Several works in the literature have focused on the analysis of key stylized facts of financial and cryptocurrency returns linked to fundamental problems of efficiency and predictability of financial and cryptocurrency markets, including heavy tails, absence of linear autocorrelations and volatility clustering. This paper provides a study of the above properties of Bitcoin and Ethereum markets using recently proposed robust, valid and statistically justified definitions of and methods for inference on market (in)efficiency, volatility clustering, and nonlinear dependence in return time series. In contrast to existing approaches, the inference methods used in the analysis are robust to heavy-tailedness, dependence and nonlinear dynamics of returns. The results of the study indicate that Bitcoin and Ethereum returns exhibit heavy tails, uncorrelatedness over time and volatility clustering largely similar to those in developed financial markets. The analysis has important implications for cryptocurrency pricing, market efficiency, econometric modelling, risk management, market participants and regulators.
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