Empirical Evaluation of LOB Imbalance, VPIN, and Market Resilience on NASDAQ TotalView-ITCH

Abstract

This paper presents the complete empirical falsification and out-of-sample evaluation behind our practitioner execution guide (From Signal to Trade, Part 1: Turning Book Imbalance and Toxicity into Desk Rules). Using 33,435,762 full-depth messages from the official NASDAQ TotalView-ITCH 5.0 feed (01302020.NASDAQ_ITCH50, January 30, 2020) across a 14-symbol universe spanning ultra-liquid ETFs (QQQ), mega-cap technology (AAPL, MSFT, AMZN, NVDA-tier AMD, INTC, CSCO, NFLX), biotech (GILD, VRTX), and wider-spread mid-cap equities (IDXX, CTAS, POOL, SBUX), we test four real-time microstructure metrics implemented in VisualHFT: LOB Imbalance (LOBImbalanceStudy), VPIN (VPINStudy), Market Resilience (MarketResilienceStudy), and Market Resilience Bias (MarketResilienceBiasStudy).

Every hypothesis is evaluated against an explicit book-free or autoregressive rival on a strict chronological hold-out split (12:45:00 ET through 16:00:00 ET), with uncertainty quantified via circular block-bootstrap confidence intervals on 5-minute intraday blocks and batch-means effective sample sizes ($n_{\text{eff}}$) to account for serial correlation in overlapping high-frequency states.

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1. Data Corpus, Causal Ordering, and Statistical Methodology

1.1 Universe and Chronological Split

The benchmark corpus processes the full binary NASDAQ TotalView-ITCH 5.0 log for January 30, 2020 across 14 symbols (AAPL, AMD, AMZN, CSCO, CTAS, GILD, IDXX, INTC, MSFT, NFLX, POOL, QQQ, SBUX, VRTX), reconstructing the complete price-level order book (OrderBook) from AddOrder, OrderExecuted, OrderCancel, OrderDelete, and OrderReplace messages.

To prevent in-sample threshold tuning from contaminating out-of-sample inference, the trading day is partitioned chronologically at 12:45:00 ET (the midpoint of the regular 09:30:00 ET to 16:00:00 ET session):

• Discovery / Calibration Half (04:00:00 ET to 12:45:00 ET): Used to lock functional parameters, exponential decay weights ($\lambda = 0.5$), threshold cutoffs ($|I| \ge 0.5$, $|I| \ge 0.7$), and rival definitions.
• Hold-Out Evaluation Half (12:45:00 ET to 16:00:00 ET): All primary scorecards, confidence intervals, and rival comparisons reported below are computed strictly on this untouched afternoon sample unless explicitly labeled full-day.

1.2 Eliminating Sub-Second Bucket Look-Ahead Bias

A critical methodological pitfall in high-frequency replay studies arises when order book snapshots are aggregated into time buckets (for example, OrderBookAggregationLevel.Ms100). In VisualHFT’s AggregatedCollection<BaseStudyModel>, when a new 100 ms bucket opens at timestamp $t_0$, the container initializes the bucket stamp to $t_0$ while overwriting the retained payload with the last update arriving inside $[t_0, t_0 + 100\text{ ms})$ (LastOrDefault selector).

If an analyst pairs a bucket’s retained imbalance value with the first mid-price change occurring after the bucket-open stamp $t_0$, the imbalance value incorporates order book transitions that occurred after the mid-price change inside the same 100 ms window. In our verification audit, that intra-bucket look-ahead inflates Equal-Weight imbalance accuracy while collapsing the measured advantage of Touch-Weighted over Equal-Weight from +15.78 percentage points (under strict causal file-order pairing) to +1.26 percentage points (under bucket-open pairing).

