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 pa-rameters controlling the strength of correlation between variables and that are governed by a latentMarkov process. To estimate model parameters by maximum likelihood, we consider a two-stepprocedure carried out through the Expectation–Maximisation algorithm. To address the main com-putational burden related to the estimation of the matrix of dependence parameters and the num-ber 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 goodfinite sample properties and the estimation procedure is computationally efficient. An applicationconcerning log-returns of five cryptocurrencies shows that the model permits identifying bull andbear market periods based on the intensity of the correlations between crypto assets.