effective for capturing the immediate and nuanced responses of CRI to SA changes, especially in recent solar cycles. This comprehensive approach provides broader insights into the dynamic interactions between cosmic ray intensity (CRI) and solar activity (SA), highlighting the importance of considering multiple correlation measures, including both linear and nonlinear approaches, in space weather research. The results suggest that Chatterjee’s correlation offers a complementary perspective on these interactions, providing additional details about how SA influences CRI over time, which may not be fully captured by Pearson’s correlation alone.
publishDate	2024
dc.date.accessioned.none.fl_str_mv	2024-10-31T21:21:48Z
dc.date.available.none.fl_str_mv	2024-10-31T21:21:48Z
dc.date.issued.none.fl_str_mv	2024
dc.date.submitted.none.fl_str_mv	2024-10-31
dc.type.coarversion.fl_str_mv	http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.driver.es_CO.fl_str_mv	info:eu-repo/semantics/article
dc.type.hasversion.es_CO.fl_str_mv	info:eu-repo/semantics/draft
dc.type.spa.es_CO.fl_str_mv	http://purl.org/coar/resource_type/c_2df8fbb1
status_str	draft
dc.identifier.citation.es_CO.fl_str_mv	Revised Cross-Correlation and Time-Lag between Cosmic Ray Intensity and Solar Activity Using Chatterjee’s Correlation Coefficient. D. Sierra-Porta. Advances in Space Research (2024).
dc.identifier.uri.none.fl_str_mv	https://hdl.handle.net/20.500.12585/12757
dc.identifier.instname.es_CO.fl_str_mv	Universidad Tecnológica de Bolívar
dc.identifier.reponame.es_CO.fl_str_mv	Repositorio Universidad Tecnológica de Bolívar
identifier_str_mv	Revised Cross-Correlation and Time-Lag between Cosmic Ray Intensity and Solar Activity Using Chatterjee’s Correlation Coefficient. D. Sierra-Porta. Advances in Space Research (2024). Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar
url	https://hdl.handle.net/20.500.12585/12757
dc.language.iso.es_CO.fl_str_mv	eng
language	eng
dc.rights.coar.fl_str_mv	http://purl.org/coar/access_right/c_abf2
dc.rights.uri.*.fl_str_mv	http://creativecommons.org/publicdomain/zero/1.0/
dc.rights.accessrights.es_CO.fl_str_mv	info:eu-repo/semantics/openAccess
dc.rights.cc.*.fl_str_mv	CC0 1.0 Universal
rights_invalid_str_mv	http://creativecommons.org/publicdomain/zero/1.0/ CC0 1.0 Universal http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv	openAccess
dc.format.extent.none.fl_str_mv	11 pag.
dc.format.mimetype.es_CO.fl_str_mv	application/pdf
dc.publisher.place.es_CO.fl_str_mv	Cartagena de Indias
dc.publisher.faculty.es_CO.fl_str_mv	Ciencias Básicas
dc.source.es_CO.fl_str_mv	Sciencedirect
institution	Universidad Tecnológica de Bolívar
bitstream.url.fl_str_mv	https://repositorio.utb.edu.co/bitstream/20.500.12585/12757/1/Cross_Correlation_Revised_Elsevier.pdf https://repositorio.utb.edu.co/bitstream/20.500.12585/12757/2/license_rdf https://repositorio.utb.edu.co/bitstream/20.500.12585/12757/3/license.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/12757/4/Cross_Correlation_Revised_Elsevier.pdf.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/12757/5/Cross_Correlation_Revised_Elsevier.pdf.jpg
bitstream.checksum.fl_str_mv	d28852b3defabc39ff811940b6e29e39 42fd4ad1e89814f5e4a476b409eb708c e20ad307a1c5f3f25af9304a7a7c86b6 6e7d42be37d4177f9bbf332c2f9a43ab 72aa21c43dca5f8c0253e36d762143d3
bitstream.checksumAlgorithm.fl_str_mv	MD5 MD5 MD5 MD5 MD5
repository.name.fl_str_mv	Repositorio Institucional UTB
repository.mail.fl_str_mv	repositorioutb@utb.edu.co
_version_	1834107731305299968
