Combining Forecasts under Structural Breaks Using Graphical LASSO

TL;DR

This paper introduces a novel machine learning approach using Graphical LASSO to improve forecast combination by accounting for common errors, structural breaks, and regime changes, demonstrated with macroeconomic data.

Contribution

It develops the Regime-Dependent Factor Graphical LASSO method for dynamic forecast combination, incorporating regime-specific error structures and scalable estimation techniques.

Findings

FGL effectively separates common and idiosyncratic forecast errors.

RD-FGL adapts to regime changes, improving forecast accuracy.

Empirical results show superior performance over traditional methods.

Abstract

In this paper we develop a novel method of combining many forecasts based on a machine learning algorithm called Graphical LASSO (GL). We visualize forecast errors from different forecasters as a network of interacting entities and generalize network inference in the presence of common factor structure and structural breaks. First, we note that forecasters often use common information and hence make common mistakes, which makes the forecast errors exhibit common factor structures. We use the Factor Graphical LASSO (FGL, Lee and Seregina (2023)) to separate common forecast errors from the idiosyncratic errors and exploit sparsity of the precision matrix of the latter. Second, since the network of experts changes over time as a response to unstable environments such as recessions, it is unreasonable to assume constant forecast combination weights. Hence, we propose Regime-Dependent Factor Graphical LASSO (RD-FGL) that allows factor loadings and idiosyncratic precision matrix to be regime-dependent. We develop its scalable implementation using the Alternating Direction Method of Multipliers (ADMM) to estimate regime-dependent forecast combination weights. The empirical application to forecasting macroeconomic series using the data of the European Central Bank's Survey of Professional Forecasters (ECB SPF) demonstrates superior performance of a combined forecast using FGL and RD-FGL.