In this paper we test for regime changes and possible regime commonalities in the price dynamics of Bitcoin, Ethereum, Litecoin and Monero, as representatives of the cryptocurrencies asset class. Several parametric models are considered for the joint dynamics of the basket price where parameters are modulated through a Hidden Markov Chain with finite state space. Best specifications within Gaussian and Autoregressive models for price differences are selected by means of the AIC and BIC information criteria and through an out-of-sample forecasting performance. The empirical results, within the period January 2016 to October 2019, suggest that three or four states may be relevant to describe the dynamics of each individual cryptocurrency, depending on the selection criteria, while the entire basket displays at most three common states. Finally, we show how the identification of appropriate models may be exploited in order to build profitable investment strategies on the considered cryptocurrencies.
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