Since the industrial revolution, the geopolitics of energy has been a driver of global prosperity and security, and determines the survival of life on our planet. This study examines the nonlinear structure and multifractal behavior of the cross-correlation between geopolitical risk and energy markets (West Texas Intermediate (WTI), Brent, natural gas and heating oil), using the multifractal detrended cross-correlation analysis. Furthermore, an in-depth analysis reveals different associations of the indices of overall geopolitical risk, geopolitical acts, and geopolitical threats against the four energy products. Based on daily data ranging from 1 January 1985 to 30 August 2021, the findings confirm the presence of nonlinear dependencies, suggesting that geopolitical risk and energy markets are interlinked. Furthermore, significant multifractal characteristics are found and the degree of multifractality is stronger between the overall geopolitical risk and WTI while the lowest degree of multifractality is with Brent. Overall, for the WTI and heating-oil markets, the influence of geopolitical threats is more pronounced rather than their fulfilment. Contrarily, the Brent and natural gas are more correlated to geopolitical acts. Energy products exhibit heterogeneous persistence levels of cross-correlation with all the indicators of geopolitical risk, being more persistent in the case of small fluctuations compared to large fluctuations.

The dramatic deregulatory reforms in US electricity markets increased competition, resulting in more complex prices compared to other commodities. This paper aims to investigate and compare the overall and time-varying multifractality and efficiency of four major US electricity regions: Mass Hub, Mid C, Palo Verde, and PJM West. Multifractal detrended fluctuation analysis (MFDFA) is employed to better quantify the intensity of self-similarity. Large daily data from 2001 to 2021 are taken in order to make a more conclusive analysis. The four electricity market returns showed strong multifractal features with PJM West having the highest multifractality (corresponding to lowest efficiency) and Mass Hub having the lowest multifractality (i.e., highest efficiency). Moreover, all series exhibited mean reverting (anti-persistent) behavior in the overall time period. The findings of MFDFA rolling window suggest Palo Verde as the most volatile index, while a significant upward trend in the efficiency of Mass Hub and PJM West is observed after the first quarter of 2014. The novel findings have important implications for policymakers, regulatory authorities, and decision makers to forecast electricity prices better and control efficiency.

There is ample evidence that Islamic stock markets perform differently from conventional stock markets, particularly when economic policy uncertainty (EPU) or any other uncertainty such as geopolitical uncertainty is present. Considering this context, this paper examines the US EPU’s cross-correlation with both conventional and Islamic stock markets from the perspective of multifractality. Daily stock market prices of five main countries are considered: US, Thailand, Indonesia, Pakistan, and India. Using the multifractal detrended cross-correlation analysis (MF-DCCA), we validate the existence of long-range cross-correlation between US EPU and all the stock markets considered, demonstrating that all pairs of US EPU have strong power law and multifractal characteristics. Furthermore, all pairs display varying levels of multifractal strength, with the US EPU and US conventional stock market exhibiting the strongest multifractal patterns. Additionally, a cross-correlation between US EPU and the different stock markets is found to be persistent. The results of this study are pertinent to the various market participants in both conventional and Islamic markets, particularly investors, who may be able to draw useful conclusions from them for purposes such as portfolio diversification.

Jump dynamics in financial markets exhibit significant complexity, often resulting in increased probabilities of subsequent jumps, akin to earthquake aftershocks. This study aims to understand these complexities within a multifractal framework. To do this, we employed the high-frequency intraday data from six major cryptocurrencies (Bitcoin, Ethereum, Litecoin, Dashcoin, EOS, and Ripple) and six major forex markets (Euro, British pound, Canadian dollar, Australian dollar, Swiss franc, and Japanese yen) between 4 August 2019 and 4 October 2023, at 5 min intervals. We began by extracting daily jumps from realized volatility using a MinRV-based approach and then applying Multifractal Detrended Fluctuation Analysis (MFDFA) to those jumps to explore their multifractal characteristics. The results of the MFDFA—especially the fluctuation function, the varying Hurst exponent, and the Renyi exponent—confirm that all of these jump series exhibit significant multifractal properties. However, the range of the Hurst exponent values indicates that Dashcoin has the highest and Litecoin has the lowest multifractal strength. Moreover, all of the jump series show significant persistent behavior and a positive autocorrelation, indicating a higher probability of a positive/negative jump being followed by another positive/negative jump. Additionally, the findings of rolling-window MFDFA with a window length of 250 days reveal persistent behavior most of the time. These findings are useful for market participants, investors, and policymakers in developing portfolio diversification strategies and making important investment decisions, and they could enhance market efficiency and stability.