Push-response anomalies in high-frequency S&P 500 price series

ArXiv ID: 2511.06177 “View on arXiv”

Authors: Dmitrii Vlasiuk, Mikhail Smirnov

Abstract

We test the hypothesis that consecutive intraday price changes in the most liquid U.S. equity ETF (SPY) are conditionally nonrandom. Using NBBO event-time data for about 1,500 regular trading days, we form for every lag L ordered pairs of a backward price increment (“push”) and a forward price increment (“response”), standardize them, and estimate the expected responses on a fine grid of push magnitudes. The resulting lag-by-magnitude maps reveal a persistent structural shift: for short lags (1-5,000 ticks), expected responses cluster near zero across most push magnitudes, suggesting high short-term efficiency; beyond that range, pronounced tails emerge, indicating that larger historical pushes increasingly correlate with nonzero conditional responses. We also find that large negative pushes are followed by stronger positive responses than equally large positive pushes, consistent with asymmetric liquidity replenishment after sell-side shocks. Decomposition into symmetric and antisymmetric components and the associated dominance curves confirm that short-horizon efficiency is restored only partially. The evidence points to an intraday, lag-resolved anomaly that is invisible in unconditional returns and that can be used to define tradable pockets and risk controls.

Keywords: Market Microstructure, High-Frequency Trading, Efficiency Analysis, Conditional Non-randomness, Liquidity

Complexity vs Empirical Score

• Math Complexity: 2.5/10
• Empirical Rigor: 9.0/10
• Quadrant: Street Traders
• Why: The paper relies on straightforward statistical conditioning (standardized push-response analysis, dominance curves) without complex stochastic calculus or advanced theory, but implements a rigorous, data-heavy methodology using event-time NBBO data across 1,500+ days, with detailed preprocessing and multi-lag estimation suitable for direct backtesting.

  flowchart TD
    A["Research Goal<br>Test conditional non-randomness<br>of consecutive SPY intraday price changes"] --> B["Data Source & Prep<br>1,500 days NBBO event-time data<br>Regular trading hours only"]
    B --> C["Methodology<br>Form ordered pairs of push (backward increment)<br>and response (forward increment) for lag L"]
    C --> D["Computation<br>Standardize increments<br>Estimate expected responses on grid of<br>push magnitudes for each lag L"]
    D --> E["Key Findings<br>Short Lag (1-5k ticks):<br>Responses cluster near zero<br>High efficiency"]
    D --> F["Key Findings<br>Long Lag (>5k ticks):<br>Pronounced tails appear<br>Larger pushes correlate with non-zero responses"]
    D --> G["Key Findings<br>Asymmetry: Large negative pushes<br>followed by stronger positive responses<br>Consistent with asymmetric liquidity replenishment"]