Page 364 - Special Topic Session (STS) - Volume 3

STS550 Matteo Mogliani
high correlation, while the the FPR remains overall very low. This result is
nevertheless not unexpected, as the Group Lasso can address the issue of
strong collinearity within the lag polynomials but is not designed to handle
strong collinearity between the high-frequency regressors. Finally, looking at
the forecasting performance, the results are broadly in line with the in-sample
analysis and suggest that the models perform overall quite similarly in terms
of point and density forecasts, although the BMIDAS-AGL-SS model seems to
perform best overall. The performance of the models deteriorates substantially
with higher correlation in the design matrix, but it is relatively stable with K
increasing.
We apply the proposed Bayesian MIDAS penalized regressions to US
quarterly GDP data. We consider 42 real and financial indicators, sampled at
monthly, weekly, and daily frequencies. The data sample starts in 1980Q1, and
we set 2000Q1 and 2017Q4 the first and last out-of-sample observations,
respectively. Estimates are carried-out recursively using an expanding window,
and h-step-ahead posterior predictive densities (ℎ= 0,1,4) are generated
through a direct forecast approach. Forecasts are compared to those from a
benchmark model represented by a simple random-walk (RW). Point and
density forecasts are evaluated by the means of standard criteria. As a
robustness check, we further consider forecasts from alternative competing
models, such as the AR(1), the combination of single-indicator Bayesian
MIDAS models, the Bayesian model selection (BMS), and the Bayesian model
averaging (BMA). Our findings suggest that the penalized BMIDAS models
outperform the benchmark RW at all the horizons, whether point or density
forecasts are considered. When compared to the set of alternative models, our
penalized BMIDAS models display predictive gains at ℎ = 0 and ℎ = 1. At ℎ =
4, the predictive performance of most of the alternative competing models is
only slightly superior or inferior to that of our penalized regressions. Looking
at the selection of predictors over the pseudo out-of-sample, the results point
to systematic inclusion of a few real high-frequency indicators. Further,
selection appears more parsimonious and stable for the BMIDAS-AGL-SS
model. Virtually no financial indicators are selected by our models at ℎ = 0,
with real hard- and soft-data conveying all the relevant information. However,
this feature tends to attenuate for ℎ = 1, where some high-frequency financial
indicators are selected. All in all, this result is broadly in line with recent
literature (Andreou et al., 2013) and suggests that financial variables may
convey some, although limited, short-term leading information which goes
beyond the predictive content of real indicators.

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