  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.