spelling	Sierra Porta, David62fe46fe-2160-4eac-8b0c-89e7fd6ce2932024-10-31T21:21:48Z2024-10-31T21:21:48Z20242024-10-31Revised Cross-Correlation and Time-Lag between Cosmic Ray Intensity and Solar Activity Using Chatterjee’s Correlation Coefficient. D. Sierra-Porta. Advances in Space Research (2024).https://hdl.handle.net/20.500.12585/12757Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis study revisits the cross-correlation between cosmic ray intensity (CRI) and solar activity (SA) by comparing traditional Pearson correlation with Chatterjee’s correlation coefficient. Traditional analyses using Pearson correlation are useful for identifying linear relationships and time lags. However, they may not fully capture more complex interactions in the data. Chatterjee’s correlation coefficient, while sensitive to different types of relationships, including nonlinear ones, provides a complementary perspective on the temporal relationships between CRI and SA. This approach broadens our understanding of potential dependencies, offering additional insights that may not be captured through Pearson correlation alone. The findings reveal that Chatterjee’s correlation complements Pearson’s insights by providing an alternative view of the relationship between cosmic ray intensity (CRI) and solar activity (SA). The results show that Chatterjee’s correlation coefficients are, on average, approximately 45-50% smaller than Pearson’s, which could reflect different sensitivities to the underlying data structure rather than solely indicating a nonlinear component. Additionally, the time lags identified using Chatterjee’s correlation are generally shorter and more consistent across different solar cycles compared to those obtained with Pearson’s correlation, suggesting that CCC may capture temporal patterns in a distinct manner. Further analysis using Dynamic Time Warping (DTW) and Mean Absolute Percentage Error (MAPE) metrics demonstrated that, in more than half of the scenarios considered, alignment based on Chatterjee’s time lags resulted in lower errors and better alignment of the series compared to Pearson’s lags. This indicates that Chatterjee’s method is particularly effective for capturing the immediate and nuanced responses of CRI to SA changes, especially in recent solar cycles. This comprehensive approach provides broader insights into the dynamic interactions between cosmic ray intensity (CRI) and solar activity (SA), highlighting the importance of considering multiple correlation measures, including both linear and nonlinear approaches, in space weather research. The results suggest that Chatterjee’s correlation offers a complementary perspective on these interactions, providing additional details about how SA influences CRI over time, which may not be fully captured by Pearson’s correlation alone.11 pag.application/pdfenghttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccessCC0 1.0 Universalhttp://purl.org/coar/access_right/c_abf2SciencedirectRevised cross-correlation and time-lag between cosmic ray intensity and solar activity using chatterjee’s correlation coefficientinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/drafthttp://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_b1a7d7d4d402bcceCosmic RaysSolar ActivityCross-CorrelationChatterjee’s correlationPearson correlationSpace WeatherLEMBCartagena de IndiasCiencias BásicasPúblico generalBishara, A. J., & Hittner, J. B. (2012). Testing the significance of a correlation 743 with nonnormal data: comparison of pearson, spearman, transformation, and 744 resampling approaches. Psychological methods, 17(3), 399. doi:https: 745 //doi.org/10.1037/a0028087Binder, A. (1959). Considerations of the place of assumptions in correlational analysis. American Psychologist, 14(8), 504. doi:https://psycnet.apa.org/doi/10.1037/h0048094.Bland, J. M., & Altman, D. G. (1994). Correlation, regression, and repeated data. BMJ: British Medical Journal, 308(6933), 896.Boschini, M., Della Torre, S., Gervasi, M. et al. (2018). Propagation of cos- mic rays in heliosphere: The helmod model. Advances in Space Research, 62(10), 2859–2879. doi:https://doi.org/10.1016/j.asr.2017.04.017.Breiman, L. (2001). Random forests. Machine learning, 45, 5–32. doi: https://doi.org/10.1023/A:1010933404324.Chatterjee, S. (2021). A new coefficient of correlation. Journal of the American Statistical Association, 116(536), 2009–2022. doi:https://doi.org/10.1080/01621459.2020.1758115Dobynde, M., Harikumaran, J., Guo, J. et al. (2023). Cosmic radiation re-liability analysis for aircraft power electronics. IEEE Transactions on Transportation Electrification, 10(1), 344–352. doi:https://doi.org/ 76010.1109/TTE.2023.3278319.Dong, M., Wang, B., Wei, J. et al. (2023). Causal identification of single-cell experimental perturbation effects with cinema-ot. Nature Methods, 20(11), 1769–1779. doi:https://doi.org/10.1038/s41592-023-02040-5.Dorman, L. I. (2021). Space weather and cosmic ray effects. In Cli-mate change (pp. 711–768). Elsevier. doi:https://doi.org/10.1016/B978-0-12-821575-3.00033-5.Gervasi, M., Rancoita, P., Usoskin, I. et al. (1999). Monte-carlo approach to galactic cosmic ray propagation in the heliosphere. Nuclear Physics B-Proceedings Supplements, 78(1-3), 26–31. doi:https://doi.org/10.1016/S0920-5632(99)00518-6.Höeffgen, S. K., Metzger, S., & Steffens, M. (2020). Investigating the effects of cosmic rays on space electronics. Frontiers in Physics, 8, 318. doi:https: //doi.org/10.3389/fphy.2020.00318.Hunter, J. S. (1986). The exponentially weighted moving average. Journal of quality technology, 18(4), 203–210. doi:https://doi.org/10.1080/ 00224065.1986.11979014.Idosa, C., Giri, A., Adhikari, B. et al. (2023). Variations of cosmic ray intensity with the solar flare index, coronal index, and geomagnetic indices: Wavelet and cross correlation approaches. Physics of Plasmas, 30(8). doi:https://doi.org/10.1063/5.0157553.Iskra, K., Siluszyk, M., Alania, M. et al. (2019). Experimental investigation of the delay time in galactic cosmic ray flux in different epochs of solar magnetic cycles: 1959–2014. Solar Physics, 294(9), 115. doi:https://doi.org/10.1007/s11207-019-1509-4.Jokipii, J., & Levy, E. (1977). Effects of particle drifts on the solar modulation of galactic cosmic rays. Astrophysical Journal, Part 2-Letters to the Editor, vol. 213, Apr. 15, 1977, p. L85-L88., 213, L85–L88. doi:https://doi.org/10.1086/182415.Knief, U., & Forstmeier, W. (2021). Violating the normality assumption may be the lesser of two evils. Behavior Research Methods, 53(6), 2576–2590. doi:https://doi.org/10.3758/s13428-021-01587-5.Koldobskiy, S. A., Kähkönen, R., Hofer, B. et al. (2022). Time lag between cosmic-ray and solar variability: Sunspot numbers and open solar mag-netic flux. Solar Physics, 297(3), 38. doi:https://doi.org/10.1007/s11207-022-01970-1.Kowalski, C. J. (1972). On the effects of non-normality on the distribution of the sample product-moment correlation coefficient. Journal of the Royal Statistical Society: Series C (Applied Statistics), 21(1), 1–12. doi:https://doi.org/10.2307/2346598.Laken, B. A., & Calogovi ˇ c, J. (2013). Composite analysis with monte carlo methods: an example with cosmic rays and clouds. Journal of Space Weather and Space