Malte Knüppel Bücher

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 joint estimation of forecast uncertainty for all horizons in such samples are investigated. Considering optimal forecasts, the efficiency gains can be substantial if the sample is not too large. If forecast uncertainty is estimated by seemingly unrelated regressions, the covariance matrix of the squared forecast errors does not have to be estimated, but simply needs to have a certain structure. In Monte Carlo studies it is found that seemingly unrelated regressions mostly yield estimates which are more efficient than the sample means even if the forecasts are not optimal. Seemingly unrelated regressions are used to address questions concerning the inflation forecast uncertainty of the Bank of England. -- Multi-step-ahead forecasts ; forecast error variance ; GLS ; SUR

The linear pool is the most popular method for combining density forecasts. We analyze the linear pool's implications concerning forecast uncertainty in a new theoretical framework that focuses on the mean and variance of each density forecast to be combined. Our results show that, if the variance predictions of the individual forecasts are unbiased, the well-known 'disagreement' component of the linear pool exacerbates the upward bias of the linear pool's variance prediction. Moreover, we find that disagreement has no predictive content for ex-post forecast uncertainty under conditions which can be empirically relevant. These findings suggest the removal of the disagreement component from the linear pool. The resulting centered linear pool outperforms the linear pool in simulations and in empirical applications to inflation and stock returns

In recent years, survey-based measures of expectations and disagreement have received increasing attention in economic research. Many forecast surveys ask their participants for fixed-event forecasts. Since fixed-event forecasts have seasonal properties, researchers often use an ad-hoc approach in order to approximate fixed-horizon forecasts using fixed-event forecasts. In this work, we derive an optimal approximation by minimizing the mean-squared approximation error. Like the approximation based on the ad-hoc approach, our approximation is constructed as a weighted sum of the fixed-event forecasts, with easily computable weights. The optimal weights tend to differ substantially from those of the ad-hoc approach. In an empirical application, it turns out that the gains from using optimal instead of ad-hoc weights are very pronounced. While our work focusses on the approximation of fixedhorizon forecasts by fixed-event forecasts, the proposed approximation method is very flexible. The forecast to be approximated as well as the information employed by the approximation can be any linear function of the underlying high-frequency variable. In contrast to the ad-hoc approach, the proposed approximation method can make use of more than two such informationcontaining functions.

Recently, several institutions have increased their forecast horizons, and many institutions rely on their past forecast errors to estimate measures of forecast uncertainty. This work addresses the question how the latter estimation can be accomplished if there are only very few errors available for the new forecast horizons. It extends upon the results of Knüppel (2014) in order to relax the condition on the data structure required for the SUR estimator to be independent from unknown quantities. It turns out that the SUR estimator of forecast uncertainty tends to deliver large efficiency gains compared to the OLS estimator (i.e. the sample mean of the squared forecast errors) in the case of increased forecast horizons. The SUR estimator is applied to the forecast errors of the Bank of England and the FOMC

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 banks own interest rate expectations. From a theoretical point of view, the latter should yield the highest forecast accuracy. The lowest accuracy can be expected from forecasts conditioned on constant interest rates. However, when investigating the predictive accuracy of the forecasts for interest rates, inflation and output growth made by the Bank of England and the Banco do Brasil, we hardly find any significant differences between the forecasts based on different interest assumptions. We conclude that the choice of the interest rate assumption, while being a major concern from a theoretical point of view, appears to be at best of minor relevance empirically.

The evaluation of multi-step-ahead density forecasts is complicated by the serial correlation of the corresponding probability integral transforms. In the literature, three testing approaches can be found which take this problem into account. However, these approaches can be computationally burdensome, ignore important information and therefore lack power, or suffer from size distortions even asymptotically. In this work, a fourth testing approach based on raw moments is proposed. It is easy to implement, uses standard critical values, can include all moments regarded as important, and has correct asymptotic size. It is found to have good size and power properties if it is based directly on the (standardized) probability integral transforms. -- Density forecast evaluation ; normality tests