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

Paper: arXiv 2610.16151

Authors: Hyeonjun Yeo, Doohwi Cha, Yoontae Hwang

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper introduces a novel method for measuring time irreversibility in limit order books using neural networks, a significant advancement in market microstructure analysis. It demonstrates strong empirical rigor with real-world Nasdaq data and provides code for reproducibility. The work offers a new benchmark for order book simulators.

Research Flowchart

  flowchart TD
    A[Research Goal: Quantify Irreversibility in LOB Paths] --> B{Key Methodology: Neural Estimation of Irreversibility Rate};
    B --> C[Data: 3 Weeks Nasdaq Market-by-Order Data];
    C --> D{Computational Process: MLP & TCN Models};
    D --> E[Outcome 1: Estimated Irreversibility Rates];
    E --> F[Outcome 2: Ordering Increment & Scale Profile];
    F --> G[Outcome 3: LOB Simulator Benchmark];

Cited References (36)

1. Time reversal invariance in finance (2009) — link
2. Irreversibility of financial time series: A graph-theoretical approach (2016) — link
3. Time series irreversibility: a visibility graph approach (2012) — link
4. Functional decomposition and estimation of irreversibility in time series via machine learning (2024) — link
5. Testing the causality of H awkes processes with time reversal (2018) — link
6. The market nanostructure origin of asset price time reversal asymmetry (2021) — link
7. The price impact of order book events (2014) — link
8. The price impact of order book events: market orders, limit orders and cancellations (2012) — link

0 of 36 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.