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

01 ABSTRACT

The study defines the irreversibility rate of a coarse-grained limit order book path as the forward-to-reverse log-density ratio per event, estimated from Nasdaq market-by-order data using an order-invariant MLP and a temporal convolutional network. For NVDA, the order-sensitive estimate is 0.054 nats per event versus 0.036 for the order-invariant, yielding an ordering increment of 0.018; the increment is positive for all 12 symbols on held-out daytime dates. A calibrated queue-reactive simulator matches the market's ordered rate (0.052 vs 0.054) but has an ordering increment of only 0.0006, far below the market's 0.018.

02 KEY FINDINGS

1. Order-sensitive and order-invariant networks estimate NVDA irreversibility at 0.054 and 0.036 nats per event, respectively, giving an ordering increment of 0.018 that is positive for all 12 symbols on held-out daytime dates.
2. Surrogates preserving the coarse one-step transition table recover 30% less irreversibility than observed paths, indicating that path order contributes additional irreversibility.
3. A queue-reactive simulator matches the market's overall ordered rate (0.052 vs 0.054) but has an ordering increment of only 0.0006, meaning its temporal asymmetry arises from block composition rather than block order.