To guarantee strict causality:

1. Every study reading $S_i$ is stamped with the exact exchange nanosecond timestamp $t_i$ of the triggering ITCH message in causal file-arrival order.
2. The target forward mid-price change $\Delta m(t_i) = m(\tau_i) - m(t_i)$ is evaluated at the first subsequent order book state $\tau_i > t_i$ where the mid-price $m(\tau_i) = \frac{1}{2}(b_0(\tau_i) + a_0(\tau_i))$ strictly differs from $m(t_i)$.
3. All states with a locked or crossed book ($a_0 \le b_0$) or one-sided depth are excluded prior to evaluation.

1.3 Serial Correlation, Effective Sample Size ($n_{\text{eff}}$), and Block Bootstrap

Because limit order book states persist across consecutive message arrivals until a mid-price change occurs, raw event counts ($n$) overstate statistical degrees of freedom. We address serial dependence using three complementary procedures:

• De-Overlapped Mid-Move Epochs (LAST, RANDOM, FIRST): Continuous sequences of order book updates sharing the same current mid-price $m(t)$ and the same next-move outcome $\text{sign}(\Delta m)$ are collapsed into a single independent epoch per actual mid-price transition.
• Batch-Means Effective Sample Size ($n_{\text{eff}}$): Following standard Markov-chain Monte Carlo variance estimation, each symbol’s hold-out series is partitioned into $B = 39$ non-overlapping 5-minute blocks. Comparing the between-block variance of block hit rates $\hat{p}b$ against the binomial variance $\hat{p}(1-\hat{p})$ yields the effective independent sample size $n{\text{eff}}$, which typically equals 1% to 15% of the raw message count $n$.
• Circular Block Bootstrap & Rotation Nulls: All 95% confidence intervals (95% CI) are computed via 1,000-draw circular block bootstrap over 5-minute intraday blocks, and regime tests (VPIN, MR) use 2,000 to 5,000 circular index rotations to preserve exact intraday seasonality and autocorrelation.

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2. LOB Imbalance (edge-LOBT1): Touch-Weighted Decay vs. Equal-Weight Summation

2.1 Mathematical Formulation

Cont, Kukanov, and Stoikov (2014) demonstrate that the short-horizon price impact of limit order book events is dominated by order flow at the best bid and ask ($k = 0$), while Lipton, Pesavento, and Sotiropoulos (2013) and Gould and Bonart (2016) show that deeper queue levels contribute with rapidly decaying marginal weight.

Given $L$ visible price levels on the bid side ${q_k^b}{k=0}^{L-1}$ and ask side ${q_k^a}{k=0}^{L-1}$ ordered by distance from the touch, the Equal-Weight (Flat) LOB Imbalance ($I_{\text{EQ}}$) and Touch-Weighted LOB Imbalance ($I_{\text{TW}}$) are defined as:

$$ I_{\text{EQ}}(t) = \frac{\sum_{k=0}^{L-1} q_k^b(t) - \sum_{k=0}^{L-1} q_k^a(t)}{\sum_{k=0}^{L-1} q_k^b(t) + \sum_{k=0}^{L-1} q_k^a(t)}, \qquad I_{\text{TW}}(t) = \frac{\sum_{k=0}^{L-1} w_k q_k^b(t) - \sum_{k=0}^{L-1} w_k q_k^a(t)}{\sum_{k=0}^{L-1} w_k q_k^b(t) + \sum_{k=0}^{L-1} w_k q_k^a(t)} $$

where the exponential touch-decay weight is $w_k = \exp(-\lambda k)$ with $\lambda = 0.5$ ($w_0 = 1.000, w_1 = 0.607, w_2 = 0.368, \dots, w_9 = 0.011$).

2.2 Locked Out-of-Sample Nomination Scorecard

Table 1 reports the five pre-registered falsification tests on the afternoon hold-out sample (12:45:00 ET to 16:00:00 ET, 10 liquid symbols with $\ge 30$ de-overlapped extreme events: AAPL, AMD, AMZN, CSCO, GILD, INTC, MSFT, NFLX, QQQ, SBUX).

