## Person: Krüger, Fabian

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#### Four Essays on Probabilistic Forecasting in Econometrics

2013, Krüger, Fabian

This dissertation is concerned with probabilistic forecasting, which has been a vivid research area within econometrics during the past few years. Probabilistic forecasts indicate a predictive probability distribution for a variable of interest. Thus, they contain forecasts of all possible features of the predictand, like its mean, quantiles, and variance, and can serve as a basis for decision making in very general settings. This is an important aspect, since decision making is arguably the key motivation behind constructing forecasts in the first place. In particular, probabilistic forecasts are useful in situations in which the forecaster and the forecast user(s) are not the same person. By issuing a probabilistic

prediction, a forecaster fully communicates her uncertainty about the future, and thus allows potential users to put the forecast in perspective. Perhaps the most popular economic examples of this situation are so-called "fan charts" of inflation issued by several central banks around the world.

The demand for probabilistic forecasts raises two basic questions: First, what is a good probabilistic forecast? Second, how can it be constructed? Broadly, each of the four chapters of this thesis deals with one or both of these questions. The chapters are stand-alone research papers which I have written, three of them jointly with coauthors as mentioned below, during my PhD studies at the University of Konstanz.

Chapters 1 and 2 deal with the case of a binary predictand. In this case, a probabilistic forecast is simply a number between zero and one. This simplifies many conceptual and technical issues about forecast evaluation. At the same time, the binary case is relevant in practice – for example, assessments of the probability of a recession, or the probability of a sovereign defaulting on its debt, are routinely reported in the financial press. Chapters 3 and 4 deal with more complicated (continuous or mixed discrete-continuous) predictands, which also arise in many applied settings.

#### Combining survey forecasts and time series models : the case of the Euribor

2010, Krüger, Fabian, Mokinski, Frieder, Pohlmeier, Winfried

This paper reinterprets Maganelli’s (2009) idea of “Forecasting with Judgment” to obtain a dynamic algorithm for combining survey expectations data and time series models for macroeconomic forecasting. Existing combination approaches typically obtain combined forecasts by linearly weighting individual forecasts. The approach presented here instead uses survey forecasts in the estimation stage of a time series model. Thus an estimate of the model parameters is obtained that reflects two sources of information: a history of realizations of the variables that are involved in the time series model and survey expectations on the future course of the variable that is to be forecast. The idea at the estimation stage is to shrink parameter estimates towards values that are compatible (in an appropriate sense) with the survey forecasts that have been observed. It is exemplified how this approach can be applied to different autoregressive time series models. In an empirical application, the approach is used to forecast the three-month Euribor at a six-month horizon.

#### Disagreement, Uncertainty and the True Predictive Density

2011, Krüger, Fabian, Nolte, Ingmar

This paper generalizes the discussion about disagreement versus uncertainty in macroeconomic survey data by emphasizing the importance of the (unknown) true predictive density. Using a forecast combination approach, we ask whether cross sections of survey point forecasts help to approximate the true predictive density. We find that although these cross-sections perform poorly individually, their inclusion into combined predictive densities can significantly improve upon densities relying solely on time series information.

#### Combining survey forecasts and time series models : the case of the Euribor

2011, Krüger, Fabian, Mokinski, Frieder, Pohlmeier, Winfried

This paper reinterprets Maganelli's (2009) idea of "Forecasting with Judgment" to obtain a dynamic algorithm for combining survey expectations data and time series models for macroeconomic forecasting. Existing combination approaches typically obtain combined forecasts by linearly weighting individual forecasts. The approach presented here instead uses survey forecasts in the estimation stage of a time series model. Thus an estimate of the model parameters is obtained that reflects two sources of information: a history of realizations of the variables that are involved in the time series model and survey expectations on the future course of the variable that is to be forecast. The idea at the estimation stage is to shrink parameter estimates towards values that are compatible (in an appropriate sense) with the survey forecasts that have been observed. It is exemplified how this approach can be applied to different autoregressive time series models. In an empirical application, the approach is used to forecast the three-month Euribor at a six-month horizon.