Generic Conditions for Forecast Dominance

Abstract

Recent studies have analyzed whether one forecast method dominates another under a class of consistent scoring functions. While the existing literature focuses on empirical tests of forecast dominance, little is known about the theoretical conditions under which one forecast dominates another. To address this question, we first derive a new characterization of dominance among forecasts of the mean functional. We then present various scenarios under which dominance occurs. Unlike existing results, our results allow for the case that the forecasts' underlying information sets are not nested, and allow for uncalibrated forecasts that suffer, e.g., from model misspecification or parameter estimation error. We illustrate the empirical relevance of our results via data examples from finance, economics and meteorology.

Testing for more positive expectation dependence with application to model comparison

“…Let π 1 and π 2 be two autocalibrated predictors. Bregman dominance reduces to the convex order for autocalibrated predictors, as pointed out by Kruger and Ziegel (2020).…”

“…Recall that a predictor π is said to be autocalibrated if π(X) = E[Y |π(X)]. We refer the reader to Kruger and Ziegel (2020) for a general presentation of this concept. By Jensen inequality, autocalibration thus ensures that π(X) cx Y .…”

“…Bregman dominance, also called forecast dominance is defined as dominance for every Bregman loss function. Precisely, π 2 outperforms π 1 in terms of Bregman dominance if the inequality E[L(Y, π 2 )] ≤ E[L(Y, π 1 )] holds true for every Bregman loss function L. We refer the interested reader to Kruger and Ziegel (2020) and the references therein for an extensive presentation of this concept.…”

Forecast dominance testing via sign randomization

“…In this case we even have the following. [32] of dominance conditions based on the concept of convex order.…”

Autocalibration and Tweedie-dominance for insurance pricing with machine learning

“…For this reason, we propose a new strategy based on the concept of autocalibration (see, e.g., Kruger and Ziegel, 2020). This approach guarantees global balance as well as local equilibrium in the spirit of the original MMT.…”