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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

Indonesian

Sebuah jalur yang tidak dapat dibedakan dari kode sendiri tidak membawa panah waktu, sehingga irreversibilitas waktu adalah kondisi yang diperlukan untuk mekanisme yang diarahkan dapat dibaca dari jalur saja. Dalam keuangan itu telah diukur hanya pada seri skalar seperti pengembalian dan volatilitas. Untuk NVDA, tingkat irreversibilitas dari jalur order-invariant dan order-sensitive estimasi audit adalah 0,036 dan 0,054 nats per peristiwa, masing-masing, dan memperkirakan perbedaan mereka, peningkatan pesanan, adalah 0,018 minggu dari data pasar Nasdaq dengan MLP order-invariant dan jaringan konvolusi temporal yang menerima blok yang identik. Untuk NVDA, estimasi order-invariant dan order-sensitive adalah 0,036 dan 0,054 nats per acara, masing-masing. Perbedaan mereka, peningkatan pesanan, adalah 0,

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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