用波动率代理变量解释市场集体相关性的缓慢变化，发现其主要来自外部驱动而非内在惯性。
Conditioning on a Volatility Proxy Compresses the Apparent Timescale of Collective Market Correlation
- 通过将波动率（VIX）作为代理变量，显著压缩了市场相关性的有效弛豫时间。
- 模型拟合度提升显著，BIC降低109，其中对数波动率信息贡献最大。
- 结果在多种控制实验下稳定，适合研究金融系统非平衡动力学的学者。
针对市场集体动态中观察到的缓慢持久现象——其是内在特性还是源自持续驱动源？我们分析了标普500指数60日滚动相关矩阵的首特征值占比ψ₁=λₘₐₓ/N（237只股票，2004–2023年）。基于与VIX耦合的奥恩斯坦-乌伦贝克模型，有效弛豫时间从298个交易日缩短至61个交易日，相较纯均值回归模型的BIC改善达ΔBIC=109。在分解样本中，仅使用log(VIX)的信息残差即可保留大部分拟合增益（ΔBIC=78.6），而机械性VIX代理变量则无改进。自相关匹配的伪随机场不支持该结论（ΔBICₘₐₓ=2.7），跨周重构仍支持场耦合模型（ΔBIC=140–151），六个锚定时间点的外样本检验亦保持优势。平静期及去除场效应后的残差自相关控制显示持久性同样坍缩。更强的隐变量扩展仅部分支持。在测试的随机模型类中，条件于可观测的VIX代理变量可吸收绝大部分表观慢动态。
原文摘要 · Abstract (English)
We address the attribution problem for apparent slow collective dynamics: is the observed persistence intrinsic, or inherited from a persistent driver? For the leading eigenvalue fraction $ψ_1=λ_{\max}/N$ of S\&P 500 60-day rolling correlation matrices ($237$ stocks, 2004--2023), a VIX-coupled Ornstein--Uhlenbeck model reduces the effective relaxation time from $298$ to $61$ trading days and improves the fit over bare mean reversion by $Δ$BIC$=109$. On the decomposition sample, an informational residual of $\log(\mathrm{VIX})$ alone retains most of that gain ($Δ$BIC$=78.6$), whereas a mechanical VIX proxy alone does not improve the fit. Autocorrelation-matched placebo fields fail ($Δ$BIC$_{\max}=2.7$), disjoint weekly reconstructions still favor the field-coupled model ($Δ$BIC$=140$--$151$), and six anchored chronological holdouts preserve the out-of-sample advantage. Quiet-regime and field-stripped residual autocorrelation controls show the same collapse of persistence. Stronger hidden-variable extensions remain only partially supported. Within the tested stochastic class, conditioning on the observed VIX proxy absorbs most of the apparent slow dynamics.
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