Interpretation of point forecasts with unkown directive

TL;DR

This paper develops a methodology to identify unknown point forecast functionals from time series data, focusing on state-dependent quantiles and expectiles, and demonstrates its effectiveness through simulations and empirical examples.

Contribution

It introduces a generalized method of moments estimator and optimality tests for unknown forecast functionals, addressing hidden directives in point forecasts.

Findings

Optimality test is better calibrated and more powerful than existing solutions.

Empirical examples show overstatement in GDP and precipitation forecasts.

Methodology effectively identifies hidden forecast functionals.

Abstract

Point forecasts can be interpreted as functionals (i.e., point summaries) of predictive distributions. We consider the situation where forecasters' directives are hidden and develop methodology for the identification of the unknown functional based on time series data of point forecasts and associated realizations. Focusing on the natural cases of state-dependent quantiles and expectiles, we provide a generalized method of moments estimator for the functional, along with tests of optimality relative to information sets that are specified by instrumental variables. Using simulation, we demonstrate that our optimality test is better calibrated and more powerful than existing solutions. In empirical examples, Greenbook gross domestic product (GDP) forecasts of the US Federal Reserve and model output for precipitation from the European Centre for Medium-Range Weather Forecasts (ECMWF) are indicative of overstatement in anticipation of extreme events.