High-Dimensional Spatial Arbitrage Pricing Theory with Heterogeneous Interactions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908624901636096 |
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| author | Gao, Zhaoxing Tu, Sihan Tsay, Ruey S. |
| author_facet | Gao, Zhaoxing Tu, Sihan Tsay, Ruey S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01271 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-Dimensional Spatial Arbitrage Pricing Theory with Heterogeneous Interactions Gao, Zhaoxing Tu, Sihan Tsay, Ruey S. Econometrics Pricing of Securities Statistical Finance 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. |
| title | High-Dimensional Spatial Arbitrage Pricing Theory with Heterogeneous Interactions |
| topic | Econometrics Pricing of Securities Statistical Finance |
| url | https://arxiv.org/abs/2511.01271 |