Journal of Statistics: Advances in Theory and ApplicationsAuthor's: Charles Shaw
Pages: [15] - [65]
Received Date: August 10, 2018; Revised September 19, 2018
Submitted by:
DOI: http://dx.doi.org/10.18642/jsata_7100121990
In a recent contribution to the financial econometrics literature, Chu et al. ([13]) 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 by 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.
autoregressive conditional heteroskedasticity (ARCH), generalized autoregressive conditional heteroskedasticity (GARCH), market volatility, nonlinear time series, Khmaladze transform.
