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

Abstract

A multivariate hidden Markov model is proposed to explain the price evolution of Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash. The observed daily log-returns of these five major cryptocurrencies are modeled jointly. They are assumed to be correlated according to a variance-covariance matrix conditionally on a latent Markov process having a finite number of states. For the purpose of comparing states according to their volatility, we estimate specific variance-covariance matrix varying across states. Maximum likelihood estimation of the model parameters is carried out by the Expectation-Maximization algorithm. The hidden states represent different phases of the market identified through the estimated expected values and volatility of the log-returns. We reach interesting results in detecting these phases of the market and the implied transition dynamics. We also find evidence of structural medium term trend in the correlations of Bitcoin with the other cryptocurrencies.