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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

Chinese

在金融中,它只被测量在规模序列中,如回报和波动性。对于NVDA,不变序列和敏感序列的审计估计为每场事件的向前到逆的日志密度比,并从纳斯达克市场按顺序数据的三周中估计为 0.05 和 0.05 纳特,其差异,订单增加为 0.018。 替代品保留可用的单步转换表恢复了30%的不可逆转性,比观察的路径增加了30天。 对于HTTP来说,对每场会议的每日分数的模拟值是0.036和0.054 纳特,而不是每场会议的10 个分数和每场会议的每一个分数的模拟值。 作为一个单一订单变更

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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