Analysis of Cryptocurrency volatility and statistical distributions using ARMA and GARCH-type models

Abstract: This study aims to investigate and model statistical properties of Bitcoin and other major cryptocurrencies. There were recent drastic changes in the level of Bitcoin prices as it moved from $740 in 2014 to $19,187 in 2017, and down to $3,830 in 2018. The current study aims to fill the gap in the analysis of cryptoccurencies, primarily Bitcoin returns statistical process. Specifically, the study selects and estimates a model that traces dynamics of returns using ARMA, and also volatility of the residual from the model. To my knowledge, there is gap in the academic literature for the case of Bitcoin to use such approach. The analysis involves data on past daily prices of Bitcoin, in British Pounds and USD, as well as those of Ethereum and Litecoin, both in Pounds. The results obtained from the study provide evidence that ARMA model in combination with eGARCH volatility model can be used for analysis of statistical process of Bitcoin returns. Moreover, significant statistical differences are identified between Bitcoin prices in UK Pounds and US Dollars. Although there is no evidence that shows the price level has an effect on volatility, significant decline is identified in the volatility of Bitcoin log-returns since 2018 as compared to the previous period. For each considered cryptocurrency, the current study determines the optimal specification of ARMA model, as well as GARCH-type model and optimal statistical distribution of the residual. The set of results can be used to estimate statistical process behind the cryptocurrency historical prices. Moreover, relation between ARMA(p, q) lag order, and type of optimal volatility model and residual distribution is explored, no significant relation is identified.