Forecast Relative Error Decomposition

TL;DR

This paper introduces new measures for analyzing forecast errors in nonlinear dynamic models, capturing nonlinear dependencies better than traditional methods, with applications across various complex data types.

Contribution

It proposes the Forecast Relative Error Decomposition (FRED), FEKD, and FELD, advancing forecast error analysis in nonlinear settings.

Findings

FRED, FEKD, and FELD outperform FEVD in nonlinear contexts.

Applications demonstrate improved insight into shocks in diverse models.

New measures effectively handle qualitative, count, and volatility data.

Abstract

We introduce a class of relative error decomposition measures that are well-suited for the analysis of shocks in nonlinear dynamic models. They include the Forecast Relative Error Decomposition (FRED), Forecast Error Kullback Decomposition (FEKD) and Forecast Error Laplace Decomposition (FELD). These measures are favourable over the traditional Forecast Error Variance Decomposition (FEVD) because they account for nonlinear dependence in both a serial and cross-sectional sense. This is illustrated by applications to dynamic models for qualitative data, count data, stochastic volatility and cyberrisk.