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Conditional heteroskedasticity in crypto-asset returns

Charles Shaw

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Abstract: This paper examines the time series properties of cryptocurrency assets, such as Bitcoin, using established econometric inference techniques, namely models of the GARCH family. The contribution of this study is twofold. I explore the time series properties of cryptocurrencies, a new type of financial asset on which there appears to be little or no literature. I suggest an improved econometric specification to that which has been recently proposed in Chu et al (2017), the first econometric study to examine the price dynamics of the most popular cryptocurrencies. Questions regarding the reliability of their study stem from the authors mis-diagnosing the distribution of GARCH innovations. Checks are performed on whether innovations are Gaussian or GED by using Kolmogorov type non-parametric tests and Khmaladze's martingale transformation. Null of gaussianity is strongly rejected for all GARCH(p,q) models, with $p,q \in \{1,\ldots,5 \}$, for all cryptocurrencies in sample. For tests of normality, I make use of the Gauss-Kronrod quadrature. Parameters of GARCH models are estimated with generalized error distribution innovations using maximum likelihood. For calculating P-values, the parametric bootstrap method is used. Arguing against Chu et al (2017), I show that there is a strong empirical argument against modelling innovations under some common assumptions.

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Date: 2018-04, Revised 2018-12
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