The underlying volatility at a given time is called conditional volatility at this particular time and is modeled by various ARMA-GARCH conditional variance equations (GARCH, EGARCH, GJR, APARCH, IGARCH). How important are oil price fluctuations and oil price volatility in foreign exchange markets and stock markets? What is the nature of the relationship between these three markets? What are the political implications if volatility, using appropriate models to determine, turns out to be important? We evaluate these questions empirically, using the specification of Narayan and Narayan (2010). This specification, in our paper, deals with the determination of volatility appropriate models, based on information criteria, of the ARMA-ARCH family conditional volatility of oil returns using daily data for each country independently (i), and revolve around an analysis of the effect of the volatility of black gold price on the returns of the other two markets in Oil Importing Developed Countries category (ii). The selection of appropriate models of oil returns according to the period of the chosen data gives the ARMA(2,2)- GJR(1,2) model for the Germany and the ARMA(2,2)-GJR(2,2) model for the Japan and the USA. The results that the conditional variances of oil returns, foreign exchange market returns and stock market returns are contested and they have a long-term relationship in different countries. In addition, the results of the granger causality tests and the study of impulse response functions have shown that it has a sending effect of the volatility of oil prices on most foreign exchange markets and stock markets, highlighting the strong explanatory power of market volatility, but bidirectional causality is not always present. Our empirical results involved in the prevention of shocks are important for policymakers, for portfolio managers seeking optimal portfolio allocation, for monetary authorities who are studying changes in the exchange rate of the national currency against currencies, for oil-importing countries seeking to minimize their spending on crude oil, and for oil-exporting countries seeking the sound management of oil reserves. They also show that the volatility of crude oil prices on the world market is generally more significant for foreign exchange and stock markets than the volatility of oil price in the local market. This main conclusion gives political implications to policymakers.

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.

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.

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