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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

José Climent Hernández (), Luis Fernando Hoyos Reyes and Domingo Rodríguez Benavides
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Luis Fernando Hoyos Reyes: Universidad Autónoma Metropolitana, México
Domingo Rodríguez Benavides: Universidad Autónoma Metropolitana, México

Contaduría y Administración, 2017, vol. 62, issue 5, 11-12

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.

Keywords: The alfa stable processes; Self-similarity exponent; Financial engineering (search for similar items in EconPapers)
JEL-codes: C14 C16 C46 D81 G12 G13 (search for similar items in EconPapers)
Date: 2017
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