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.

Keywords: Spatial Arbitrage Pricing Theory, Asset Pricing, High-dimensional statistics, Shrinkage estimation, Factor models, Equities

Complexity vs Empirical Score

• Math Complexity: 9.2/10
• Empirical Rigor: 6.8/10
• Quadrant: Holy Grail
• Why: The paper introduces highly advanced mathematical techniques including ridge-regularized Yule-Walker equations, eigenanalysis for latent factor extraction, and establishes asymptotic properties under high-dimensional settings where both dimension and sample size diverge, indicating very high mathematical complexity. The empirical rigor is substantial due to the inclusion of both simulated and real data examples, demonstration of efficacy, and discussion of implementation challenges, though it lacks the explicit code or backtest metrics that would push it toward maximum rigor.

  flowchart TD
    A["Research Goal<br>Estimate & Infer SAPT Model<br>in High-Dimensions"] --> B{"Factor Type?"}
    
    B --> C["Observable Factors"]
    B --> D["Latent Factors"]
    
    C --> E["SYW Estimation<br>Ridge Regression"]
    D --> F["Autocovariance Eigenanalysis<br>Extract Factors"]
    F --> E
    
    E --> G["Key Outcomes<br>Generalized Shrinkage Yule-Walker<br>Asymptotic Properties<br>Spatial Rho Metric"]