Resumen
In this paper we propose the local maximum likelihood method for dynamically estimate copula parameters. We study the estimates statistical properties and derive the expression for their asymptotic variance in the case of Gaussian copulas. The local estimates are able to detect temporal changes in the strength of dependence among assets. These dynamics are combined with a GARCH type modeling of each individual asset to estimate the Value- at-Risk. The performance of the proposed estimates is investigated through Monte Carlo simulation experiments. In an application using real data, an out-of-sample test indicated that the new methodology may outperform the constant copula model when it comes to Value-at-Risk estimation.