Tests for Forecast Instability and Forecast Failure under a Continuous Record Asymptotic Framework

TL;DR

This paper introduces a new continuous-time asymptotic framework for testing forecast stability over time, applicable to macroeconomic and financial data, with improved power against short-lasting and tail-end instabilities.

Contribution

It develops a novel continuous-time approach for forecast instability testing, offering robust, powerful tests that outperform existing methods, especially for short or tail-end instabilities.

Findings

Test statistics control size well

High power against short-lasting instabilities

Robust to heteroskedasticity and serial correlation

Abstract

We develop a novel continuous-time asymptotic framework for inference on whether the predictive ability of a given forecast model remains stable over time. We formally define forecast instability from the economic forecaster's perspective and highlight that the time duration of the instability bears no relationship with stable period. Our approach is applicable in forecasting environment involving low-frequency as well as high-frequency macroeconomic and financial variables. As the sampling interval between observations shrinks to zero the sequence of forecast losses is approximated by a continuous-time stochastic process (i.e., an Ito semimartingale) possessing certain pathwise properties. We build an hypotheses testing problem based on the local properties of the continuous-time limit counterpart of the sequence of losses. The null distribution follows an extreme value distribution. While controlling the statistical size well, our class of test statistics feature uniform power over the location of the forecast failure in the sample. The test statistics are designed to have power against general form of insatiability and are robust to common forms of non-stationarity such as heteroskedasticty and serial correlation. The gains in power are substantial relative to extant methods, especially when the instability is short-lasting and when occurs toward the tail of the sample.