Conditional Heteroskedasticity in Crypto-Asset Returns

27 Pages Posted: 3 Jan 2018 Last revised: 8 Nov 2018

Date Written: March 24, 2018


In a recent contribution to the financial econometrics literature, Chu et al. (2017) provide the first examination of the time-series price behaviour of the most popular cryptocurrencies. However, insufficient attention was paid to correctly diagnosing the distribution of GARCH innovations. When these data issues are controlled for, their results lack robustness and may lead to either underestimation or overestimation of future risks. The main aim of this paper therefore is to provide an improved econometric specification. Particular attention is paid to correctly diagnosing the distribution of GARCH innovations by means of Kolmogorov type non-parametric tests and Khmaladze's martingale transformation. Numerical computation is carried out by implementing a Gauss-Kronrod quadrature. Parameters of GARCH models are estimated using maximum likelihood. For calculating P-values, the parametric bootstrap method is used. Further reference is made to the merits and demerits of statistical techniques presented in the related and recently published literature.

Keywords: Autoregressive conditional heteroskedasticity (ARCH), generalized autoregressive conditional heteroskedasticity (GARCH), market volatility, nonlinear time series, Khmaladze transform

JEL Classification: C22, C58

Suggested Citation

Shaw, Charles, Conditional Heteroskedasticity in Crypto-Asset Returns (March 24, 2018). Available at SSRN: or

Charles Shaw (Contact Author)

Independent ( email )

No Address Available

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