IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v388y2009i23p4845-4855.html
   My bibliography  Save this article

The dynamics of exchange rate time series and the chaos game

Author

Listed:
  • Cristescu, C.P.
  • Stan, C.
  • Scarlat, E.I.

Abstract

This work presents a novel method of reconstructing some relevant characteristics of exchange rate time series by the superposition of two components: a mostly deterministic one, the chaos game as expressed by the Yuan/USD exchange rate and a purely stochastic one, Gaussian white noise. We analyzed 20 economic systems with the average Index of Economic Freedom above 50. The considered characteristics (the Lempel–Ziv complexity index, the slimness of the distribution and the Iterated Function Systems clumpiness test) are well reproduced by the reconstruction process. Additional confirmation is obtained by an analysis of the exchange rate of the Romanian national currency as an example of an application of the method to a transition economy, and by an analysis of the time series of the Euro-zone as an example of an application to a multinational system using a shorter time series.

Suggested Citation

  • Cristescu, C.P. & Stan, C. & Scarlat, E.I., 2009. "The dynamics of exchange rate time series and the chaos game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(23), pages 4845-4855.
  • Handle: RePEc:eee:phsmap:v:388:y:2009:i:23:p:4845-4855
    DOI: 10.1016/j.physa.2009.08.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437109006098
    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.2009.08.005?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. Chen, Liang & Chen, Guanrong, 2007. "Controlling chaos in an economic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 349-358.
    2. Scarlat, E.I. & Stan, Cristina & Cristescu, C.P., 2007. "Self-similar characteristics of the currency exchange rate in an economy in transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 188-198.
    3. Stanley, H.Eugene, 2003. "Statistical physics and economic fluctuations: do outliers exist?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(1), pages 279-292.
    4. Wang, Yiming & Tong, Hanfei, 2008. "Modeling and estimating the jump risk of exchange rates: Applications to RMB," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6575-6583.
    5. Giglio, Ricardo & Matsushita, Raul & Figueiredo, Annibal & Gleria, Iram & Da Silva, Sergio, 2008. "Algorithmic complexity theory and the relative efficiency of financial markets," MPRA Paper 8704, University Library of Munich, Germany.
    6. Matsushita, Raul & Gleria, Iram & Figueiredo, Annibal & Da Silva, Sergio, 2007. "The Chinese chaos game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 427-442.
      • Raul, Matsushita & Iram, Gleria & Annibal, Figueiredo & Sergio, Da Silva, 2006. "The Chinese Chaos Game," MPRA Paper 1847, University Library of Munich, Germany.
    7. repec:ebl:ecbull:v:7:y:2003:i:2:p:1-13 is not listed on IDEAS
    8. Scarlat, E.I. & Stan, Cristina & Cristescu, C.P., 2007. "Chaotic features in Romanian transition economy as reflected onto the currency exchange rate," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 396-404.
    9. Chávez Muñoz, Pablo & Fernandes da Silva, Marcus & Vivas Miranda, José & Claro, Francisco & Gomez Diniz, Raimundo, 2007. "Influence of government controls over the currency exchange rate in the evolution of Hurst's exponent: An autonomous agent-based model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(2), pages 786-790.
    10. repec:ebl:ecbull:v:7:y:2008:i:6:p:1-12 is not listed on IDEAS
    11. R. Cross & M. Grinfeld & H. Lamba & T. Seaman, 2007. "Stylized facts from a threshold-based heterogeneous agent model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 213-218, May.
    12. Giglio, Ricardo & Matsushita, Raul & Figueiredo, Annibal & Gleria, Iram & Da Silva, Sergio, 2008. "Algorithmic complexity theory and the relative efficiency of financial markets - Updated," MPRA Paper 11150, University Library of Munich, Germany.
    13. Sergio Da Silva & Annibal Figueiredo & Iram Gleria & Raul Matsushita, 2003. "Fractal structure in the Chinese yuan/US dollar rate," Economics Bulletin, AccessEcon, vol. 7(2), pages 1-13.
    14. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    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. Vasilios Plakandaras & Rangan Gupta & Luis A. Gil-Alana & Mark E. Wohar, 2019. "Are BRICS exchange rates chaotic?," Applied Economics Letters, Taylor & Francis Journals, vol. 26(13), pages 1104-1110, July.
    2. Goodness C. Aye & Rangan Gupta & Chi Keung Marco Lau & Xin Sheng, 2019. "Is there a role for uncertainty in forecasting output growth in OECD countries? Evidence from a time-varying parameter-panel vector autoregressive model," Applied Economics, Taylor & Francis Journals, vol. 51(33), pages 3624-3631, July.
    3. Li, Ranran & Hu, Yucai & Heng, Jiani & Chen, Xueli, 2021. "A novel multiscale forecasting model for crude oil price time series," Technological Forecasting and Social Change, Elsevier, vol. 173(C).
    4. Cristescu, Constantin P. & Stan, Cristina & Scarlat, Eugen I. & Minea, Teofil & Cristescu, Cristina M., 2012. "Parameter motivated mutual correlation analysis: Application to the study of currency exchange rates based on intermittency parameter and Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2623-2635.

