Four Essays on Probabilistic Forecasting in Econometrics

Abstract

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 probabilisticprediction, 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.