LGB+: A Macroeconomic Forecasting Road Test

2026-05-10

AI Summary

This study addresses the challenge that traditional gradient boosting trees struggle to effectively model time series dominated by linear dynamics in small-sample macroeconomic forecasting. To overcome this limitation, the authors propose LGB+, an enhanced method that jointly embeds linear and nonlinear basis functions within a boosting framework. At each boosting iteration, LGB+ dynamically selects the superior basis function based on out-of-bag data—or alternatively employs a fixed alternating strategy (denoted LGB^A+)—without requiring prior specification of functional forms. The approach naturally decomposes predictions into interpretable components, including variable importance and historical weights. Empirical results on U.S. quarterly macroeconomic forecasting demonstrate that LGB+ significantly improves predictive accuracy for targets exhibiting strong autoregressive behavior or mixed linear–nonlinear signals.

Abstract

Needless to say, linear dynamics are pervasive in economic time series, particularly autoregressive ones. While gradient boosting with trees excels at capturing nonlinearities, it is inefficient in small samples when much of the predictive content is linear, expending splits to approximate relationships better captured by simple linear terms. This paper proposes LGB+, a boosting procedure operating on a more inclusive set of basis functions. The idea comes in two flavors. LGB+ evaluates a tree and a linear candidate at each step against out-of-bag data; only the winner advances. The simpler variant, LGB^A+, alternates on a fixed schedule: a block of tree updates, then a greedy linear correction, repeat. Both designs avoid ex ante commitments to any particular functional form or predictor selection. Because the prediction is the sum of a linear and a tree component, forecasts decompose natively into linear and nonlinear contributions, and so does permutation-based variable importance and historical proximity weights. In a quarterly U.S. macroeconomic forecasting exercise, LGB+ delivers strong gains for targets with pronounced autoregressive dynamics or mixed linear-nonlinear signals. Variables dominating the linear channel are those operating through autoregressive persistence or near-accounting relationships to the target (e.g., initial claims for unemployment and building permits for housing starts).

Problem

• macroeconomic forecasting
• linear dynamics
• gradient boosting
• autoregressive processes
• nonlinearities

Innovation

• LGB+
• linear-tree boosting
• macroeconomic forecasting
• adaptive basis functions
• forecast decomposition