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This article proposes a new methodology to estimate the Value at Risk (VaR) in a time varying heteroscedastic dynamic regression context. The methodology assumes that the form of the model and its information set may also change over time and takes into account the uncertainty associated with the joint selection of model and information set, providing more reliability to the elaborated forecasts. A Bayesian framework is adopted and a cross validation selection criterion, asymptotically equivalent to the Bayes factor, is proposed. Finally, we estimate the VaR on line of five international equity indexes. Our VaR estimations tend to follow the evolution of the series more closely than classical procedures by keeping the coverage properties.
