High-Dimensional Spatial Arbitrage Pricing Theory with Heterogeneous Interactions

Battle Count: 124

The paper is highly relevant to quantitative trading as it directly addresses asset pricing with spatial interactions in high-dimensional settings. The SAPT model provides a framework for understanding how geographic proximity and spatial spillovers affect expected returns, which can inform sector/region-based trading strategies. The out-of-sample forecasting results on S&P 500 returns demonstrate practical predictive advantages over QMLE and Fama-French models. The spatial rho parameter offers a new risk factor for portfolio construction. However, the model is primarily a pricing/forecasting tool rather than a direct trading signal generator, and implementation requires careful estimation of spatial weight matrices.

The methodology involves multiple steps: (1) constructing spatial weight matrices based on geographic or economic distances, (2) implementing the Yule-Walker estimation with ridge regularization for each of N panel units, (3) for latent factors, performing autocovariance-based eigenanalysis to extract factors, (4) selecting penalty parameters via cross-validation, and (5) determining the number of factors via information criteria or ratio-based methods. The asymptotic theory requires careful verification of conditions (N=o(T), stationarity, mixing). Computational efficiency is a stated advantage over QMLE, but the per-unit estimation for large N still requires N separate ridge regressions. The paper provides detailed formulas but no code.

The paper specifies R programming with a fixed random seed (1234) for simulations. Data sources are identified: S&P 500 stock returns from Pelger (2020) at https://mpelger.people.stanford.edu/data-and-code, and U.S. housing prices from Aquaro et al. (2021). The spatial weight matrix construction is clearly defined. However, no code repository is explicitly provided, and the full estimation procedure requires careful implementation of the Yule-Walker equations with ridge regularization and eigenanalysis.