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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
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    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. Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. 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.
    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)

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    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

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