An Algebraic Estimator for Large Spectral Density Matrices

• 成果类型: Article
• 署名作者: Barigozzi, Matteo; Farne, Matteo
• 署名单位: University of Bologna; University of Bologna
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2126780
• 发表日期: 2024
• 页码: 498-510
• 关键词: dynamic-factor model; thresholding algorithm; frequency-domain; time-series; covariance; shrinkage; CONVERGENCE; regression; causality; number

摘要

We propose a new estimator of high-dimensional spectral density matrices, called ALgebraic Spectral Estimator (ALSE), under the assumption of an underlying low rank plus sparse structure, as typically assumed in dynamic factor models. The ALSE is computed by minimizing a quadratic loss under a nuclear norm plus ti norm constraint to control the latent rank and the residual sparsity pattern. The loss function requires as input the classical smoothed periodogram estimator and two threshold parameters, the choice of which is thoroughly discussed. We prove consistency of ALSE as both the dimension p and the sample size T diverge to infinity, as well as the recovery of latent rank and residual sparsity pattern with probability one. We then propose the UNshrunk ALgebraic Spectral Estimator (UNALSE), which is designed to minimize the Frobenius loss with respect to the pre-estimator while retaining the optimality of the ALSE. When applying UNALSE to a standard U.S. quarterly macroeconomic dataset, we find evidence of two main sources of comovements: a real factor driving the economy at business cycle frequencies, and a nominal factor driving the higher frequency dynamics. The article is also complemented by an extensive simulation exercise. Supplementary materials for this article are available online.