The common practice for GDP nowcasting in a data-rich environment is to employ either sparse regression using LASSO-type regularization or a dense approach based on factor models or ridge regression, which differ in the way they extract information from high-dimensional datasets. This paper aims to investigate whether sparse plus dense mixed frequency regression methods can improve the nowcasts of the US GDP growth. We propose two novel MIDAS regressions and show that these novel sparse plus dense methods greatly improve the accuracy of nowcasts during the COVID pandemic compared to either only sparse or only dense approaches. Using monthly macro and weekly financial series, we further show that the improvement is particularly sharp when the dense component is restricted to be macro, while the sparse signal stems from both macro and financial series.
This study introduces a bootstrap test of the validity of factor regression within a high-dimensional factor-augmented sparse regression model that integrates factor and sparse regression techniques. The test provides a means to assess the suitability of the classical dense factor regression model compared to a sparse plus dense alternative augmenting factor regression with idiosyncratic shocks. Our proposed test does not require tuning parameters, eliminates the need to estimate covariance matrices, and offers simplicity in implementation. The validity of the test is theoretically established under time-series dependence. Through simulation experiments, we demonstrate the favorable finite sample performance of our procedure. Moreover, using the FRED-MD dataset, we apply the test and reject the adequacy of the classical factor regression model when the dependent variable is inflation but not when it is industrial production. These findings offer insights into selecting appropriate models for high-dimensional datasets.