IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v421y2015icp124-133.html
   My bibliography  Save this article

Long-range correlations and trends in Colombian seismic time series

Author

Listed:
  • Martín-Montoya, L.A.
  • Aranda-Camacho, N.M.
  • Quimbay, C.J.

Abstract

We study long-range correlations and trends in time series extracted from the data of seismic events occurred from 1973 to 2011 in a rectangular region that contains mainly all the continental part of Colombia. The long-range correlations are detected by the calculation of the Hurst exponents for the time series of interevent intervals, separation distances, depth differences and magnitude differences. By using a modification of the classical R/S method that has been developed to detect short-range correlations in time series, we find the existence of persistence for all the time series considered except for magnitude differences. We find also, by using the DFA until the third order, that the studied time series are not influenced by trends. Additionally, an analysis of the Hurst exponent as a function of the number of events in the time and the maximum window size is presented.

Suggested Citation

  • Martín-Montoya, L.A. & Aranda-Camacho, N.M. & Quimbay, C.J., 2015. "Long-range correlations and trends in Colombian seismic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 124-133.
    • Handle: RePEc:eee:phsmap:v:421:y:2015:i:c:p:124-133
    DOI: 10.1016/j.physa.2014.10.073
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711400911X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2014.10.073?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yanhui Liu & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1997. "Correlations in Economic Time Series," Papers cond-mat/9706021, arXiv.org.
    2. Trinidad Segovia, J.E. & Fernández-Martínez, M. & Sánchez-Granero, M.A., 2012. "A note on geometric method-based procedures to calculate the Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(6), pages 2209-2214.
    3. Jiménez, Abigail, 2011. "Comparison of the Hurst and DEA exponents between the catalogue and its clusters: The California case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2146-2154.
    4. Blesić, S. & Milošević, S. & Stratimirović, Dj. & Ljubisavljević, M., 1999. "Detrended fluctuation analysis of time series of a firing fusimotor neuron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(3), pages 275-282.
    5. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    6. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    7. Ivanova, K & Ausloos, M, 1999. "Application of the detrended fluctuation analysis (DFA) method for describing cloud breaking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 349-354.
    8. Ashkenazy, Yosef & Havlin, Shlomo & Ivanov, Plamen Ch. & Peng, Chung-K. & Schulte-Frohlinde, Verena & Stanley, H.Eugene, 2003. "Magnitude and sign scaling in power-law correlated time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 19-41.
    9. Domino, Krzysztof, 2011. "The use of the Hurst exponent to predict changes in trends on the Warsaw Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 98-109.
    10. Telesca, Luciano & Lovallo, Michele & Lapenna, Vincenzo & Macchiato, Maria, 2007. "Long-range correlations in two-dimensional spatio-temporal seismic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 279-284.
    11. Chen, Chien-chih & Lee, Ya-Ting & Chang, Young-Fo, 2008. "A relationship between Hurst exponents of slip and waiting time data of earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(18), pages 4643-4648.
    12. Grau-Carles, Pilar, 2000. "Empirical evidence of long-range correlations in stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 396-404.
    13. Sánchez Granero, M.A. & Trinidad Segovia, J.E. & García Pérez, J., 2008. "Some comments on Hurst exponent and the long memory processes on capital markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5543-5551.
    14. Liu, Yanhui & Cizeau, Pierre & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Correlations in economic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 437-440.
    15. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Oussama Tilfani & Paulo Ferreira & My Youssef El Boukfaoui, 2021. "Dynamic cross-correlation and dynamic contagion of stock markets: a sliding windows approach with the DCCA correlation coefficient," Empirical Economics, Springer, vol. 60(3), pages 1127-1156, March.
    2. Oussama Tilfani & Paulo Ferreira & Andreia Dionisio & My Youssef El Boukfaoui, 2020. "EU Stock Markets vs. Germany, UK and US: Analysis of Dynamic Comovements Using Time-Varying DCCA Correlation Coefficients," JRFM, MDPI, vol. 13(5), pages 1-23, May.
    3. Lahmiri, Salim, 2017. "On fractality and chaos in Moroccan family business stock returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 29-39.
    4. Fan, Xingxing & Lin, Min, 2017. "Multiscale multifractal detrended fluctuation analysis of earthquake magnitude series of Southern California," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 225-235.
    5. Sun, Xuelian & Liu, Zixian, 2016. "Optimal portfolio strategy with cross-correlation matrix composed by DCCA coefficients: Evidence from the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 667-679.
