Testing Quantile Forecast Optimality

TL;DR

This paper develops misspecification tests for quantile forecasts across multiple horizons and quantiles, assessing their optimality and providing insights into sub-optimality causes in financial and macroeconomic data.

Contribution

It introduces new tests based on Mincer-Zarnowitz regressions for evaluating the optimality of quantile forecasts over multiple horizons and information sets.

Findings

Tests reveal instances of forecast sub-optimality in financial returns.

Empirical applications demonstrate the tests' ability to diagnose causes of forecast inefficiency.

Simulation shows good finite sample performance of the proposed tests.

Abstract

Quantile forecasts made across multiple horizons have become an important output of many financial institutions, central banks and international organisations. This paper proposes misspecification tests for such quantile forecasts that assess optimality over a set of multiple forecast horizons and/or quantiles. The tests build on multiple Mincer-Zarnowitz quantile regressions cast in a moment equality framework. Our main test is for the null hypothesis of autocalibration, a concept which assesses optimality with respect to the information contained in the forecasts themselves. We provide an extension that allows to test for optimality with respect to larger information sets and a multivariate extension. Importantly, our tests do not just inform about general violations of optimality, but may also provide useful insights into specific forms of sub-optimality. A simulation study investigates the finite sample performance of our tests, and two empirical applications to financial returns and U.S. macroeconomic series illustrate that our tests can yield interesting insights into quantile forecast sub-optimality and its causes.