Bridging Factor and Sparse Models

Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimension. They seemingly mutually exclusive. In this paper, we propose simple lifting method that combines the merits of these supervised learning methodology allows efficiently explore all information high-dimensional datasets. The is based on flexible model for panel data, called factor-augmented regression with both observable, latent common factors, as well idiosyncratic components covariate variables. This not only includes factor specific but also significantly weakens cross-sectional dependence hence facilitates selection interpretability. consists three steps. At each step, remaining cross-section can be inferred by novel test covariance high-dimensions. We developed asymptotic theory demonstrated validity multiplier bootstrap testing structure. further extended partial structures. supported an extensive simulation study applications construction network financial returns prediction exercise large macroeconomic time series from FRED-MD database.