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Board of Governors of the Federal Reserve System (US)
Finance and Economics Discussion Series
A Unified Framework for Dimension Reduction in Forecasting
Alessandro Barbarino
Efstathia Bura
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.


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Alessandro Barbarino & Efstathia Bura, A Unified Framework for Dimension Reduction in Forecasting, Board of Governors of the Federal Reserve System (US), Finance and Economics Discussion Series 2017-004, 12 Jan 2017.
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Keywords: Diffusion Index ; Dimension Reduction ; Factor Models ; Forecasting ; Partial Least Squares ; Principal Components
DOI: 10.17016/FEDS.2017.004
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