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

Point forecasts can be obtained at each moment of time when forecasting conditional correlations that evolve according to a Dynamic Conditional Correlation (DCC) model. However, measuring the uncertainty associated with these forecasts is of interest in many situations. The finite sample properties of a bootstrap procedure for approximating the forecast densities of future returns, volatilities and correlations, are analyzed using simulated data and illustrated by obtaining conditional forecast intervals and regions in the context of a three-dimensional system of daily exchange rate returns.