Row	Hypothesis / Test Specification	Out-of-Sample Point Estimate	95% Block-Bootstrap CI	Rival / Null Benchmark	Advantage vs. Rival	Symbol Breadth
Row 1	Unfiltered Base Rate: $P(\text{sign}(\Delta m) = \text{sign}(I_{\text{TW}}) \mid |I_{\text{TW}}| \ge 0.7)$ vs. unconditional base rate	73.92%	[69.5%, 78.2%]	51.69% (unconditional)	+22.23 pp	10 / 10 (+12.2 to +29.4 pp)
Row 2	Confirming Filter on Reversal: $P(\text{hit} \mid \text{Reversal} \wedge |I_{\text{TW}}| \ge 0.5)$ vs. book-free Bounce Filter ($	\Delta m_{\text{prev}}	> \text{median}$)	78.17%	[74.8%, 81.4%]	73.33% (bounce filter) / 68.14% (raw reversal)
Row 3	Standalone vs. Last-Move Reversal: Standalone $|I_{\text{TW}}| \ge 0.7$ hit rate vs. unconditional $-\text{sign}(\Delta m_{\text{prev}})$	73.92%	[69.5%, 78.2%]	68.14% (last-move reversal)	+5.78 pp ([-0.51, +12.06])	7 / 10 (loses on AMD, CSCO, INTC)
Row 4	Spread-to-Move Economic Barrier: Median ratio of quoted spread $s(t)$ to conditional $	\Delta m	$ at $|I_{\text{TW}}| \ge 0.7$	6.18x	[3.1x, 9.2x]	1.00x (breakeven taker threshold)
Row 5	Formula Head-to-Head: Touch-Weighted ($|I_{\text{TW}}| \ge 0.7$) vs. Equal-Weight ($|I_{\text{EQ}}| \ge 0.7$) on identical timestamps	73.92%	[69.5%, 78.2%]	58.15% (Equal-Weight 10-level)	+15.78 pp ([+11.98, +19.57])	10 / 10 (+3.9 to +25.6 pp)

2.3 Complete 14-Symbol Hold-Out Breakdown

Table 2 details the hold-out performance across every symbol in the 14-ticker corpus, including raw message counts ($n$), batch-means effective sample sizes ($n_{\text{eff}}$), confirming-filter lift (Row 2), formula head-to-head lift (Row 5), and the spread-to-move ratio (Row 4). The four thinner mid-cap symbols (CTAS, IDXX, POOL, VRTX) have fewer than 30 de-overlapped afternoon events at $|I_{\text{TW}}| \ge 0.7$ and are reported separately in the lower panel.

Symbol	Hold-Out Events ($n$ at $|I_{\text{TW}}| \ge 0.7$)	Effective $n_{\text{eff}}$ (5-min blocks)	Touch-Weighted Hit Rate (Row 1)	Base Rate Null	Reversal + $I_{\text{TW}}$ Confirm (Row 2)	Reversal + Bounce Rival	Row 2 Lift (pp)	Equal-Weight Hit Rate	Row 5 Lift: TW vs. EQ (pp)	Spread / Mean $|\Delta m|$ (Row 4)
AAPL	12,331	380	75.9%	50.8%	82.0%	79.2%	+2.8	55.6%	+20.3	2.7x
AMD	83,355	1,142	70.2%	53.7%	80.7%	76.2%	+4.5	48.0%	+22.2	6.8x
AMZN	1,091	164	64.1%	51.9%	71.4%	60.5%	+10.9	53.6%	+10.5	3.3x
CSCO	18,954	412	82.1%	52.8%	92.0%	86.4%	+5.7	64.9%	+17.2	2.3x
GILD	13,205	395	80.6%	51.9%	85.9%	81.9%	+4.0	63.7%	+16.9	3.1x
INTC	40,219	690	80.5%	51.1%	88.9%	86.2%	+2.7	54.9%	+25.6	6.2x
MSFT	32,782	615	69.1%	50.7%	76.4%	73.1%	+3.3	56.2%	+12.9	6.2x
NFLX	1,648	198	67.8%	51.7%	58.0%	56.4%	+1.6	63.9%	+3.9	9.5x
QQQ	29,405	540	72.3%	50.8%	65.5%	55.9%	+9.6	60.8%	+11.5	6.3x
SBUX	10,874	345	76.5%	51.5%	80.9%	77.6%	+3.4	59.9%	+16.6	7.1x
10-Symbol Mean	243,864	4,881	73.92%	51.69%	78.17%	73.33%	+4.84	58.15%	+15.78	6.18x (median)
CTAS (thin)	142	28	66.9%	50.2%	64.8%	58.1%	+6.7	59.2%	+7.7	8.4x
IDXX (thin)	186	31	68.3%	50.9%	66.2%	59.4%	+6.8	61.3%	+7.0	7.9x
POOL (thin)	214	35	65.4%	50.4%	63.9%	57.8%	+6.1	58.4%	+7.0	8.8x
VRTX (thin)	310	44	67.1%	51.0%	67.4%	61.2%	+6.2	59.7%	+7.4	7.5x

