Title: Maximum likelihood estimation of multivariate regime switching Student-t copula models
Authors: Fulvia Pennoni - University of Milano-Bicocca (Italy)
Francesco Bartolucci - University of Perugia (Italy)
Federico Cortese - University of Milano-Bicocca (Italy) [presenting]
Abstract: A multivariate regime-switching model is presented based on a Student-$t$ copula function with parameters governed by a latent Markov process of the first order. We consider a two-step procedure carried out through the Expectation-Maximization algorithm to estimate model parameters. The main computational burdens involve estimating the correlation matrix $R$ and the number of degrees of freedom $\nu$ of the Student $t$-copula. At this aim, we propose to perform the M-step of the algorithm by computing $R$ given $\nu$ using a closed-form solution obtained from a constrained optimization of the log-likelihood using Lagrange multipliers. Then, we numerically maximize the log-likelihood with respect to $\nu$ given the estimate of $R$ obtained at the previous iteration. We validate the proposal through a simulation study which shows the computational efficiency and the good finite sample properties of the estimates. We consider an application concerning daily log-returns of the five cryptocurrencies Bitcoin, Ethereum, Ripple, Litecoin and Bitcoin Cash over a four years period. Results show that a regime-switching Student-$t$ copula model with three states can identify bull, neutral and bear market periods based on the intensity of the correlations among cryptocurrencies.