IDEAS home Printed from https://ideas.repec.org/a/nax/conyad/v62y2017i5p11-12.html
   My bibliography  Save this article

The a-stable processes and their relationship with theexponent of self-similarity: Exchange rates of USADollar, Canadian Dollar, Euro and Yen

Author

Listed:
  • José Antonio Climent Hernández

    (Universidad Autónoma Metropolitana, México)

  • Luis Fernando Hoyos Reyes

    (Universidad Autónoma Metropolitana, México)

  • Domingo Rodríguez Benavides

    (Universidad Autónoma Metropolitana, México)

Abstract

This research work analyzes the yields of the exchange rate parities of the American dollar, Canadian dollar, Euro, and Yen; estimates the basic statistics and the a-stables; carries out the Kolmogorov–Smirnov, Anderson–Darling, and Lilliefors goodness of fit tests; estimates the self-similar exponents and carries out the t and F tests, ruling out that the series of parities are multifractal. It also estimates the confidence intervals of the exchange rate parities and concludes that the estimated a-stable distributions are more efficient than the Gaussian distribution to quantify the risks of the market, and that the series are self-similar. Through the index, we can infer the risk of the events, indicating that the parities are anti-persistent and thus have short-term memory, mean reversion, and a negative correlation with the high risk in the short and medium term. The estimation and validation of the a-stable distributions and the self-similar exponent are important in the evaluation and creation of innovative investment instruments through financial engineering, risk administration, and the evaluation of derived products.

Suggested Citation

  • José Antonio Climent Hernández & Luis Fernando Hoyos Reyes & Domingo Rodríguez Benavides, 2017. "The a-stable processes and their relationship with theexponent of self-similarity: Exchange rates of USADollar, Canadian Dollar, Euro and Yen," Contaduría y Administración, Accounting and Management, vol. 62(5), pages 11-12, Diciembre.
    • Handle: RePEc:nax:conyad:v:62:y:2017:i:5:p:11-12
    as

    Download full text from publisher

    File URL: http://www.cya.unam.mx/index.php/cya/article/view/1839/1211
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rodríguez Aguilar Román, 2014. "El coeficiente de Hurst y el parámetro -estable para el análisis de series financieras Aplicación al mercado cambiario mexicano," Contaduría y Administración, Accounting and Management, vol. 59(1), pages 149-173, enero-mar.
    2. Barunik, Jozef & Kristoufek, Ladislav, 2010. "On Hurst exponent estimation under heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3844-3855.
    3. Borak, Szymon & Härdle, Wolfgang Karl & Weron, Rafał, 2005. "Stable distributions," SFB 649 Discussion Papers 2005-008, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Epaminondas Panas, 2001. "Estimating fractal dimension using stable distributions and exploring long memory through ARFIMA models in Athens Stock Exchange," Applied Financial Economics, Taylor & Francis Journals, vol. 11(4), pages 395-402.
    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. Emilian DOBRESCU, 2016. "Controversies over the Size of the Public Budget," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 5-34, December.
    2. Kristoufek, Ladislav & Vosvrda, Miloslav, 2013. "Measuring capital market efficiency: Global and local correlations structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 184-193.
    3. Gómez-Águila, A. & Sánchez-Granero, M.A., 2021. "A theoretical framework for the TTA algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    4. 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.
    5. 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.
    6. Jiang, Yonghong & Nie, He & Ruan, Weihua, 2018. "Time-varying long-term memory in Bitcoin market," Finance Research Letters, Elsevier, vol. 25(C), pages 280-284.
    7. Ladislav Kristoufek & Paulo Ferreira, 2018. "Capital asset pricing model in Portugal: Evidence from fractal regressions," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 17(3), pages 173-183, November.
    8. Ayoub Ammy-Driss & Matthieu Garcin, 2021. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Working Papers hal-02903655, HAL.
    9. Ayoub Ammy-Driss & Matthieu Garcin, 2020. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Papers 2007.10727, arXiv.org, revised Nov 2021.
    10. repec:diw:diwwpp:dp1647 is not listed on IDEAS
    11. Ladislav KRISTOUFEK & Petra LUNACKOVA, 2013. "Long-term Memory in Electricity Prices: Czech Market Evidence," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 63(5), pages 407-424, November.
    12. Sensoy, Ahmet & Hacihasanoglu, Erk, 2014. "Time-varying long range dependence in energy futures markets," Energy Economics, Elsevier, vol. 46(C), pages 318-327.
    13. Dassios, Angelos & Qu, Yan & Zhao, Hongbiao, 2018. "Exact simulation for a class of tempered stable," LSE Research Online Documents on Economics 86981, London School of Economics and Political Science, LSE Library.
    14. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.
    15. Avishek Bhandari & Bandi Kamaiah, 2021. "Long Memory and Fractality Among Global Equity Markets: a Multivariate Wavelet Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 23-37, March.
    16. Stavros Degiannakis & Alexandra Livada & Epaminondas Panas, 2008. "Rolling-sampled parameters of ARCH and Levy-stable models," Applied Economics, Taylor & Francis Journals, vol. 40(23), pages 3051-3067.
    17. Kristoufek, Ladislav, 2018. "On Bitcoin markets (in)efficiency and its evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 257-262.
    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. Ferreira, Paulo & Kristoufek, Ladislav, 2017. "What is new about covered interest parity condition in the European Union? Evidence from fractal cross-correlation regressions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 554-566.
    20. Al-Shboul, Mohammad & Alsharari, Nizar, 2019. "The dynamic behavior of evolving efficiency: Evidence from the UAE stock markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 73(C), pages 119-135.
    21. Sensoy, Ahmet & Tabak, Benjamin M., 2016. "Dynamic efficiency of stock markets and exchange rates," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 353-371.

    More about this item

    Keywords

    The alfa stable processes; Self-similarity exponent; Financial engineering;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:nax:conyad:v:62:y:2017:i:5:p:11-12. 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: Alberto García-Narvaez (Technical Editor) (email available below). General contact details of provider: https://edirc.repec.org/data/fcunamx.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.