2.4 De-Overlap Sensitivity and Lead-Time Stratification

To verify that Row 1 (+22.23 pp) and Row 5 (+15.78 pp) are not artifacts of fast message bursts right before a price change, we re-evaluated the hold-out sample under two robustness checks:

1. Epoch De-Overlapping (LAST, RANDOM, FIRST): When consecutive messages within the same mid-price epoch are collapsed into a single observation per mid-price move, the Touch-Weighted vs. Equal-Weight advantage remains +17.9 percentage points under RANDOM draw (10 / 10 symbols positive) and +13.9 percentage points under FIRST arrival (10 / 10 symbols positive).
2. Lead-Time Stratification ($\tau_i - t_i$): Grouping hold-out events by the elapsed time until the next mid-price change shows that directional agreement remains stable across four orders of magnitude of lead time:
   • $1\ \mu\text{s} - 1\text{ ms}$: 74.3% hit rate (+22.6 pp over null)
   • $1\text{ ms} - 10\text{ ms}$: 76.4% hit rate (+24.7 pp over null)
   • $10\text{ ms} - 100\text{ ms}$: 74.5% hit rate (+22.8 pp over null)
   • $> 100\text{ ms}$: 69.4% hit rate (+17.7 pp over null)

2.5 Intraday Frequency of Sustained Actionable Leans

For human and semi-automated workflows, instantaneous microsecond spikes are less relevant than sustained near-touch leans that persist long enough to act on. Defining a sustained event as $|I_{\text{TW}}| \ge 0.7$ held continuously for at least 2.0 seconds after a clean 60-second baseline without prior crossings yields 588 events across the 14-symbol session (POOL: 154, CTAS: 122, VRTX: 95, IDXX: 89, NFLX: 74, INTC: 13, MSFT: 13, GILD: 9, SBUX: 7, AMZN: 6, AAPL: 5, CSCO: 1, AMD: 0, QQQ: 0).

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3. Book-Depth Sensitivity Analysis (edge-DEPTH: 5 vs. 10 vs. 20 Levels)

3.1 Motivation: Signal Dilution vs. Deep-Book Information

Because VisualHFT ingests feeds ranging from 5-level exchange snapshots to full depth-of-book (TotalView-ITCH), a central architectural question is how many price levels $L \in {5, 10, 20}$ should enter the imbalance calculation. Cao, Hansch, and Wang (2009) find that limit order book depth beyond the best quote contains incremental price discovery information, but only when weighted appropriately against near-touch liquidity.

3.2 Empirical Depth Comparison Across 10 Liquid Symbols

Table 3 compares Equal-Weight ($I_{\text{EQ}}$) and Touch-Weighted ($I_{\text{TW}}$, $\lambda = 0.5$) across $L = 5$, $L = 10$, and $L = 20$ levels per side on the afternoon hold-out sample.

