IDEAS home Printed from https://ideas.repec.org/a/avo/emipdu/v29y2020i1p3-28.html

Can Croatian Urban Hierarchy Be Approximated With The Fibonacci Sequence? An Analysis On Historical Population Data

Author

Listed:
  • Hrvoje Josic

    (University of Zagreb)

  • Berislav Zmuk

    (University of Zagreb)

Abstract

Fibonacci numbers can be found in nature and have application in various fields of human activity. The Fibonacci sequence can also be used to predict population of settlements. The goal of this paper is to examine whether the hierarchy of the Croatian urban system can be approximated with the Fibonacci sequence on historical census data from 1857 to 2011. Actual values of urban rank according to settlements size were compared to the predicted values using two Fibonacci methods from the Fibonacci sequence. First method divides the population of the largest city by the golden ratio constant while the second method takes the population of each successive city and divides it by the golden ratio constant. The conducted analysis has shown that Croatian urban system conforms to the Fibonacci sequence with very good precision. Method 2 gives more precise overlaps of the actual number of inhabitants by settlements in the urban hierarchy of Croatia with the Fibonacci sequence than Method 1. If the largest city Zagreb is excluded from the analysis, the estimations are more precise with smaller mean MAPE.

Suggested Citation

  • Hrvoje Josic & Berislav Zmuk, 2020. "Can Croatian Urban Hierarchy Be Approximated With The Fibonacci Sequence? An Analysis On Historical Population Data," Economic Thought and Practice, Department of Economics and Business, University of Dubrovnik, vol. 29(1), pages 3-28, june.
    • Handle: RePEc:avo:emipdu:v:29:y:2020:i:1:p:3-28
    as

    Download full text from publisher

    File URL: https://hrcak.srce.hr/clanak/347733
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ramzi Suleiman, 2017. "Economic Harmony: An Epistemic Theory of Economic Interactions," Games, MDPI, vol. 8(1), pages 1-15, January.
    2. William Goetzmann, 2003. "Fibonacci and the Financial Revolution," Yale School of Management Working Papers ysm432, Yale School of Management, revised 01 Mar 2004.
    3. Violeta Gaucan, 2011. "How to use Fibonacci retracement to predict forex market," Journal of Knowledge Management, Economics and Information Technology, ScientificPapers.org, vol. 1(2), pages 1-1, February.
    4. Rosen, Kenneth T. & Resnick, Mitchel, 1980. "The size distribution of cities: An examination of the Pareto law and primacy," Journal of Urban Economics, Elsevier, vol. 8(2), pages 165-186, September.
    5. Zora Živanović & Branka Tošić & Teodora Nikolić & Dragica Gatarić, 2019. "Urban System in Serbia—The Factor in the Planning of Balanced Regional Development," Sustainability, MDPI, vol. 11(15), pages 1-19, August.
    6. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
    Full references (including those not matched with items on IDEAS)

    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. Hasan Engin Duran, 2025. "The future of urban hierearchy and Zipf law: ARIMA and BATS forecasting," Letters in Spatial and Resource Sciences, Springer, vol. 18(1), pages 1-14, December.
    2. Ho Yeon KIM & Petra de Jong & Jan Rouwendal & Aleid Brouwer, 2012. "Shrinking population and the urban hierarchy [Housing preferences and attribute importance among Dutch older adults: a conjoint choice experiment]," ERSA conference papers ersa12p350, European Regional Science Association.
    3. Lena SANDERS, 2012. "Regards Scientifiques Croisés Sur La Hiérarchie Des Systèmes De Peuplement : De L’Empirie Aux Systèmes Complexes," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 36, pages 127-146.
    4. Duranton, Gilles & Puga, Diego, 2014. "The Growth of Cities," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 5, pages 781-853, Elsevier.
    5. Sebastien TERRA, 2009. "Zipf's Law for Cities: On a New Testing Procedure," Working Papers 200920, CERDI.
    6. Clémentine Cottineau, 2022. "What do analyses of city size distributions have in common?," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(3), pages 1439-1463, March.
    7. Valente J. Matlaba & Mark J. Holmes & Philip McCann & Jacques Poot, 2013. "A Century Of The Evolution Of The Urban System In Brazil," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 25(3), pages 129-151, November.
    8. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2019. "Zipf’s law, the coherence of the urban system and city size distribution: Evidence from Pakistan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 87-103.
    9. Michel Dimou & Alexandra Schaffar, 2009. "Urban Hierarchies and City Growth in the Balkans," Urban Studies, Urban Studies Journal Limited, vol. 46(13), pages 2891-2906, December.
    10. Fazio, Giorgio & Modica, Marco, 2012. "Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities," SIRE Discussion Papers 2012-54, Scottish Institute for Research in Economics (SIRE).
    11. Pankaj Bajracharya & Selima Sultana, 2020. "Rank-size Distribution of Cities and Municipalities in Bangladesh," Sustainability, MDPI, vol. 12(11), pages 1-26, June.
    12. Angelina Hackmann & Torben Klarl, 2020. "The evolution of Zipf's Law for U.S. cities," Papers in Regional Science, Wiley Blackwell, vol. 99(3), pages 841-852, June.
    13. Rafael González‐Val, 2019. "Historical urban growth in Europe (1300–1800)," Papers in Regional Science, Wiley Blackwell, vol. 98(2), pages 1115-1136, April.
    14. Ronan Lyons & Elisa Maria Tirindelli, 2022. "The Rise & Fall of Urban Concentration in Britain: Zipf, Gibrat and Gini across two centuries," Trinity Economics Papers tep0522, Trinity College Dublin, Department of Economics.
    15. Mark Lorenzen & Kristina Vaarst Andersen, 2009. "Centrality and Creativity: Does Richard Florida's Creative Class Offer New Insights into Urban Hierarchy?," Economic Geography, Clark University, vol. 85(4), pages 363-390, October.
    16. Soo, Kwok Tong, 2005. "Zipf's Law for cities: a cross-country investigation," Regional Science and Urban Economics, Elsevier, vol. 35(3), pages 239-263, May.
    17. Tomoya Mori & Tony E. Smith, 2009. "A Reconsideration of the NAS Rule from an Industrial Agglomeration Perspective," KIER Working Papers 669, Kyoto University, Institute of Economic Research.
    18. Chen, Zhihong & Fu, Shihe & Zhang, Dayong, 2010. "Searching for the parallel growth of cities," MPRA Paper 21528, University Library of Munich, Germany.
    19. Kim, Ho Yeon, 2012. "Shrinking population and the urban hierarchy," IDE Discussion Papers 360, Institute of Developing Economies, Japan External Trade Organization(JETRO).
    20. Taner Osman, 2026. "Does Zipf’s law account for the size distribution of subcenters within metropolitan regions? Evidence from the US," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 75(1), pages 1-23, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • P25 - Political Economy and Comparative Economic Systems - - Socialist and Transition Economies - - - Urban, Rural, and Regional Economics
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • R23 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Regional Migration; Regional Labor Markets; Population

    Statistics

    Access and download statistics

    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:avo:emipdu:v:29:y:2020:i:1:p:3-28. 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: Nebojsa Stojcic (email available below). General contact details of provider: https://edirc.repec.org/data/oedubhr.html .

    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.