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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.

Macroeconomic Forecasting and Variable Selection with a Very Large Number of Predictors: A Penalized Regression Approach