Climate, 3, A29. doi:https://doi.org/10.1051/swsc/2013051.Lin, Z., & Han, F. (2023). On boosting the power of chatterjee’s rank cor- relation. Biometrika, 110(2), 283–299. doi:https://doi.org/10.1093/ biomet/asac048.Lucas, J. M., & Saccucci, M. S. (1990). Exponentially weighted moving aver- age control schemes: properties and enhancements. Technometrics, 32(1), 1–12. doi:https://doi.org/10.1080/00401706.1990.10484583.Maghrabi, A., Aldosari, A., & Almutairi, M. (2021). Correlation analyses be- tween solar activity parameters and cosmic ray muons between 2002 and 2012 at high cutoff rigidity. Advances in Space Research, 68(7), 2941–2952. doi:https://doi.org/10.1016/j.asr.2021.05.016.Mishra, A., Gupta, M., & Mishra, V. (2006). Cosmic ray intensity variations in relation with solar flare index and sunspot numbers. Solar Physics, 239,475–491. doi:https://doi.org/10.1007/s11207-006-0138-x.Mishra, V., & Mishra, A. (2018). Long-term modulation of cosmic819 ray intensity and correlation analysis using solar and heliospheric pa820 rameters. Solar Physics, 293, 1–22. doi:https://doi.org/10.1007/s11207-018-1357-7.Müller, M. (2007). Dynamic time warping. Information retrieval for music and motion, (pp. 69–84). doi:https://doi.org/10.1007/978-3-540-74048-3_4.Potgieter, M. S. (2013). Solar modulation of cosmic rays. Living Reviews in So826 lar Physics, 10, 1–66. doi:https://doi.org/10.12942/lrsp-2013-3.Puth, M.-T., Neuhäuser, M., & Ruxton, G. D. (2014). Effective use of pearson’s product–moment correlation coefficient. Animal behaviour, 93, 183–189. doi:https://doi.org/10.1016/j.anbehav.2014.05.003.Sadeghi, B. (2022). Chatterjee correlation coefficient: a robust alternative for classic correlation methods in geochemical studies-(including “triplecpy”python package). Ore Geology Reviews, 146, 104954. doi:https://doi.org/10.1016/j.oregeorev.2022.104954.Sakoe, H., & Chiba, S. (1978). Dynamic programming algorithm optimiza835 tion for spoken word recognition. IEEE transactions on acoustics, speech, and signal processing, 26(1), 43–49. doi:https://doi.org/10.1109/TASSP.1978.1163055.Schober, P., Boer, C., & Schwarte, L. A. (2018). Correlation coefficients: ap839 propriate use and interpretation. Anesthesia & analgesia, 126(5), 1763–1768. doi:https://doi.org/10.1213/ANE.0000000000002864.Senin, P. (2008). Dynamic time warping algorithm review. Information and Computer Science Department University of Hawaii at Manoa Hon olulu, USA, 855(1-23), 40. URL: https://www.researchgate.net/profile/Pavel-Senin/publication/228785661_Dynamic_Time_ Warping_Algorithm_Review/links/02bfe5100f11a7929f000000/Dynamic-Time-Warping-Algorithm-Review.pdf.Shi, H., Drton, M., & Han, F. (2022). On the power of chatterjee’s rank cor848 relation. Biometrika, 109(2), 317–333. doi:https://doi.org/10.1093/biomet/asab028Sierra-Porta, D. (2018). Cross correlation and time-lag between cosmic ray intensity and solar activity during solar cycles 21, 22 and 23. Astro852 physics and Space Science, 363, 1–5. doi:https://doi.org/10.1007/s10509-018-3360-8.Sierra-Porta, D. (2022). On the fractal properties of cosmic rays and sun dy namics cross-correlations. Astrophysics and Space Science, 367(12), 116. doi:https://doi.org/10.1007/s10509-022-04151-5.Sierra-Porta, D., & Domínguez-Monterroza, A.