: Plain or crude Monte Carlo simulation (CMC) is commonly applied for estimating multiperiod tail risk measures such as value-at-risk (VaR) and expected shortfall (ES). After fitting a volatility model to the past history of returns and estimating the conditional distribution of innovations, one...

We develop a theoretical model to compare forecast uncertainty estimated from time-series models to those available from survey density forecasts. The sum of the average variance of individual densities and the disagreement is shown to approximate the predictive uncertainty from well-specified...