The uncertainty of conditional returns, volatilities and correlations in DCC models

When forecasting conditional correlations that evolve according to a Dynamic Conditional Correlation (DCC) model, only point forecasts can be obtained at each moment of time. In this paper, we analyze the finite sample properties of a bootstrap procedure to approximate the density of these forecast that also allows obtaining conditional densities for future returns and volatilities. The procedure is illustrated by obtaining conditional forecast intervals and regions of returns, volatilities and correlations in the context of a system of daily exchange rates returns of the Euro, Japanese Yen and Australian Dollar against the US Dollar.