Metric / Scorecard Row	$L = 5$ Levels	$L = 10$ Levels (Default)	$L = 20$ Levels	Structural Mechanism
Equal-Weight Hit Rate at $|I_{\text{EQ}}| \ge 0.7$	64.39%	58.15%	53.30%	Severe Dilution: Deep passive liquidity swamps top-of-book queue pressure.
Touch-Weighted Hit Rate at $|I_{\text{TW}}| \ge 0.7$ (Row 1)	73.89%	73.92%	73.90%	Touch Invariance: Exponential decay ($\lambda = 0.5$) protects front-of-queue sensitivity.
Formula Lead: Touch-Weighted minus Equal-Weight (Row 5)	+9.50 pp	+15.78 pp	+20.60 pp	Advantage of exponential weighting more than doubles from 5 to 20 levels.
Confirming Filter Lift on Reversal (Row 2: $I_{\text{TW}}$ vs. Bounce Rival)	+2.21 pp	+4.84 pp	+7.01 pp	3.2x Lift Expansion: Deep levels filter out false touch bounces when weighted smoothly.
QQQ Extreme Signal Rate ($|I_{\text{EQ}}| \ge 0.5$)	5.75%	4.14%	0.68%	Flat summation silences deep ETF books by averaging symmetric passive walls.
MSFT Extreme Signal Rate ($|I_{\text{EQ}}| \ge 0.5$)	20.51%	9.14%	1.03%	20-level flat summation eliminates 95% of extreme imbalance readings on MSFT.

The empirical takeaway for feed configuration is twofold:

1. If a connector provides only 5 levels of depth, Equal-Weight summation already loses +9.50 percentage points to Touch-Weighted decay.
2. If a connector provides 20 levels of depth, Equal-Weight summation degrades toward a coin flip (53.30%), whereas Touch-Weighted Imbalance preserves its 73.90% standalone accuracy while tripling its out-of-sample confirming-filter lift on reversal entries from +2.21 pp to +7.01 pp.

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4. Volume-Synchronized Flow Toxicity (edge-VPINC1)

4.1 Theoretical Background and Empirical Horserace

Easley, López de Prado, and O’Hara (2012) introduced VPIN to estimate order-flow toxicity in volume time by dividing the session into equal volume buckets of size $V$ and computing the rolling average of absolute order imbalance across $N$ buckets:

$$ \text{VPIN}b = \frac{1}{N} \sum{j=b-N+1}^{b} \frac{|V_j^B - V_j^S|}{V} $$

Andersen and Bondarenko (2014) subsequently demonstrated that VPIN’s predictive power for future return volatility is largely mediated by trailing trading intensity and realized volatility (RV), particularly when trade direction is inferred via tick-based classification rules.

To test both propositions rigorously on our NASDAQ corpus, we evaluated VPINStudy across three forward horizons ($H \in {60\text{ s}, 300\text{ s}, 900\text{ s}}$) against two strict benchmarks:

1. Partial Spearman Correlation ($\rho_{\text{partial}}$): Rank correlation between $\text{VPIN}(t)$ and forward realized volatility $\text{RV}{[t, t+H]}$ controlling for trailing realized volatility $\text{RV}{[t-H, t]}$, evaluated against 2,000 circular block rotations.
2. HAR-RV + Time-of-Day Rival (Diebold-Mariano QLIKE Test): Out-of-sample volatility forecast comparison pitting a ridge-regularized HAR-RV + Diurnal spline model against the same model augmented with VPIN.

4.2 Per-Symbol VPIN Volatility Horserace Table

Because VisualHFT’s default bucket sizing uses the whole-file median print size multiplied by bucketVolumeSize = 50, symbols with heavy pre-market (04:00:00 ET to 09:30:00 ET) odd-lot activity (AAPL, AMD, AMZN, INTC, MSFT, NFLX, QQQ) experience a small median trade size (3 to 25 shares) that saturates buckets during regular hours (1 to 3 trades per bucket). Table 4 reports the complete afternoon hold-out results for the 7 symbols with active regular-hours VPIN variance (CSCO, CTAS, GILD, IDXX, POOL, SBUX, VRTX), along with the 20-trade bucket floor calibration result.

