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Order-Flow Filtration and Directional Association with Short-Horizon Returns

Authors: Aditya Nittur Anantha, Shashi Jain, Prithwish Maiti Institution: Indian Institute of Science / SigmaQuant Technologies / AlgoQuant Technologies Year: 2025 (submitted December 2025) arXiv: 2507.22712 Categories: q-fin.TR, q-fin.CP, q-fin.GN, q-fin.ST, stat.ME

Plain-language abstract

Electronic markets are flooded with transient orders (fleeting limit orders, rapid modifications, aggressive cancellations) that dilute the directional signal in order book imbalance (OBI). This paper asks: can simple structural filters — order lifetime, modification count, or modification timing — sharpen the OBI–return relationship? Using BankNifty index futures on NSE India across three days spanning a monthly expiry cycle, the authors find that filtering the aggregate order flow makes little difference, but applying the same filters to parent orders of executed trades produces systematically stronger Hawkes cross-excitation from OBI regimes to return regimes. The framework doubles as a policy diagnostic: OBI–return association becomes a measurable proxy for market quality under regulatory schemes (India's "Persistent Noise Creator" rules) that penalise noisy order flow.

Key contributions

  1. Three structural filters at the order level (not aggregated): lifetime \(T_j\), modification count \(M_j\), and inter-modification time \(\mathcal{M}_j\). Cancellations and trades are coupled as "exit events"; modifications handled separately.
  2. Two imbalance constructions:
  3. Order-based OBI (events at best quotes, all directional messages);
  4. Trade-based OBI^(T) (signed executed trades only) — an execution-based benchmark immune to quote flicker.
  5. Three-layer diagnostic ladder for association strength:
  6. Pearson correlation between values;
  7. Discretised regime alignment (9-regime OBI × 3-regime returns), with a smooth anti-diagonal directional mask (\(\gamma = 0.2\));
  8. Hawkes kernel norms from OBI regimes to return regimes (used as diagnostic, not forecast).
  9. Residualised + lagged variants: fit univariate ARMA to each regime-count series and rerun the scores on residuals + across a grid of positive lags to isolate genuinely predictive alignment from serial co-movement.
  10. Parent-order filtration is the key finding — applying filters to the parents of executed trades (not the aggregate flow) yields systematically stronger Hawkes cross-excitation norms.
  11. Policy framing: interprets OBI–return association as a market-quality diagnostic, directly relevant to Indian regulators' 2021–22 Persistent Noise Creator surveillance on excessive modifications/cancellations.

Method summary

Data

  • BankNifty index futures, NSE India, tick-by-tick with per-order IDs.
  • Three trading days selected to span early / middle / late points of a monthly futures expiry cycle.

Quantities per evaluation window \((\tau-h, \tau]\)

Symbol Definition
\(\Delta N^{b/s}\) directional event counts
\(\text{OBI}(\tau, h)\) \((\Delta N^b - \Delta N^s) / (\Delta N^b + \Delta N^s)\) over all events
\(\text{OBI}^{(T)}(\tau, h)\) same ratio over signed trades only
\(\tilde r_{(\tau-h,\tau]}\) realised return: last-trade \(-\) first-trade mid in window

Filters

  • Lifetime: remove events from orders with \(T_j = t_j^{(2)} - t_j^{(1)} < \bar T\).
  • Modification count: remove events with \(M_j > \bar M\).
  • Modification time: remove orders whose last two modifications are less than a threshold apart.

Each filter applied independently. Applied twice: (i) to the aggregate event stream, producing \(\text{OBI}^{(F)}\); (ii) to the parent orders of realised trades, producing a filtered trade-based imbalance.

Scoring ladder

  1. Contemporaneous correlation: \(S^{\rho}(\mathcal{F}, \tau) = \text{corr}(\text{OBI}, \tilde r)\).
  2. Regime scores: for each window compute regime-count vectors \(Q_\tau \in \mathbb{R}^9\) (OBI) and \(R_\tau \in \mathbb{R}^3\) (returns). Produces:
  3. Directional correlation score — weighted sum of the \(9\times 3\) correlation matrix via a smooth anti-diagonal mask (weights \(>1\) on aligned pairs, \(<1\) on misaligned, \(\approx 1\) near neutral).
  4. Regression regime score — \(\sum_\tau R^2\) of OLS regression \(R_\tau = \beta Q_\tau + \epsilon_\tau\). Both variants also computed on ARMA residuals and at positive lags.
  5. Hawkes diagnostics: promote regime transitions to point-process events; fit a parametric multivariate Hawkes process and interpret kernel norms / branching ratios as OBI → return excitation strength.

Main results

  • Aggregate-flow filtration is disappointing: lifetime/modification filters applied to all events produce only marginal changes in Pearson correlation, regime scores, and Hawkes norms across the three days. The intuition from the fleeting-order literature does not straightforwardly translate into sharper signals when the filter is applied globally.
  • Parent-order filtration works: the same filters, when applied only to orders that actually participated in executed trades, yield systematically stronger Hawkes cross-excitation kernel norms from OBI to return regimes. This holds across all three filter types and across all three trading days in the sample.
  • Interpretation: not all trades contribute equally to price formation; trades whose parent orders survive the filters (i.e., were not fleeting or over-revised) carry more of the directional information.
  • Unfiltered BankNifty OBI is already strong — consistent with prior literature; the paper is framed as "can filtering improve on a known-strong baseline?", and the answer is "only if you filter in the right way".
  • The paper is deliberately diagnostic, not forecasting: no P&L or OOS forecast evaluation is claimed.

Limitations

  • Single instrument: BankNifty index futures only; equity cash, options, and cross-exchange behaviour untested.
  • Three days, expiry-structured sample: designed to stratify by activity level, not to span a full regime set (no extreme-volatility days, no regulatory-change days).
  • Thresholds not optimised: filter thresholds \(\bar T, \bar M\) are discussed but not tuned — results are comparative across filters, not at an optimal operating point.
  • Diagnostic, not predictive: Hawkes models are used for kernel-norm interpretation only; no out-of-sample forecast or trading evaluation.
  • Policy framing is suggestive: the paper links OBI–return association to market-quality diagnostics under NPC rules, but stops short of causal claims about regulation effects.

Connections