| 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 α-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 α-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 α-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. |
