Multifractal Intermittency in US Equity Markets: A Tick-Level Empirical Study

Abstract

We analyze the statistical microstructure of US equity markets using 2.6 terabytes of tick-level trade data spanning 2,375 trading days (2016–2025) across all US exchanges. At 100-millisecond VWAP resolution, log returns exhibit raw kurtosis exceeding 2,987—approximately 996 times the Gaussian value of 3—which, to our knowledge, is among the largest systematically documented tick-level kurtosis values in the peer-reviewed literature on US equities. We characterize the decay of kurtosis across timescales from 100 milliseconds to 15 minutes and show that it follows a power-law relationship inconsistent with independent, identically distributed (i.i.d.) returns; the novelty of the kurtosis contribution is concentrated at **sub-second** timescales (minute-level values fall within ranges previously reported by Andersen, Liu, Lux, and others). Structure function analysis reveals **anomalous scaling consistent with multifractal (rather than monofractal) dynamics** at the timescales studied: the ratio zeta(p)/p is a strictly decreasing function of order p. At sub-second VWAP resolution, structure function exponents zeta(p) are negative, reflecting bid-ask mean-reversion that suppresses structure function growth; the concavity diagnostic on zeta(p)/p is reported regardless of the sign of zeta(p). We further document a systematic hierarchy in Securities Information Processor (SIP) latency across 17 US exchanges, with median propagation delays ranging from 19 microseconds (FINRA ADF) to 347 microseconds (NYSE), and identify a previously unreported anomaly in NASDAQ participant timestamps—including a 0.005% negative-latency rate—that affects latency calculations in the Polygon.io dataset. Cross-period validation using a mid-quarter baseline week (October 14–18, 2024) confirms **directional** anomalous scaling at 70/70 cross-period ticker-timescale combinations, with statistical significance (paired t-test, p < 0.05) at 58/70 (83%). Kurtosis point estimates vary by up to ~2× between the two weeks: we claim **order-of-magnitude** robustness (always ≫ 3), not stability of single-week means. These findings provide baseline empirical facts for tick-level market microstructure and inform the design of high-frequency volatility estimators and manipulation detection systems.