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. First, I explore the time series properties of cryptocurrencies, a new type of financial asset on which there appears to be little or no literature. Second, 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. In this regards, checks are performed on whether innovations are Gaussian or GED by using Kolmogorov type non-parametric tests and Khmaladze’s martingale transformation. Arguing against Chu et al (2017), I show that there is a strong empirical argument against modelling innovations under Gaussian assumptions. Arguing against Chu et al (2017), I also demonstrate a theoretical case for not relying on Skewed GED (SGED) assumptions, but using GED innovations instead. I prove that the moment generating of the SGED fails to exist under some conditions. Other formal results are presented in support of above arguments. The unique contribution of this study to the financial econometrics literature is that results in this paper can be used to arrive at a option pricing methodology under equivalent martingale measure. Further reference is made to statistical techniques, and in some cases the limitations of such techniques, presented in the recently published literature.
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3094024Keywords: Autoregressive conditional heteroskedasticity (ARCH), generalized autoregressive conditional heteroskedasticity (GARCH), market volatility, nonlinear time series, Khmaladze transform
