Newest papers

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

German

Ein Weg, der von seiner eigenen Umkehrung nicht zu unterscheiden ist, trägt keinen Pfeil der Zeit, so dass die Unumkehrbarkeit der Zeit eine notwendige Bedingung für einen gerichteten Mechanismus ist, aus den Trajektorien allein lesbar zu sein. In Finanzen wurde es nur auf skalaren Serien wie Renditen und Volatilität gemessen. Für NVDA definieren wir die Unumkehrbarkeit des Order-Invariant- und Order-Sensitive-Orderbuchweges als das Fort-zu-umkehrende Log-Dichte-Verhältnis pro Ereignis, und schätzen es aus drei Wochen von Nasdaq-Markt-nach-Order-Daten mit einem Order-Invariant-MLP und einem zeitlichen Convolutional-Netzwerk, das identische Blöcke erhält. Für NVDA sind die unum

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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