High-dimensional Forecasting with Known Knowns and Known Unknowns

Forecasts play a central role in decision making under uncertainty. After abrief review of the general issues, this paper considers ways of usinghigh-dimensional data in forecasting. We consider selecting variables from aknown active set, known knowns, using Lasso and OCMT, and approximatingunobserved latent factors, known unknowns, by various means. This combines bothsparse and dense approaches. We demonstrate the various issues involved invariable selection in a high-dimensional setting with an application toforecasting UK inflation at different horizons over the period 2020q1-2023q1.This application shows both the power of parsimonious models and the importanceof allowing for global variables.