On stylized facts of cryptocurrencies returns and their relationship with other assets, with a focus on the impact of COVID-19

This study provides an empirical analysis on the main univariate and multivariate stylized facts iin return series of the two of the largest cryptocurrencies, namely Ethereum and Bitcoin. A Markov-Switching Vector AutoRegression model is considered to further explore the dynamic relationships between cryptocurrencies and other financial assets. We estimate the presence of volatility clustering, a rapid decay of the autocorrelation function, an excess of kurtosis and multivariate little cross-correlation across the series, except for contemporaneous returns. The analysis covers the pandemic period and sheds lights on the behaviour of cryptocurrencies under unexpected extreme events.

Local and Overall Deviance R-Squared Measures for Mixtures of Generalized Linear Models.

In generalized linear models (GLMs), measures of lack of fit are typically defined as the deviance between two nested models, and a deviance-based R2 is commonly used to evaluate the fit. In this paper, we extend deviance measures to mixtures of GLMs, whose parameters are estimated by maximum likelihood (ML) via the EM algorithm. Such measures are defined both locally, i.e., at cluster-level, and globally, i.e., with reference to the whole sample. At the cluster-level, we propose a normalized two-term decomposition of the local deviance into explained, and unexplained local deviances. At the sample-level, we introduce an additive normalized decomposition of the total deviance into three terms, where each evaluates a different aspect of the fitted model: (1) the cluster separation on the dependent variable, (2) the proportion of the total deviance explained by the fitted model, and (3) the proportion of the total deviance which remains unexplained. We use both local and global decompositions to define, respectively, local and overall deviance R2 measures for mixtures of GLMs, which we illustrate-for Gaussian, Poisson and binomial responses-by means of a simulation study. The proposed fit measures are then used to assess, and interpret clusters of COVID-19 spread in Italy in two time points.