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SqrtImpactFlowSignal

Incremental, causal technical analysis documentation

Summary

SqrtImpactFlowSignal is a streaming research signal built from the square-root market impact law and Cont-style signed order flow. It is designed for Massive/Polygon aggregate bars (close, volume, optional VWAP) and can also consume tick-derived signed dollar volume when you aggregate the tape yourself.

The economic idea:

  1. Average price impact of a metaorder scales like \(Y\,\sigma\sqrt{Q/V}\) (Tóth et al.; Bouchaud surveys; 2025 work on impact, imbalance, and volatility).
  2. If a bar’s signed volume implies more impact than the return that realized, impact is “unfinished” → continuation in the flow direction.
  3. If the return overshoots volume-implied impact → temporary impact reversion.
  4. Optional VWAP gap aligns trade-price pressure with the bar’s volume-weighted location (Polygon aggregate vw).

Update API

# Aggregate path (tick-rule flow from close-to-close)
out = rtta.SqrtImpactFlowSignal().update(close, volume)
# out.signal, out.score, out.impact, out.residual, out.continuation,
# out.reversion, out.participation, out.flow, out.volatility, out.vwap_gap

# Optional: true signed dollar volume from ticks + bar VWAP
out = rtta.SqrtImpactFlowSignal().update(
    close, volume, signed_dollar_volume=signed_dv, vwap=bar_vwap
)

# OHLCV-compatible overload (open/high/low ignored)
out = rtta.SqrtImpactFlowSignal().update(open, high, low, close, volume)

batch = rtta.SqrtImpactFlowSignal().batch(close, volume)

Constructor knobs:

Argument Default Role
impact_coefficient 1.0 \(Y\) in \(I = Y\sigma\sqrt{Q/V}\)
adv_span 50 EWMA span for average dollar volume \(V\)
vol_span 20 EWMA span for return scale \(\sigma\)
continuation_weight 1.0 weight on unfinished impact
reversion_weight 0.5 weight on overshoot reversion
vwap_weight 0.25 weight on VWAP-gap alignment
entry_z / exit_z 0.75 / 0.25 hysteresis for discrete signal
fillna True 0 vs NaN on warmup

Theory Of Operation

Square-root impact

Empirically and theoretically, the average absolute mid/price displacement associated with trading quantity \(Q\) against recent activity \(V\) is

\[I_t = Y\,\sigma_t\sqrt{\frac{Q_t}{V_t}}\]

with \(\sigma_t\) a local volatility scale. RTTA sets \(Q_t = C_t V^{\mathrm{sh}}_t\) (dollar volume of the bar) and \(V_t\) an EWMA of dollar volume (ADV proxy).

Signed flow

On aggregates without a tape, flow sign is the tick rule on close:

\[s_t = \mathrm{sign}(\log C_t - \log C_{t-1}).\]

When you supply signed_dollar_volume from tick classification (tick rule / Lee-Ready on quotes), \(s_t = \mathrm{sign}(\mathrm{signed\_dollar})\).

Continuation vs reversion

Let \(r_t = \log(C_t/C_{t-1})\) and \(I_t\) as above.

\[\begin{aligned} \mathrm{continuation}_t &= s_t\cdot\frac{\max(0,\, I_t - |r_t|)}{\sigma_t} \\ \mathrm{reversion}_t &= -\mathrm{sign}(r_t)\cdot\frac{\max(0,\, |r_t| - I_t)}{\sigma_t} \end{aligned}\]

VWAP alignment

If bar VWAP \(W_t\) is available:

\[g_t = \frac{C_t}{W_t} - 1, \qquad \mathrm{align}_t = s_t\cdot\frac{g_t}{\sigma_t}.\]

Buying into a close above VWAP (or selling below) reinforces pressure.

Score and discrete signal

\[\mathrm{raw}_t = \tanh\bigl( w_c\,\mathrm{continuation}_t + w_r\,\mathrm{reversion}_t + w_v\,\mathrm{align}_t \bigr)\]

score is \(\mathrm{raw}_t\). An online z-score of score with hysteresis (entry_z / exit_z) produces discrete signal \(\in \{-1,0,+1\}\).

Recurrence

State: previous close, EWMA ADV \(V_t\), EWMA \(|r|\) as \(\sigma_t\), score EWMA mean/variance, discrete position.

  1. \(r_t = \log(C_t/C_{t-1})\), \(Q_t = C_t\cdot\mathrm{volume}_t\).
  2. \(V_t = (1-\alpha_V)V_{t-1} + \alpha_V Q_t\).
  3. \(\sigma_t = (1-\alpha_\sigma)\sigma_{t-1} + \alpha_\sigma |r_t|\).
  4. \(I_t = Y\sigma_t\sqrt{Q_t/V_t}\), residual \(r_t - s_t I_t\).
  5. Form continuation, reversion, VWAP align → tanh score → z-hysteresis signal.

All updates are \(O(1)\) and causal.

Trading (buy / sell)

The discrete trade directive is result.signal:

signal Action (see example)
+1 BUY / hold long
-1 SELL short, or exit long if long-only
0 FLAT / exit

score is optional confidence/size. A full paper-trading loop (CSV with action in {BUY,SELL,COVER,HOLD,...}, long-only vs --allow-short, --min-score) lives in:

examples/sqrt_impact_flow_from_massive_speedup.py

Implementation Notes

Implemented in src/rtta/indicator.cpp in class SqrtImpactFlowSignal.

This is not a full LOB metaorder reconstructor. It is a bar-level / optional tape-signed proxy of the square-root impact residual structure emphasized in recent impact–imbalance research, engineered for Polygon/Massive fields.

Reference