The linear pool is the most popular method for combining density forecasts. We analyze its implications concerning forecast uncertainty, using a new framework that focuses on the means and variances of the individual and combined forecasts. Our results show that, if the variance predictions of...

Multivariate distributional forecasts have become widespread in recent years. To assess the quality of such forecasts, suitable evaluation methods are needed. In the univariate case, calibration tests based on the probability integral transform (PIT) are routinely used. However, multivariate...

The interest rate assumptions for macroeconomic forecasts differ considerably among central banks. Common approaches are given by the assumption of constant interest rates, interest rates expected by market participants, or the central bank's own interest rate expectations. From a theoretical...

A probabilistic assessment about the set of possible trajectories that a random variable may follow over time is summarized by the simultaneous confidence region generated from its forecast generating distribution. However, if the null model is only approximative or altogether unavailable, one...

In this paper, we investigate the implications of the two concepts of asymmetry defined by Sichel (1993) - deepness and steepness - for first-order autoregressive processes with a Markov-switching intercept. In order to do so, we derive the two required formulas determining the coefficient of...

This paper discusses methods to quantify risk and uncertainty in macroeconomic forecasts. Both, parametric and non-parametric procedures are developed. The former are based on a class of asymmetrically weighted normal distributions whereas the latter employ asymmetric bootstrap simulations. Both...

Macroeconomic risk assessments play an important role in the forecasts of many institutions. However, to the best of our knowledge their performance has not been investigated yet. In this work, we study the Bank of England?s risk forecasts for inflation. We find that these forecasts do not...

Multi-step-ahead forecasts of forecast uncertainty in practice are often based on the horizon-specific sample means of recent squared forecast errors, where the number of available past forecast errors decreases one-to-one with the forecast horizon. In this paper, the efficiency gains from the...

Measuring and displaying uncertainty around path-forecasts, i.e. forecasts made in period T about the expected trajectory of a random variable in periods T+1 to T+H is a key ingredient for decision making under uncertainty. The probabilistic assessment about the set of possible trajectories that...

Macroeconomic risk assessments play an important role in the forecasts of many institutions. A risk forecast is related to the potential asymmetry of the forecast density. In this work, we investigate how the optimality of such risk forecasts can be tested. We find that the Pearson mode skewness...