Page 359 - Special Topic Session (STS) - Volume 3

STS550 Matteo Mogliani

Bayesian MIDAS penalized regressions:
Estimation, selection, and prediction
Matteo Mogliani
Banque de France, International Macroeconomics Division, 31 Rue Croix des Petits Champs,
75049 Paris CEDEX 01, France

Abstract
We propose a new approach to modeling and forecasting with mixed-
frequency regressions (MI-DAS) in presence of a large number of predictors.
Our approach resorts to penalized regressions such as Group Lasso, allowing
for simultaneously selecting the relevant regressors and estimating the non-
zero parameters, and Bayesian techniques for estimation. In particular, the
penalty hyper-parameters governing the model shrinkage are automatically
tuned via an adaptive MCMC algorithm. To achieve sparsity and improve the
variable selection ability of the model, we also consider a Group Lasso
estimator augmented with a spike-and-slab prior. Simulations show that the
proposed models have good in and out of sample performance, even when
the design matrix presents high cross-correlation. When applied to a
forecasting model of U.S. GDP, the results suggest that high-frequency
financial variables may have some, although limited, short-term predictive
content.

Keywords
MIDAS regressions; Penalized regressions; Variable selection; Forecasting;
Bayesian estimation

1. Introduction
The outstanding increase in the availability of economic data has led
econometricians to the development of new regression techniques based on
Machine Learning algorithms, such as the family of penalized regressions. This
consists in regressions with a modified objective function, such that
coefficients estimated close to zero are shrunk to exactly zero, leading to
simultaneous selection and estimation of coefficients associated to relevant
variables only. While some of these techniques have been successfully applied
to multivariate and usually highly parameterized macroeconomic models,
such as Vector Autoregressions (Gefang, 2014; Korobilis and Pettenuzzo, in
press), only a few contributions in the literature have paid attention to mixed-
frequency (MIDAS) regressions. In the classic MIDAS framework (Andreou et
al., 2010), the researcher can regress high-frequency variables (e.g. monthly
variables such as surveys) directly on low-frequency variables (e.g. quarterly
variables such as GDP) by matching the sampling frequency through specific
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