Exploring the dependencies among main cryptocurrency log-returns: A hidden Markov model

A hidden Markov model is proposed for the analysis of time-series of daily log-returns of the last 4 years of Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash. These log-returns are assumed to have a multivariate Gaussian distribution conditionally on a latent Markov process having a finite number of regimes or states. The hidden regimes represent different market phases identified through distinct vectors of expected values and variance–covariance matrices of the log-returns, so that they also differ in terms of volatility. Maximum-likelihood estimation of the model parameters is carried out by the expectation–maximisation algorithm, and regimes are singularly predicted for every time occasion according to the maximum-a-posteriori rule. Results show three positive and three negative phases of the market. In the most recent period, an increasing tendency towards positive regimes is also predicted. A rather heterogeneous correlation structure is estimated, and evidence of structural medium term trend in the correlation of Bitcoin with the other cryptocurrencies is detected.