    6. Meraz, M. & Alvarez-Ramirez, J. & Rodriguez, E., 2022. "Multivariate rescaled range analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    7. Zhou, Yu & Leung, Yee & Chan, Lung Sang, 2017. "Oscillatory tendency of interevent direction in earthquake sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 120-130.
    8. Hayat, Umar & Barkat, Adnan & Ali, Aamir & Rehman, Khaista & Sifat, Shazia & Iqbal, Talat, 2019. "Fractal analysis of shallow and intermediate-depth seismicity of Hindu Kush," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 71-82.
    9. Ke Ma & Long Guo & Wangheng Liu, 2018. "Investigation of the Spatial Clustering Properties of Seismic Time Series: A Comparative Study from Shallow to Intermediate-Depth Earthquakes," Complexity, Hindawi, vol. 2018, pages 1-10, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. M. Fern'andez-Mart'inez & M. A S'anchez-Granero & Mar'ia Jos'e Mu~noz Torrecillas & Bill McKelvey, 2016. "A comparison among some Hurst exponent approaches to predict nascent bubbles in $500$ company stocks," Papers 1601.04188, arXiv.org.
    2. Fernández-Martínez, M. & Sánchez-Granero, M.A. & Trinidad Segovia, J.E., 2013. "Measuring the self-similarity exponent in Lévy stable processes of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5330-5345.
    3. Santos, J.V.C. & Moreira, D.M. & Moret, M.A. & Nascimento, E.G.S., 2019. "Analysis of long-range correlations of wind speed in different regions of Bahia and the Abrolhos Archipelago, Brazil," Energy, Elsevier, vol. 167(C), pages 680-687.
    4. Lu, Feiyu & Yuan, Naiming & Fu, Zuntao & Mao, Jiangyu, 2012. "Universal scaling behaviors of meteorological variables’ volatility and relations with original records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4953-4962.
    5. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    6. Gu, Gao-Feng & Zhou, Wei-Xing, 2007. "Statistical properties of daily ensemble variables in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 497-506.
    7. Michele Caraglio & Fulvio Baldovin & Attilio L. Stella, 2021. "How Fast Does the Clock of Finance Run?—A Time-Definition Enforcing Stationarity and Quantifying Overnight Duration," JRFM, MDPI, vol. 14(8), pages 1-15, August.
    8. Saha, Debajyoti & Shaw, Pankaj Kumar & Ghosh, Sabuj & Janaki, M.S. & Sekar Iyengar, A.N., 2018. "Quantification of scaling exponent with Crossover type phenomena for different types of forcing in DC glow discharge plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 300-310.
    9. Yang, Honglin & Wan, Hong & Zha, Yong, 2013. "Autocorrelation type, timescale and statistical property in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1681-1693.
    10. Yuan, Naiming & Fu, Zuntao & Mao, Jiangyu, 2010. "Different scaling behaviors in daily temperature records over China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(19), pages 4087-4095.
    11. Stavros-Richard G. Christopoulos & Nicholas V. Sarlis, 2017. "An Application of the Coherent Noise Model for the Prediction of Aftershock Magnitude Time Series," Complexity, Hindawi, vol. 2017, pages 1-27, February.
    12. Alvarez-Ramirez, Jose & Ibarra-Valdez, Carlos & Rodriguez, Eduardo & Dagdug, Leonardo, 2008. "1/f-Noise structures in Pollocks's drip paintings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 281-295.
    13. Serinaldi, Francesco, 2010. "Use and misuse of some Hurst parameter estimators applied to stationary and non-stationary financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2770-2781.
    14. Miguel Ángel Sánchez & Juan E Trinidad & José García & Manuel Fernández, 2015. "The Effect of the Underlying Distribution in Hurst Exponent Estimation," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-17, May.
    15. Lavička, Hynek & Kracík, Jiří, 2020. "Fluctuation analysis of electric power loads in Europe: Correlation multifractality vs. Distribution function multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    16. Muchnik, Lev & Bunde, Armin & Havlin, Shlomo, 2009. "Long term memory in extreme returns of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4145-4150.
    17. Laura Raisa Miloş & Cornel Haţiegan & Marius Cristian Miloş & Flavia Mirela Barna & Claudiu Boțoc, 2020. "Multifractal Detrended Fluctuation Analysis (MF-DFA) of Stock Market Indexes. Empirical Evidence from Seven Central and Eastern European Markets," Sustainability, MDPI, vol. 12(2), pages 1-15, January.
    18. Vasile Brătian & Ana-Maria Acu & Camelia Oprean-Stan & Emil Dinga & Gabriela-Mariana Ionescu, 2021. "Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion," Mathematics, MDPI, vol. 9(22), pages 1-20, November.
    19. A. Gómez-Águila & J. E. Trinidad-Segovia & M. A. Sánchez-Granero, 2022. "Improvement in Hurst exponent estimation and its application to financial markets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-21, December.
    20. Jiang, Lei & Zhang, Jiping & Liu, Xinwei & Li, Fei, 2016. "Multi-fractal scaling comparison of the Air Temperature and the Surface Temperature over China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 783-792.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:421:y:2015:i:c:p:124-133. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.