Unpacking the Complexities of Bitcoin Volatility: A Time Series Data with Long-term Memory or Long-range Dependence

This article explores the complexities of cryptocurrency price volatility during times of crisis. We analyze time series data with long-term memory or long-range dependence to understand the impacts of crises on cryptocurrency prices. Specifically, we examine the effects of the Covid-19 pandemic and the Russo-Ukrainian war on cryptocurrency markets, as well as the role of investor sentiment in price fluctuations during periods of uncertainty. To do so, we use fractionally integrated models to analyze the short- and long-term effects of these external factors on cryptocurrency prices. Our study mainly focuses on Bitcoin returns volatility using specific fractionally integrated models during four sub-period of historical crises from 2014. It assesses and compares the fractionally integrated models of the GARCH, the FIGARCH-BBM, the FIGARCH-CHUNG, FIEGARCH, and the FIAPARCH-BBM during the sub-periods of the pre-Covid-19, of the Covid-19 situation, between the Covid-19 and the Russo-Ukrainian War, and of the Russo-Ukrainian War. Conditional volatility models' parameters are first estimated from the four sub-sample data series BTC/USD exchange rate returns and it is calculated. Estimated conditional volatilities are then compared to specific volatilities relying on information criteria, after which the models are ranked. Finally, we test the specifics fractionally integrated volatility models with the normality test, the Q-Statistics on Standardized Residuals Test, the ARCH Test, and the graphic analysis. The specific volatility model of the first sub-period pre-Covid-19 is FIAPARCH-BBM (2,1). BTC/USD returns evolution during the Covid-19 crisis indicates that the FIEGARCH (2,2) is the appropriate volatility model. In addition, our results find that the FIEGARCH (2,1) is the appropriate model of volatility over the third sub-period and during the Russo-Ukrainian War period. By extrapolating the results of the four events, the study showed that the series of BTC/USD returns sampled over the four sub-periods were not immune to risk leading to historical crisis situations. The fluctuations of Bitcoin data during a political or economic event influence the choice of volatility models and their coefficients. More specifically, the parameters of the determined models of conditional volatility show that a war will make cryptocurrency more important on the exchange market even than an epidemic in the example of Covid-19. Our results suggest that the pandemic and geopolitical tensions have had a significant impact on cryptocurrency prices, but investor sentiment has played a crucial role in exacerbating price volatility. Additionally, we demonstrate the effectiveness of fractionally integrated models in predicting cryptocurrency prices during times of crisis. In summary, this study provides important insights into the dynamics of cryptocurrency markets during global crises, highlighting the need for sophisticated modeling techniques to effectively capture the complexities of these markets.