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Neural Estimation of Irreversibility in Real and Simulated Limit Order Book Paths

Hyeonjun Yeo, Doohwi Cha, Yoontae Hwang · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.16151 · cited by 0 works (OpenAlex) · open-access PDF

Korean

코드 자체의 반전으로부터 구별할 수없는 경로는 시간의 화살표를 운반하지 않으므로 시간의 반전성은 지향적 메커니즘이 경로에서만 읽을 수있는 필수 조건입니다. 금융에서 그것은 반전과 변동성과 같은 스칼라 시리즈에서만 측정되었습니다. NVDA의 경우 순서의 변동성과 순서에 민감한 순서 책 경로의 반전성 비율은 각 이벤트 당 앞으로 반전 로그 밀도 비율으로 정의되며, 세 주간 Nasdaq 시장 순서 데이터에서 읽을 수 있습니다. 순서별 MLP와 동일한 블록을받는 일시적 통합 네트워크에서만 측정되었습니다. NVDA의 경우 순서의 변동성과 순서에 민감한 감사 추정은 각각 0.036 및

Machine translation (Meta M2M100); the English original follows.

Abstract

A path indistinguishable from its own reverse carries no arrow of time, so time irreversibility is a necessary condition for a directed mechanism to be readable from trajectories alone. In finance it has been measured only on scalar series such as returns and volatility. We define the irreversibility rate of a coarse-grained limit order book path as the forward-to-reverse log-density ratio per event, and estimate it from three weeks of Nasdaq market-by-order data with an order-invariant MLP and a temporal convolutional network that receive identical blocks. For NVDA, the order-invariant and order-sensitive estimates are 0.036 and 0.054 nats per event, respectively. Their difference, the ordering increment, is 0.018. A surrogate preserving the coarse one-step transition table recovers 30 percent less irreversibility than the observed paths. The increment is positive for all twelve symbols on every held-out daytime date, and for NVDA in each session window. It changes more than tenfold with the coarse-graining scale. Neither a linear score nor any single feature group reproduces the full fitted rate. A queue-reactive simulator calibrated on the same days matches the market's ordered rate, 0.052 against 0.054, yet its ordering increment is 0.0006 against 0.018, building temporal asymmetry out of block composition instead of block order. We propose the ordering and scale profile of path irreversibility as a benchmark for order book simulators. Code and audit materials are available at https://github.com/hjyeo30/lob-irreversibility.

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Topics: Path (computing), Mathematics, Limit (mathematics), Benchmark (surveying), Block (permutation group theory), Asymmetry

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