Symbol	Median Print (Shares)	Bucket Volume $V$ (Shares)	Mean Trades / Bucket (RTH)	Unconditional Spearman $\rho(\text{VPIN}, \text{RV}_{300\text{s}})$	Partial Spearman $\rho_{\text{partial}}$ ($H = 300\text{s}$ | $\text{RV}_{\text{trail}}$)	Block Rotation $p$-Value	HAR-RV Rival QLIKE ($H = 300\text{s}$)	HAR-RV + VPIN QLIKE	Diebold-Mariano $p$-Value	Zero-Tick Share vs. $|V^B - V^S|/V$ ($\rho_{\text{sticky}}$)
CSCO	100	5,000	24.8	+0.384	-0.112	0.892	0.214	0.219	0.781	+0.412
CTAS	44	2,200	18.2	+0.291	-0.184	0.941	0.342	0.358	0.844	+0.289
GILD	100	5,000	29.4	+0.419	-0.095	0.815	0.198	0.203	0.742	+0.465
IDXX	27	1,350	16.5	+0.264	-0.218	0.962	0.389	0.411	0.885	+0.198
POOL	38	1,900	17.9	+0.312	-0.146	0.910	0.355	0.369	0.812	+0.244
SBUX	100	5,000	26.1	+0.442	-0.068	0.760	0.187	0.191	0.715	+0.571
VRTX	49	2,450	19.7	+0.338	-0.129	0.884	0.310	0.321	0.795	+0.331

4.3 Two Structural Microstructure Findings on VPIN

Table 4 establishes two important engineering rules for deploying VPIN in production:

1. Why Unconditional VPIN Tracks Volatility While Partial VPIN Does Not: Unconditionally, VPIN correlates positively with forward 5-minute volatility across every active symbol ($\rho \in [+0.264, +0.442]$), making the tile an effective visual regime monitor on a trading desk. However, once trailing realized volatility $\text{RV}{\text{trail}}$ and diurnal time-of-day are controlled for, partial correlations turn slightly negative ($\rho{\text{partial}} \in [-0.218, -0.068]$). The last column of Table 4 shows why: under the trade-to-trade tick rule (trade.Price >= prevPrice), consecutive prints at an unchanged price inherit the prior aggressor sign ($\rho_{\text{sticky}} \in [+0.198, +0.571]$). Quiet, sticky-price consolidations therefore generate long runs of identical tick-rule signs. Wiring exchange-native aggressor flags (Trade.IsBuy from ITCH OrderExecuted) removes the zero-tick persistence artifact.
2. The 20-Trade Bucket Floor (D4 Calibration Rule): When a single print exceeds bucket volume $V$, a naive two-print split (50% buy, 50% sell) pins bucket imbalance at 0.500. Calibrating bucketVolumeSize on regular-hours (09:30:00 ET to 16:00:00 ET) median trade sizes so that each bucket aggregates at least 20 trades restores full dynamic range across all 14 symbols.

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5. Post-Shock Liquidity Replenishment (edge-MR4 & edge-MRB3)

5.1 Theoretical Foundation and Trigger Architecture

Classical market microstructure models (Kyle, 1985) and empirical limit order book recovery studies (Large, 2007; Obizhaeva and Wang, 2013) characterize resiliency as the speed at which quoted spreads and book depth revert to equilibrium following an liquidity shock.

In VisualHFT, MarketResilienceStudy (MR) and MarketResilienceBiasStudy (MRB) are governed by a three-part state detector (MarketResilienceCalculator + ImmediacyDepthProbe):

1. Trade Shock: Incoming trade flow exceeds the rolling baseline threshold.
2. Spread Shock (IsSpreadShock): The quoted bid-ask spread widens past its dynamic z-score threshold (>= 2.0 standard deviations above the rolling mean).
3. Depth Depletion (ImmediacyDepthProbe): Near-touch volume thins past the depletion threshold, initiating a recovery timer (thisRecoveryMs) until depth and spread normalize.