    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. Cristescu, Constantin P. & Stan, Cristina & Scarlat, Eugen I. & Minea, Teofil & Cristescu, Cristina M., 2012. "Parameter motivated mutual correlation analysis: Application to the study of currency exchange rates based on intermittency parameter and Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2623-2635.
    2. Lucio Maria Calcagnile & Fulvio Corsi & Stefano Marmi, 2020. "Entropy and Efficiency of the ETF Market," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 143-184, January.
    3. Lahmiri, Salim & Bekiros, Stelios & Avdoulas, Christos, 2018. "Time-dependent complexity measurement of causality in international equity markets: A spatial approach," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 215-219.
    4. Da Silva, Sergio, 2015. "Financial Market Efficiency Should be Gauged in Relative Rather than Absolute Terms," MPRA Paper 64497, University Library of Munich, Germany.
    5. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2010. "Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1891-1901.
    6. Alvarez-Ramirez, J. & Rodriguez, E. & Espinosa-Paredes, G., 2012. "A partisan effect in the efficiency of the US stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4923-4932.
    7. Wang, Fang & Gacesa, Marko, 2023. "Semi-strong efficient market of Bitcoin and Twitter: An analysis of semantic vector spaces of extracted keywords and light gradient boosting machine models," International Review of Financial Analysis, Elsevier, vol. 88(C).
    8. Lucio Maria Calcagnile & Fulvio Corsi & Stefano Marmi, 2016. "Entropy and efficiency of the ETF market," Papers 1609.04199, arXiv.org.
    9. Andrey Shternshis & Piero Mazzarisi, 2022. "Variance of entropy for testing time-varying regimes with an application to meme stocks," Papers 2211.05415, arXiv.org, revised Jun 2023.
    10. Shternshis, Andrey & Mazzarisi, Piero & Marmi, Stefano, 2022. "Measuring market efficiency: The Shannon entropy of high-frequency financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    11. Barunik, Jozef & Vacha, Lukas, 2010. "Monte Carlo-based tail exponent estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4863-4874.
    12. Matsushita, Raul & Gleria, Iram & Figueiredo, Annibal & Rathie, Pushpa & Da Silva, Sergio, 2004. "Exponentially damped Lévy flights, multiscaling, and exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 353-369.
    13. Wang, Xiao-Tian & Li, Zhe & Zhuang, Le, 2017. "European option pricing under the Student’s t noise with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 848-858.
    14. Wang, Dong-Hua & Yu, Xiao-Wen & Suo, Yuan-Yuan, 2012. "Statistical properties of the yuan exchange rate index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3503-3512.
    15. Villena, Marcelo J. & Araneda, Axel A., 2017. "Dynamics and stability in retail competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 134(C), pages 37-53.
    16. Kanjamapornkul, K. & Pinčák, Richard & Bartoš, Erik, 2016. "The study of Thai stock market across the 2008 financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 117-133.
    17. Shi, Yanlin & Ho, Kin-Yip, 2015. "Long memory and regime switching: A simulation study on the Markov regime-switching ARFIMA model," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 189-204.
    18. Alberto Ciacci & Takumi Sueshige & Hideki Takayasu & Kim Christensen & Misako Takayasu, 2020. "The microscopic relationships between triangular arbitrage and cross-currency correlations in a simple agent based model of foreign exchange markets," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    19. Jean-Philippe Bouchaud & Damien Challet, 2016. "Why have asset price properties changed so little in 200 years," Papers 1605.00634, arXiv.org.
    20. Xin, Baogui & Chen, Tong, 2011. "On a master-slave Bertrand game model," Economic Modelling, Elsevier, vol. 28(4), pages 1864-1870, July.

    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:388:y:2009:i:23:p:4845-4855. 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.