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This study introduces a bootstrap test of the validity of factor regressionwithin a high-dimensional factor-augmented sparse regression model thatintegrates factor and sparse regression techniques. The test provides a meansto assess the suitability of the classical dense factor regression modelcompared to a sparse plus dense alternative augmenting factor regression withidiosyncratic shocks. Our proposed test does not require tuning parameters,eliminates the need to estimate covariance matrices, and offers simplicity inimplementation. The validity of the test is theoretically established undertime-series dependence. Through simulation experiments, we demonstrate thefavorable finite sample performance of our procedure. Moreover, using theFRED-MD dataset, we apply the test and reject the adequacy of the classicalfactor regression model when the dependent variable is inflation but not whenit is industrial production. These findings offer insights into selectingappropriate models for high-dimensional datasets.

Tuning-free testing of factor regression against factor-augmented sparse alternatives