  This paper studies macroeconomic forecasting and variable selection using a
folded-concave penalized regression with a very large number of predictors. The
penalized regression approach leads to sparse estimates of the regression
coefficients, and is applicable even if the dimensionality of the model is much
larger than the sample size. The first half of the paper discusses the
theoretical aspects of a folded-concave penalized regression when the model
exhibits time series dependence. Specifically, we show the oracle inequality
and the oracle property for ultrahigh-dimensional time-dependent regressors.
The latter half of the paper shows the validity of the penalized regression
using two motivating empirical applications. The first forecasts U.S. GDP with
the FRED-MD data using the MIDAS regression framework, where there are more
than 1000 covariates, while the sample size is at most 200. The second examines
how well the penalized regression screens the hidden portfolio with around 40
stocks from more than 1800 potential stocks using NYSE stock price data. Both
applications reveal that the penalized regression provides remarkable results
in terms of forecasting performance and variable selection.
