This paper develops the ability of the normal inverse Gaussian distribution (NIG) to fit the returns of bitcoin (BTC). As the first cryptocurrency created, the behavior of this new asset is characterized by great volatility. The lack of a proper definition or classification under existing theory exacerbates this property in such a way that explosive periods followed by a rapid decline have been observed along the series, meaning bubble episodes. By detecting the periods in which a bubble rises and collapses, it is possible to study the statistical properties of such segments. In particular, adjusting a theoretical distribution may help to determine better strategies to hedge against these episodes. The NIG is an appropriate candidate not only because of its heavy-tailed property but also because it has been proven to be closed under convolution, a characteristic that can be implemented to measure multivariate value at risk. Using data on the price of BTC with respect to seven of the main global currencies, the NIG was able to fit every time segment despite the bubble behavior. In the out-of-sample tests, the NIG was proven to have an adjustment similar to that of a generalized hyperbolic (GH) distribution. This result could serve as a starting point for future studies regarding the statistical properties of cryptocurrencies as well as their multivariate distributions.
El objetivo de esta investigación es analizar la presencia de burbujas financieras o un comportamiento explosivo en cuatro criptomonedas: Ethereum, Ripple, Bitcoin Cash y EOS. La selección de los activos se basó en la capitalización de mercado. La metodología implementada fue una prueba simple y generalizada (SADF y GSADF) de una variación de la prueba aumentada de Dickey-Fuller propuesta por Phillips et al. (2011, 2015). Encontramos diez, siete, seis y siete comportamientos exuberantes en los activos mencionados, respectivamente. Esta metodología ha sido en gran parte inexplorada y podría emplearse de manera estándar en el sector financiero para cualquier otro activo. Esta es la primera investigación que detecta este tipo de comportamiento para un grupo de criptomonedas con frecuencia diaria. Con el presente trabajo y el artículo de Li et al. (2018), el 68,47% del mercado ha sido analizado bajo la metodología. En consecuencia, este comportamiento podría estar disperso en todo el sector.
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