Bridging factor and sparse models

Arbeitspapier

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

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Texto para discussão ; No. 681

Classification and Topics

• Classification: Wirtschaft ; Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes ; Single Equation Models; Single Variables: Panel Data Models; Spatio-temporal Models ; Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models ; Multiple or Simultaneous Equation Models: Panel Data Models; Spatio-temporal Models
• Subject: Factor models ; sparse regression ; high-dimensional ; supervised learning ; hypothesis testing ; covariance structure

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Fan, Jianqing ; Masini, Ricardo ; Medeiros, Marcelo C.
• Event: Veröffentlichung
• (who): Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Departamento de Economia
• (where): Rio de Janeiro
• (when): 2021

Further information

• Handle: http://hdl.handle.net/10419/249729
• Last update: 10.03.2025, 11:41 AM CET