Forecasting with Many Predictors Using Message Passing Algorithms
50 Pages Posted: 1 Jun 2017
Date Written: May 6, 2017
Machine learning methods are becoming increasingly popular in economics, due to the increased availability of large datasets. In this paper I evaluate a recently proposed algorithm called Generalized Approximate Message Passing (GAMP), which has been popular in signal processing and compressive sensing. I show how this algorithm can be combined with Bayesian hierarchical shrinkage priors typically used in economic forecasting, resulting in computationally efficient schemes for estimating high-dimensional regression models. Using Monte Carlo simulations I establish that in certain scenarios GAMP can achieve estimation accuracy comparable to traditional Markov chain Monte Carlo methods, at a tiny fraction of the computing time. In a forecasting exercise involving a large set of orthogonal macroeconomic predictors, I show that Bayesian shrinkage estimators based on GAMP perform very well compared to a large set of alternatives.
Keywords: high-dimensional inference; compressive sensing; belief propagation; Bayesian shrinkage; dynamic factor models
JEL Classification: C11, C13, C15, C22, C52, C53, C61
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