  A new robust stochastic volatility (SV) model having Student-t marginals is
proposed. Our process is defined through a linear normal regression model
driven by a latent gamma process that controls temporal dependence. This gamma
process is strategically chosen to enable us to find an explicit expression for
the pairwise joint density function of the Student-t response process. With
this at hand, we propose a composite likelihood (CL) based inference for our
model, which can be straightforwardly implemented with a low computational
cost. This is a remarkable feature of our Student-t SV process over existing SV
models in the literature that involve computationally heavy algorithms for
estimating parameters. Aiming at a precise estimation of the parameters related
to the latent process, we propose a CL Expectation-Maximization algorithm and
discuss a bootstrap approach to obtain standard errors. The finite-sample
performance of our composite likelihood methods is assessed through Monte Carlo
simulations. The methodology is motivated by an empirical application in the
financial market. We analyze the relationship, across multiple time periods,
between various US sector Exchange-Traded Funds returns and individual
companies' stock price returns based on our novel Student-t model. This
relationship is further utilized in selecting optimal financial portfolios.
