A new theory of forecasting - Simone Manganelli (European Central Bank (ECB), 2006)
This paper argues that forecast estimators should minimise the loss function in a statistical, rather than deterministic, way. We introduce two new elements into the classical econometric analysis: a subjective guess on the variable to be forecasted and a probability reflecting the confidence associated to it. We then propose a new forecast estimator based on a test of whether the first derivatives of the loss function evaluated at the subjective guess are statistically different from zero. We show that the classical estimator is a special case of this new estimator, and that in general the two estimators are asymptotically equivalent. We illustrate the implications of this new theory with a simple simulation, an application to GDP forecast and an example of mean-variance portfolio selection.
Keywords: C13; C53; G11; 330; asset allocation; Decision under uncertainty; estimation; overfitting; Prognoseverfahren; Schätztheorie; Theorie; Entscheidung unter Risiko