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

Abstract

Abstract 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.