a b s t r a c tIn this paper, we establish the asymptotic validity and analyse the finite sample performance of a simple bootstrap procedure for constructing multi-step multivariate forecast densities in the context of non-Gaussian unrestricted VAR models. This bootstrap procedure avoids the backward representation, and, as a consequence, can be used to obtain multivariate forecast densities in, for example, VARMA or VAR-GARCH models. In the context of bivariate stationary VAR(p) models, we show that its finite sample properties are comparable to those of alternatives based on the backward representation. The bootstrap procedure is also implemented in a VAR-DCC model which lacks a backward representation. Finally, joint forecast densities of US quarterly inflation, unemployment and GDP growth are obtained.

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 forecasts 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. Keywords February 2014Abstract 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 forecasts 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.

VAR models are popular to forecast macroeconomic time series. However, the model, the parameters, and the error distribution are rarely known without uncertainty, so bootstrap methods are applied to deal with these sources of uncertainties. In this paper, the performance of the popular forecast Bonferroni cubes based on the Gaussian method and variants of the bootstrap procedure that incorporate error distribution, parameter uncertainty, bias correction, and lag order uncertainty are compared. Monte Carlo simulations suggest that the best performance of bootstrap cubes are obtained when the parameter uncertainty is considered, being the bias and model uncertainties important for long‐run forecast regions in persistent VAR models. Similar conclusions are found in an empirical application based on a four variate system containing US monthly percent changes of the industrial production index, the S&P500 stock market index, its dividend yield, and the unemployment rate.

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