High-Dimensional Spatial Arbitrage Pricing Theory with Heterogeneous Interactions

TL;DR

This paper develops a high-dimensional spatial arbitrage pricing model incorporating spatial interactions and multiple factors, with estimation methods for both observable and latent factors, supported by theoretical properties and empirical validation.

Contribution

It introduces a novel SAPT framework with spatial effects and develops a shrinkage Yule-Walker estimation method suitable for high-dimensional data, including latent factor extraction.

Findings

The proposed estimators are asymptotically consistent in high-dimensional settings.

Simulation studies demonstrate the accuracy of the estimation methods.

Real data applications show the model's practical usefulness.

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.