Shrinkage Estimation

High-Dimensional Spatial Arbitrage Pricing Theory with Heterogeneous Interactions ArXiv ID: 2511.01271 “View on arXiv” Authors: Zhaoxing Gao, Sihan Tu, Ruey S. Tsay Abstract This paper investigates estimation and inference of a Spatial Arbitrage Pricing Theory (SAPT) model that integrates spatial interactions with multi-factor analysis, accommodating both observable and latent factors. Building on the classical mean-variance analysis, we introduce a class of Spatial Capital Asset Pricing Models (SCAPM) that account for spatial effects in high-dimensional assets, where we define {"\it spatial rho"} as a counterpart to market beta in CAPM. We then extend SCAPM to a general SAPT framework under a {"\it complete"} market setting by incorporating multiple factors. For SAPT with observable factors, we propose a generalized shrinkage Yule-Walker (SYW) estimation method that integrates ridge regression to estimate spatial and factor coefficients. When factors are latent, we first apply an autocovariance-based eigenanalysis to extract factors, then employ the SYW method using the estimated factors. We establish asymptotic properties for these estimators under high-dimensional settings where both the dimension and sample size diverge. Finally, we use simulated and real data examples to demonstrate the efficacy and usefulness of the proposed model and method. ...

Shocks-adaptive Robust Minimum Variance Portfolio for a Large Universe of Assets ArXiv ID: 2410.01826 “View on arXiv” Authors: Unknown Abstract This paper proposes a robust, shocks-adaptive portfolio in a large-dimensional assets universe where the number of assets could be comparable to or even larger than the sample size. It is well documented that portfolios based on optimizations are sensitive to outliers in return data. We deal with outliers by proposing a robust factor model, contributing methodologically through the development of a robust principal component analysis (PCA) for factor model estimation and a shrinkage estimation for the random error covariance matrix. This approach extends the well-regarded Principal Orthogonal Complement Thresholding (POET) method (Fan et al., 2013), enabling it to effectively handle heavy tails and sudden shocks in data. The novelty of the proposed robust method is its adaptiveness to both global and idiosyncratic shocks, without the need to distinguish them, which is useful in forming portfolio weights when facing outliers. We develop the theoretical results of the robust factor model and the robust minimum variance portfolio. Numerical and empirical results show the superior performance of the new portfolio. ...

Block-diagonal idiosyncratic covariance estimation in high-dimensional factor models for financial time series ArXiv ID: 2407.03781 “View on arXiv” Authors: Unknown Abstract Estimation of high-dimensional covariance matrices in latent factor models is an important topic in many fields and especially in finance. Since the number of financial assets grows while the estimation window length remains of limited size, the often used sample estimator yields noisy estimates which are not even positive definite. Under the assumption of latent factor models, the covariance matrix is decomposed into a common low-rank component and a full-rank idiosyncratic component. In this paper we focus on the estimation of the idiosyncratic component, under the assumption of a grouped structure of the time series, which may arise due to specific factors such as industries, asset classes or countries. We propose a generalized methodology for estimation of the block-diagonal idiosyncratic component by clustering the residual series and applying shrinkage to the obtained blocks in order to ensure positive definiteness. We derive two different estimators based on different clustering methods and test their performance using simulation and historical data. The proposed methods are shown to provide reliable estimates and outperform other state-of-the-art estimators based on thresholding methods. ...