{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T09:41:07Z","timestamp":1792230067505,"version":"4.4.0"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":0,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.uspto.gov\/ip-policy\/copyright-policy\/copyright-basics"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Recent empirical work has documented a persistent gap between historical and optionimplied Hurst estimates for SPX volatility, typically interpreted as a nonzero-maturity smoothing bias of the estimator. We reinterpret the gap as a formal specification signal. Building on the paper-1 deterministic likelihood filter for rough Bergomi and the paper-2 identification failure under path-dependent volatility, we develop a measure-invariance framework in which the pathwise H\u00f6lder exponent H and, in the Guyon-Lekeufack class, the entire diffusion parameter vector, are Girsanov-invariant. The framework yields an asymmetric falsifiability result: rough Bergomi retains a level parameter \u03be 0 that absorbs the variance risk premium, while Guyon-Lekeufack 4F PDV structurally cannot-and is therefore provably misspecified as a joint (P, Q) description in any market with nontrivial VRP. We construct a joint deterministic likelihood combining the WCE spot-return filter with a Q-side observation channel from either the multi-maturity ARS zero-vanna estimator (for option-chain data) or the CBOE VIX and SKEW pair at 30 days (for public data), together with a two-stage diagnostic architecture: model-class selection via surface residual, withinclass specification via Wald test on the measure-invariant subvector. Monte Carlo experiments confirm essentially perfect model-class identification at N = 10 3 trading days. We apply the diagnostic to SPX over 1990-2026 using CBOE public data, segmenting by VVIX-quantile regimes and rate-hike-cycle windows. The framework yields an economically interpretable regime-conditional outcome rather than a straightforward model selection: \u0124P \u2248 0.11 across regimes matches the paper-2 attractor value consistently, while \u0124Q separates from \u0124P under low-VVIX calm and median conditions (W \u2265 7.5, reject at 5%) but agrees under high-VVIX stress, all three rate-hike cycles, and both the 2008 and 2020 crisis episodes. The pattern is consistent with the variance-risk-premium literature-the discrepancy emerges in regimes where the proportional VRP is documented to be largest-though we do not claim to establish a mechanistic mapping between VRP magnitude and the observed H-gap. GL is preferred by AIC in every regime slice on the Q side but faces the no-VRP obstruction of Theorem 1 against being a single-parameter-vector joint (P, Q) specification.<\/jats:p>","DOI":"10.2139\/ssrn.7620660","type":"posted-content","created":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T08:41:36Z","timestamp":1792226496000},"source":"Crossref","is-referenced-by-count":0,"title":["A Measure-invariant Specification Test for Rough and Path-dependent Volatility Models&amp;nbsp;"],"prefix":"10.2139","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-7758-5062","authenticated-orcid":true,"given":"Alireza","family":"Javaheri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T08:41:36Z","timestamp":1792226496000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7620660"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7620660","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}