Abstract. In this article we propose a statistical model to adjust, interpolate and forecast the term structure of interest rates. This model is based on extensions for the term structure model of interest rates proposed by [Diebold & Li, 2006], through a Bayesian estimation using Markov Chain Monte Carlo. The proposed extensions involve the use of a more flexible parametric form for the yield curve, making all parameters time-varying using a structure of latent factors, and adding a stochastic volatility structure to control the presence of conditional heteroscedasticity observed in the interest rates.The Bayesian estimation enables the exact distribution of estimators in finite samples, and as a sub product, the estimation enables obtaining the distribution of forecasts for the term structure of interest rates. The methodology developed does not need a pre-interpolation of the yield curve as it happens in some econometric models of term structure. We do an empirical exercise of this methodology in which we adjust daily data of the term structure of interest rates implicit in Swap DI-PRÉ contracts traded in the Mercantile and Futures Exchange (BM&F)

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The parameters of popular multivariate GARCH (MGARCH) models are restricted so that their estimation is feasible in large systems and covariance stationarity and positive definiteness of conditional covariance matrices are guaranteed. These restrictions limit the dynamics that the models can represent, assuming, for example, that volatilities evolve in an univariate fashion, not being related neither among them nor with the correlations. This paper updates previous surveys on parametric MGARCH models focusing on their limitations to represent the dynamics observed in real systems of financial returns. The conclusions are illustrated using simulated data and a five-dimensional system of exchange rate returns.

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