Queue Imbalance as a One-Tick-Ahead Price Predictor in a Limit Order Book¶

Authors: Martin D. Gould, Julius Bonart Institution: CFM–Imperial Institute of Quantitative Finance, Imperial College London Year: 2015 (December 2015) arXiv: 1512.03492 Categories: q-fin.TR

Plain-language abstract¶

Does the queue imbalance at the best bid/ask genuinely forecast the direction of the next mid-price move? Despite widespread practitioner use of this signal, rigorous quantification of its predictive power had been limited. This paper fits logistic regressions of mid-price direction on queue imbalance for 10 liquid Nasdaq stocks over 2014. All 10 are strongly statistically significant. vs a "no-signal" null, the logistic model improves binary direction classification by 50–60% for large-tick stocks and 10–30% for small-tick stocks; probabilistic predictions improve by 20–30% and 2–6% respectively. Local logistic regression (semi-parametric) marginally improves on the global fit but at much higher compute cost.

Key contributions¶

Rigorous baseline for the queue-imbalance signal:

$$I(t) = \frac{n^b(b(t), t) - n^a(a(t), t)}{n^b(b(t), t) + n^a(a(t), t)} \in [-1, 1]$$

where $n^b, n^a$ are the total queue sizes at best bid/ask.

Two-model evaluation framework:
Binary classifier — logistic regression of $\text{sgn}(\Delta m)$ on $I$.
Probabilistic classifier — $P(\Delta m > 0 \mid I)$ via the logistic sigmoid.
Formal out-of-sample evaluation across 10 Nasdaq stocks, 2014 — first paper to quantify QI's predictive power with full LOBSTER data at event-by-event resolution under a proper null.
Local (non-parametric) logistic regression as a semi-parametric counterpart that relaxes the logistic-sigmoid shape constraint. Reveals that the true conditional direction probability is flatter in the tails than the sigmoid implies for small-tick stocks — suggesting tick-size-specific functional forms.
Tick-size dependence: large-tick vs small-tick stocks show very different magnitudes of predictive improvement. Large-tick improvements are ~2–3× the small-tick improvements, consistent with the thesis that large-tick LOBs concentrate predictive information at the top of book.

Method summary¶

Data¶

LOBSTER full event stream for 10 Nasdaq stocks spanning tick-size regimes.
Entire calendar year 2014 — 252 trading days.
Trading hours filtered to 10:00–15:30 ET (exclude opening/closing 30-min auctions).
Tick size $\pi = \$0.01$ (constant across Nasdaq names); relative tick size $\pi / \text{price}$ drives the regime classification.

Inputs & target¶

Input $I$ computed at every change in best bid or ask (event time, not calendar time).
Target: sign of the next mid-price change (binary) or probability that next change is upward (probabilistic).

Models¶

\[\Pr(\Delta m > 0 \mid I) = \sigma(\alpha + \beta I) \qquad \sigma(x) = \frac{1}{1 + e^{-x}}\]

Global logistic regression: one $(\alpha, \beta)$ per stock.
Local logistic regression: kernel-weighted logistic regression evaluated at each prediction point; trades parametric rigidity for computational cost.

Null model¶

Random guess biased by the unconditional up-frequency — the baseline any non-trivial predictor must beat.

Main results¶

Binary classification (accuracy vs null)¶

Tick regime	Global logistic	Local logistic
Large-tick	+50–60%	slightly better
Small-tick	+10–30%	slightly better

Probabilistic classification (log-loss / calibration vs null)¶

Tick regime	Global logistic	Local logistic
Large-tick	+20–30%	slightly better
Small-tick	+2–6%	slightly better

All 10 stocks reject the null at high statistical significance — QI is genuinely predictive.
Local logistic wins marginally but cost-per-sample is orders of magnitude higher; rarely worth it in practice.
Large-tick dominance echoes the finding seen across the wiki: large-tick LOBs concentrate predictive information at the best quotes.

Limitations¶

Single country, single venue: Nasdaq 2014. Cross-venue / cross-country robustness not tested.
Linear feature only: only $I$ is used; multi-level imbalance (mlofi-xu-gould-howison) not combined here.
Sigmoid shape constraint shown to be restrictive for small-tick stocks — but the paper doesn't try other parametric forms (e.g., piecewise-linear, tanh-like with different scale).
Static fit: no regime-aware fitting across intraday periods or volatility regimes.
No trading simulation: predictive accuracy only; no P&L after costs.

Connections¶

Sister paper to lipton-quote-imbalance: Lipton–Pesavento–Sotiropoulos (2013) model the same queue-imbalance signal via a diffusive queue process and derive a closed-form $P_\uparrow(q^b, q^a) = \phi / \varpi$. Gould–Bonart here take the empirical/econometric route and fit logistic regressions. Together these two give a theoretical-model + empirical-regression pair on the exact same signal.
Distinct from OFI: QI is the instantaneous ratio of queue sizes at best bid/ask; OFI is the cumulative sum of signed event contributions over an interval. Both are short-horizon LOB signals; QI is simpler to compute but discards event-time structure.
Multi-level sibling mlofi-xu-gould-howison by the same Gould (co-author) extends QI-style thinking to multiple price levels; the tick-size magnitudes (65–75% / 15–30% for MLOFI vs 50–60% / 10–30% here) are remarkably consistent.
Tick-size regime theme: now confirmed across four papers in the wiki — Briola (2024), Bieganowski–Ślepaczuk (2026), Xu–Gould–Howison (2019), and this. The large-tick/small-tick divide is the single most robust cross-study finding in the microstructure cluster.
Stoikov microprice builds directly on QI: microprice $= m + f(I)$ with $f$ fit from local dynamics. The Gould–Bonart local logistic regression is exactly a non-parametric estimator of Stoikov's adjustment function.