This article proposes a time-varying nonparametric estimator and a time-varying semiparametric estimator of the correlation matrix. We discuss representation, estimation based on kernel smoothing and inference. An extensive Monte Carlo simulation study is performed to compare the semiparametric and nonparametric models with the DCC speci fication. Our bivariate simulation results show that the semiparametric and nonparametric models are best in DGPs with gradual changes or structural breaks in correlations. However, in DGPs with rapid changes or constancy in correlations the DCC delivers the best outcome. Moreover, in multivariate simulations the semiparametric and nonparametric models fare the best in DGPs
with substantial time-variability in correlations, while when allowing for little variability in the correlations the DCC is the dominant speci fication. The methodologies are illustrated by estimating the correlations for two interesting portfolios. The rst portfolio consists of
the equity sectors SPDRs and the S&P 500 composite, while the second one contains major currencies that are actively traded in the foreign exchange market. Portfolio evaluation results show that the nonparametric estimator generally dominates its competitors, with a statistically significant lower portfolio variance.