Statistical modelling of cryptocurrencies

Abstract

There has been tremendous interest invested by researchers and academics in Bitcoin since it's introduction to the financial market. However, in recent years there has been an advancement of the cryptocurrency market where other cryptocurrencies such as Ethereum, Litecoin and Ripple have grown relatively quickly and could potentially challenge the dominant placement of Bitcoin. These cryprocurrencies have been utilized globally as a virtual currency for multiple transactions. The returns of cryptocurrencies are known to be volatile and have been observed to fluctuate quite a bit in recent times. This study assesses and differentiates the performance of generalized autoregressive score (GAS) models integrated with a few heavy-tailed distributions in Value-at-Risk (VaR) estimation of the four most popular cryptocurrencies' returns, i.e. Bitcoin returns, Ethereum returns, Litecoin returns and Ripple returns. This paper proposed VaR models for Bitcoin, Ethereum, Litecoin and Ripple returns, i.e. GAS models combined with the generalized hyperbolic distribution (GHD), the variance gamma (VG) distribution, the normal inverse Gaussian (NIG) distribution and the generalized lambda distribution (GLD). The Kupiec likelihood ratio test was adopted to evaluate the proposed models' adequacy and Backtesting VaR was used to select the superior set of models.