A Unified Framework for Dimension Reduction in Forecasting

Abstract

Factor models are widely used in summarizing large datasets with few underlying latent factors and in building time series forecasting models for economic variables. In these models, the reduction of the predictors and the modeling and forecasting of the response y are carried out in two separate and independent phases. We introduce a potentially more attractive alternative, Sufficient Dimension Reduction (SDR), that summarizes x as it relates to y, so that all the information in the conditional distribution of y|x is preserved. We study the relationship between SDR and popular estimation methods, such as ordinary least squares (OLS), dynamic factor models (DFM), partial least squares (PLS) and RIDGE regression, and establish the connection and fundamental differences between the DFM and SDR frameworks. We show that SDR significantly reduces the dimension of widely used macroeconomic series data with one or two sufficient reductions delivering similar forecasting performance to that of competing methods in macro-forecasting. JEL Classification Number: C32, C53, C55, E17

FRED-QD: A Quarterly Database for Macroeconomic Research

“…FRED-MD has been successful. It has been used as a foil for applying big data methods including random subspace methods (Boot and Nibberin, 2019), sufficient dimension reduction (Barbarino and Bura, 2017), dynamic factor models (Stock and Watson, 2016), large Bayesian VARs (Giannone, Lenza, and Primiceri, 2018), various lasso-type regressions (Smeekes and Wijler, 2018), functional principal components, (Hu and Park, 2017), complete subset regression (Kotchoni, Lerous, and Stevanovich, 2019), and random forests (Medeiros, Vasconcelos, Veiga, and Zilberman, 2019). In addition, these various methods have been used to study a wide variety of economic and financial topics including bond risk premia (Bauer and Hamilton, 2017), the presence of real and financial tail risk (Nicolò and Lucchetta, 2016), liquidity shocks (Ellington, Florackis, and Milas, 2017), recession forecasting (Davig and Hall, 2019), identification of uncertainty shocks (Angelini, Bacchiocchi, Caggiano, and Fanelli, 2019), and identification of monetary policy shocks (Miranda-Agrippino and Ricco, 2017).…”

FRED-QD: A Quarterly Database for Macroeconomic Research

“…FRED-MD has been successful. It has been used as a foil for applying big data methods including random subspace methods (Boot and Nibberin, 2019), sufficient dimension reduction (Barbarino and Bura, 2017), dynamic factor models (Stock and Watson, 2016), large Bayesian VARs (Giannone, Lenza, and Primiceri, 2018), various lasso-type regressions (Smeekes and Wijler, 2018), functional principal components, (Hu and Park, 2017), complete subset regression (Kotchoni, Lerous, and Stevanovich, 2019), and random forests (Medeiros, Vasconcelos, Veiga, and Zilberman, 2019). In addition, these various methods have been used to study a wide variety of economic and financial topics including bond risk premia (Bauer and Hamilton, 2017), the presence of real and financial tail risk (Nicolò and Lucchetta, 2016), liquidity shocks (Ellington, Florackis, and Milas, 2017), recession forecasting (Davig and Hall, 2019), identification of uncertainty shocks (Angelini, Bacchiocchi, Caggiano, and Fanelli, 2019), and identification of monetary policy shocks (Miranda-Agrippino and Ricco, 2017).…”