# Conditioning on a Volatility Proxy Compresses the Apparent Timescale of Collective Market Correlation

arXiv: https://arxiv.org/abs/2603.14072 · HTML: https://mlsanity.com/paper/2603.14072/

## Key facts

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- First posted on arXiv 14 Mar 2026.

## Abstract (arXiv)

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 psi1=λmax/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 DeltaBIC=109. On the decomposition sample, an informational residual of log(VIX) alone retains most of that gain (DeltaBIC=78.6), whereas a mechanical VIX proxy alone does not improve the fit. Autocorrelation-matched placebo fields fail (DeltaBICmax=2.7), disjoint weekly reconstructions still favor the field-coupled model (DeltaBIC=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.