Multifractal Cross-Correlations of Dirty and Clean Cryptocurrencies with main financial indices

We investigate the long-range cross-correlation and cross-multifractality between the “dirty” and “clean” cryptocurrencies and the major financial assets: the Dow Jones Index (DJI), the Euro–Dollar exchange rate (EURUSD), and Gold. The analysis shows a high long-range correlation between most pairs with some exceptions, including the DJI–Ripple and Gold–Polygon. When the DJI is paired with clean cryptocurrencies such as Polygon and Cardano, they exhibit multifractal properties. As for the EURUSD–BTC and Gold–BTC, these two pairs demonstrated the highest level of multifractality in their corresponding pairs. All pairs of cryptocurrencies and main financial indices are persistent, with the exceptions of EURUSD–POLYGON (H = 0 . 4970 ± 0 . 0048 for q =2), GOLD–BTC (H = 0 . 5039 ± 0 . 0058 for q =2) and GOLD–LTC (H = 0 . 5044 ± 0 . 0057 for q =2) that are Brownian, and GOLD–POLYGON (H = 0 . 4917 ± 0 . 0055 for q =2) which is anti-persistent. For q =5, all are anti-persistent, except DJI-Eth, XRP, and ADA are Brownian, and EURUSD-XRP is persistent. We also assessed the asymmetric persistence behavior when the market is upward or downward and found that for the pairs involving dirty cryptocurrencies with DJI and EURUSD, there is a higher level of persistence during the downward market. On the other hand, Gold-related pairs were almost symmetric. Thus, we identified the complexity and variability of the cryptocurrency pairs with the traditional financial instruments, which shows their various reactions to the changes in the market and types of assets. • Most crypto-financial pairs show strong long-range correlation, with some exceptions. • DJI pairs with clean cryptos like Polygon and Cardano show notable multifractality. • BTC pairs show the highest multifractality: EURUSD–BTC and Gold–BTC lead overall. • Most pairs are persistent, except EURUSD–POLYGON, GOLD–BTC, GOLD–LTC, and GOLD–POLYGON. • Dirty cryptos stay linked to DJI, EURUSD in downturns; Gold shows symmetric behavior.