Contrasting cryptocurrencies with other assets: Full distributions and the COVID impact

We investigate any similarity and dependence based on the full distributions of cryptocurrency assets, stock indices and industry groups. We characterize full distributions with entropies to account for higher moments and non-Gaussianity of returns. Divergence and distance between distributions are measured by metric entropies, and are rigorously tested for statistical significance. We assess the stationarity and normality of assets, as well as the basic statistics of cryptocurrencies and traditional asset indices, before and after the COVID-19 pandemic outbreak. These assessments are not subjected to possible misspecifications of conditional time series models which are also examined for their own interests. We find that the NASDAQ daily return has the most similar density and co-dependence with Bitcoin daily return, generally, but after the COVID-19 outbreak in early 2020, even S&P500 daily return distribution is statistically closely dependent on, and indifferent from Bitcoin daily return. All asset distances have declined by 75% or more after the COVID-19 outbreak. We also find that the highest similarity before the COVID-19 outbreak is between Bitcoin and Coal, Steel and Mining industries, and after the COVID-19 outbreak is between Bitcoin and Business Supplies, Utilities, Tobacco Products and Restaurants, Hotels, Motels industries, compared to several others. This study shed light on examining distribution similarity and co-dependence between cryptocurrencies and other asset classes.