-R. (2022). Linking cosmic ray intensities to cutoff rigidity through multifractal detrented fluctuation anal859 ysis. Physica A: Statistical Mechanics and its Applications, 607, 128159. doi:https://doi.org/10.1016/j.physa.2022.128159.SILSO World Data Center (1964-2024). The international sunspot number. International Sunspot Number Monthly Bulletin and online catalogue,Stansby, D., Green, L. M., van Driel-Gesztelyi, L. et al. (2021). Active region contributions to the solar wind over multiple solar cycles. Solar Physics, 296(8), 116. doi:https://doi.org/10.1007/s11207-021-01861-x.Sullivan, J. H., Warkentin, M., & Wallace, L. (2021). So many ways for as867 sessing outliers: What really works and does it matter? Journal of Business Research, 132, 530–543. doi:https://doi.org/10.1016/j.jbusres.2021.03.066.Tomassetti, N., Bertucci, B., & Fiandrini, E. (2022). Temporal evolution and rigidity dependence of the solar modulation lag of galactic cosmic rays.Physical Review D, 106(10), 103022. doi:https://doi.org/10.1103/PhysRevD.106.103022.Usoskin, I., Koldobskiy, S., Kovaltsov, G. et al. (2020). Revised gle database: Fluences of solar energetic particles as measured by the neutron-monitor network since 1956. Astronomy & Astrophysics, 640, A17. doi:https://doi.org/10.1051/0004-6361/202038272.Usoskin, I. G., Mursula, K., Solanki, S. et al. (2004). Reconstruction of so879 lar activity for the last millennium using be data. Astronomy & Astro880 physics, 413(2), 745–751. doi:https://doi.org/10.1051/0004-6361: 20031533.Usoskin, I. G., Solanki, S. K., Krivova, N. A. et al. (2021). Solar cyclic activity over the last millennium reconstructed from annual 14c data. Astronomy & Astrophysics, 649, A141. doi:https://doi.org/10.1051/0004-6361/202140711.Ventura-León, J., Peña-Calero, B. N., & Burga-León, A. (2023). The effect of normality and outliers on bivariate correlation coefficients in psychology: A monte carlo simulation. The Journal of General Psychology, 150(4), 405– 422. doi:https://doi.org/10.1080/00221309.2022.2094310.Wu, C. J., Usoskin, I. G., Krivova, N. et al. (2018). Solar activity over nine mil- lennia: A consistent multi-proxy reconstruction. Astronomy & Astrophysics, 615, A93. doi:https://doi.org/10.1051/0004-6361/201731892.Zheng, Y., Jun, I., Tu, W. et al. (2024). Overview, progress and next steps for our understanding of the near-earth space radiation and plasma environment: Science and applications. Advances in Space Research, . doi:https://doi.org/10.1016/j.asr.2024.05.017.http://purl.org/coar/resource_type/c_6501ORIGINALCross_Correlation_Revised_Elsevier.pdfCross_Correlation_Revised_Elsevier.pdfapplication/pdf624937https://repositorio.utb.edu.co/bitstream/20.500.12585/12757/1/Cross_Correlation_Revised_Elsevier.pdfd28852b3defabc39ff811940b6e29e39MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.utb.edu.co/bitstream/20.500.12585/12757/2/license_rdf42fd4ad1e89814f5e4a476b409eb708cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/12757/3/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD53TEXTCross_Correlation_Revised_Elsevier.pdf.txtCross_Correlation_Revised_Elsevier.pdf.txtExtracted texttext/plain68298https://repositorio.utb.edu.co/bitstream/20.500.12585/12757/4/Cross_Correlation_Revised_Elsevier.pdf.txt6e7d42be37d4177f9bbf332c2f9a43abMD54THUMBNAILCross_Correlation_Revised_Elsevier.pdf.jpgCross_Correlation_Revised_Elsevier.pdf.jpgGenerated Thumbnailimage/jpeg7438https://repositorio.utb.edu.co/bitstream/20.500.12585/12757/5/Cross_Correlation_Revised_Elsevier.pdf.jpg72aa21c43dca5f8c0253e36d762143d3MD5520.500.12585/12757oai:repositorio.utb.edu.co:20.500.12585/127572024-11-01 00:15:43.525Repositorio Institucional UTBrepositorioutb@utb.edu.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

Revised cross-correlation and time-lag between cosmic ray intensity and solar activity using chatterjee’s correlation coefficient

Publicaciones similares