Maximum Likelihood Estimation of Multivariate Regime Switching Student-t Copula Models

We propose a multivariate regime switching model based on a Student- $t$ copula function with parameters controlling the strength of correlation between variables and that are governed by a latent Markov process. To estimate model parameters by maximum likelihood, we consider a two-step procedure carried out through the Expectation–Maximisation algorithm. To address the main computational burden related to the estimation of the matrix of dependence parameters and the number of degrees of freedom of the Student- $t$ copula, we show a novel use of the Lagrange multipliers, which simplifies the estimation process. The simulation study shows that the estimators have good finite sample properties and the estimation procedure is computationally efficient. An application concerning log-returns of five cryptocurrencies shows that the model permits identifying bull and bear market periods based on the intensity of the correlations between crypto assets.