Page 360 - Special Topic Session (STS) - Volume 3

STS550 Matteo Mogliani
aggregating (weighting) functions. The inclusion of many high-frequency
variables into MIDAS regressions may nevertheless lead to overparameterized
models, with poor predictive performance. This happens because the MIDAS
regression approach can efficiently address the dimensionality issue arising
from the number of high-frequency lags in the model, but not that arising
from the number of high-variables. Hence, recent literature has focused on
MIDAS penalized regressions, based mainly on the so-called Lasso and Elastic-
Net penalizations (Marsilli, 2014; Siliverstovs, 2017; Uematsu and Tanaka, in
press).
In the present paper, we propose a similar approach, but we depart from
the existing literature on several points. First, we consider MIDAS regressions
resorting to Almon lag polynomial weighting schemes, which depend only on
a bunch of functional parameters governing the shape of the weighting
function and keep linearity in the regression model. Second, we consider a
Group Lasso penalty, which operates on distinct groups of regressors, and we
set as many groups as the number of high-frequency predictors, allowing each
group to include the entire Almon lag polynomial of each predictor. This
grouping structure is motivated by the fact that if one high-frequency
predictor is irrelevant, it should be expected that zero-coefficients occur in all
the parameters of its lag polynomial. Third, we implement Bayesian techniques
for the estimation of our penalized MIDAS regressions. The Bayesian approach
offers two attractive features in our framework. The first one is the inclusion of
spike-and-slab priors that, combined with the penalized likelihood approach,
aim at improving the selection ability of the model by adding a probabilistic
recovery layer to the hierarchy. The second one is the estimation of the penalty
hyper-parameters through an automatic and data-driven approach that does
not resort to extremely time-consuming pilot runs. In this paper we consider
an algorithm based on stochastic approximations, which consists in
approximating the steps necessary to estimate the hyper-parameters in such
a way that simple analytic solutions can be used. It turns out that penalty
hyper-parameters can be automatically tuned with a small computational
effort compared to existing and very popular alternative algorithms.

2. Methodology
Consider the variable t, which is observed at discrete times (i.e. only once
between t − 1 and t), and suppose that we want to use information stemming
()
()
from a set of predictors () = 1, ,... , , )’, which are observed times

()
between t − 1 and t, for forecasting purposes. The variables t and , for
,
= 1, … , are said to be sampled at different frequencies. For instance,
quarterly and monthly frequencies, respectively, in which case = 3. Let us

define the high-frequency lag operator 1/m , such that L 1/m () = () .
, ,−1/
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