5.2 Self-Normalization of the MR Recovery Score (edge-MR4)

When a shock recovers in elapsed time $T_{\text{curr}} = \text{thisRecoveryMs}$, MarketResilienceCalculator computes the recovery sub-score relative to the symbol’s rolling historical recovery average $\bar{T}_{\text{hist}} = \text{avgHistoricalRecoveryMs}$:

$$ S_{\text{rec}} = \frac{\bar{T}{\text{hist}}}{\bar{T}{\text{hist}} + T_{\text{curr}}} $$

Notice the mathematical symmetry of this ratio: whenever a symbol recovers at its own typical historical speed ($T_{\text{curr}} \approx \bar{T}{\text{hist}}$), the sub-score evaluates to $S{\text{rec}} = \frac{1}{1 + 1} = 0.50$, regardless of whether $\bar{T}_{\text{hist}}$ is 5 milliseconds (on AAPL or QQQ) or 5,000 milliseconds (on a thin mid-cap). Consequently, the composite MR score self-normalizes around 0.50 in steady state and deflects downward (0.25 to 0.35) only during active, unrecovered shocks.

Table 5 reports the 12 symbols where MR varies during the session (AMD and QQQ remain pinned at 1.00 because their 1-cent minimum tick spread rarely triggers a spread z-score shock), testing whether post-shock MR levels predict forward 60-second time-weighted spread or 1-second passive markouts under 5,000 circular label rotations.

Symbol	Total MR Updates	Distinct Value Changes	Depletion Events (6,715 Total)	Activity-Matched Firing Lift (ImmediacyDepthProbe)	Depth-Z Matched Firing Lift	Mean MR in Fast-Recovery Regime	Mean MR in Slow-Recovery Regime	Rotation $p$-Value (60s Spread)	Rotation $p$-Value (1s Markout)
AAPL	14,820	312	842	4.2x	1.4x	0.54	0.48	0.412	0.518
AMZN	4,190	184	418	3.9x	1.3x	0.53	0.46	0.385	0.442
CSCO	8,910	96	390	3.8x	1.2x	0.55	0.50	0.520	0.601
CTAS	1,840	74	285	4.1x	1.3x	0.52	0.47	0.490	0.534
GILD	7,640	118	462	4.0x	1.3x	0.54	0.49	0.465	0.498
IDXX	1,620	68	264	3.9x	1.2x	0.51	0.46	0.512	0.556
INTC	11,450	142	612	4.1x	1.4x	0.55	0.49	0.438	0.489
MSFT	13,210	265	795	4.3x	1.4x	0.54	0.48	0.394	0.471
NFLX	3,890	156	510	3.7x	1.2x	0.52	0.45	0.362	0.415
POOL	1,490	62	245	3.8x	1.2x	0.52	0.47	0.530	0.572
SBUX	6,980	128	512	4.0x	1.3x	0.54	0.48	0.448	0.509
VRTX	2,310	89	340	4.1x	1.3x	0.53	0.47	0.476	0.521
Pooled / Summary	78,350	1,694	6,715 (incl. AMD, QQQ)	4.0x (47.6% vs 12.0%, $p = 0.0002$)	1.3x (47.6% vs 37.4%)	0.53	0.47	Self-normalized	Self-normalized

5.3 Depletion Clustering and Selective Firing of MRB (edge-MRB3)

Two empirical findings explain how MR and MRB behave on live equity feeds:

1. Event-State Specificity (4.0x Activity-Matched Clustering): Across all 6,715 inner-depth depletion events in the 14-symbol corpus, MR updates within 500 ms on 47.6% of depletions versus 12.0% at activity-matched random times (4.0x lift, $p = 0.0002$). When matched strictly on depth z-score without a spread breakout (IsSpreadShock = false), the lift is 1.3x (1.0x under spread-neutral thinning), proving that MR specifically isolates compound spread-and-depth shocks.
2. Selective Conversion of MRB (127 / 6,715 = 1.89%): MarketResilienceBiasStudy emits a directional bias (+1 bullish replenishment or -1 bearish replenishment) only when post-shock depth recovery is both fast and one-sided by more than 30%. Out of 6,715 raw depth depletions, only 127 events (1.89%) pass all three gates, with a median directional state hold of 30.03 seconds (interquartile range 12.00s to 78.42s).

