Precision Least Squares: Estimation and Inference in High-Dimensions

Summary, in English

The least squares estimator can be cast as depending only on the precision matrix of the data, similar to the weights of a global minimum variance portfolio. We give conditions under which any plug-in precision matrix estimator produces an unbiased and consistent least squares estimator for stationary time series regressions, in both low- and high-dimensional settings. Such conditions define a class of “Precision Least Squares” (PrLS) estimators, which are shown to be approximately Gaussian, efficient, and to provide automatic family-wise error control in large samples. For estimating high-dimensional sparse regression models, we propose a LASSO Cholesky estimator of the plug-in precision matrix. We show its consistency and how to properly bias correct it, thereby obtaining a LASSO Cholesky-based PrLS (LC-PrLS) estimator. LC-PrLS performs well in finite samples and better than state-of-the-art high-dimensional estimators. We employ LC-PrLS to investigate the dynamic network of predictive connections among a large set of global bank stock returns. We find that crisis years correspond to a collapse of predictive linkages.

• Author: Luca Margaritella; Rosnel Sessinou
• Department/s: Department of Economics
• Publishing year: 2025-02
• Language: English
• Pages: 884-896
• Publication/Series: Journal of Business & Economic Statistics
• Volume: 43
• Issue: 4
• Links: http://dx.doi.org/10.1080/07350015.2024.2440573
• Document type: Journal article
• Publisher: Taylor & Francis
• Topic: Economics
• Keywords: Precision Least Squares; High-Dimensional Inference; Predictive Networks; C32; C55; C12; G19
• Status: Published
• ISBN/ISSN/Other: ISSN: 1537-2707