Table 6 reports the directional agreement of those 127 MRB firings at $H = 5\text{ s}$ and $H = 30\text{ s}$ against each symbol’s unconditional up-rate and a 5-second signed aggressor-volume rival.

Evaluation Metric	$H = 5\text{ Seconds}$	$H = 30\text{ Seconds}$	Structural Interpretation
Total Selective MRB Firings Across 14 Symbols	127 (of 6,715 depletions, 1.89%)	127 (1.89% conversion)	High-selectivity state filter; ignores 98.1% of routine depth flickers.
MRB Directional Agreement with Forward Mid-Price	52.0%	53.5%	Tracks book replenishment state rather than standalone drift.
5s Signed Aggressor-Volume Rival Agreement	56.7% (p = 0.28 diff)	55.1% (p = 0.64 diff)	Statistically indistinguishable from signed tape flow on standalone drift.
Median State Persistence (Hold Duration)	30.03 seconds	IQR: 12.00s to 78.42s	Ideal cadence for human desk supervision and post-sweep re-quoting gates.

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6. Deterministic Multi-Condition Evaluation in TriggerEngineService

To translate these statistical properties into automated desk alerts without introducing GC pauses or UI thread contention, VisualHFT decouples signal calculation from alert routing via TriggerEngineService:

1. Zero-Allocation Hot-Path Emission: Each study plugin computes its metric on its dedicated background consumer channel and emits BaseStudyModel snapshots to TriggerEngineService.
2. Cross-Plugin AND Conjunctions: Rules combine conditions across distinct plugins (for example, LOB Imbalance <= -0.70 AND VPIN >= 0.70 or Market Resilience >= 0.50) with configurable CooldownDuration windows (TimeSpan) to suppress duplicate triggers during a single microsecond burst.
3. Asynchronous Webhook Dispatch: When all conditions in a rule evaluate to true, TriggerEngineService dispatches the templated JSON payload asynchronously over HTTP (RestApiAction), isolating network I/O from order book processing.

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7. References

1. Andersen, T. G., & Bondarenko, O. (2014). VPIN and the Flash Crash. Journal of Financial Markets, 17, 1-46.
2. Cao, C., Hansch, O., & Wang, X. (2009). The Information Content of an Open Limit-Order Book. Journal of Futures Markets, 29(1), 16-41.
3. Cont, R., Kukanov, A., & Stoikov, S. (2014). The Price Impact of Order Book Events. Journal of Financial Econometrics, 12(1), 47-88.
4. Easley, D., López de Prado, M. M., & O’Hara, M. (2012). Flow Toxicity and Liquidity in a High-Frequency World. Review of Financial Studies, 25(5), 1457-1493.
5. Gould, M. D., & Bonart, J. (2016). Queue Imbalance as a One-Tick-Ahead Price Predictor in a Limit Order Book. Market Microstructure and Liquidity, 2(02), 1650006.
6. Kyle, A. S. (1985). Continuous Auctions and Insider Trading. Econometrica, 53(6), 1315-1335.
7. Large, J. (2007). Measuring the Resiliency of an Electronic Limit Order Book. Journal of Financial Markets, 10(1), 1-25.
8. Lipton, A., Pesavento, U., & Sotiropoulos, M. G. (2013). Trade Arrival Dynamics and Quote Imbalance in a Limit Order Book. arXiv preprint arXiv:1312.0514.
9. Obizhaeva, A. A., & Wang, J. (2013). Optimal Trading Strategy and Supply/Demand Dynamics. Journal of Financial Markets, 16(1), 1-32.