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A Frequency-Controlled Comparison of Tick- and Minute-Based Information Bars for Cryptocurrency Markets

Muhammad Toheed Fayyaz, Abdul Jabbar, Faheem Ahmad Qureshi, Syed Qaisar Jalil

arXiv:2608.26158v1q-fin.STcs.CE

TL;DR

The paper asks whether raw tick data materially improves information-bar construction relative to minute OHLCV data. It compares six bar types through common adaptive calibration and tick-native signals, finding that tick advantages depend on bar type and sampling frequency. The results also show that statistical bar quality does not guarantee directional forecastability.

  • Problem

    Prior work lacked a controlled, systematic comparison of the same information bar types constructed from tick-level trades versus minute-level OHLCV data.

  • Method

    The study compares six information bar types from Binance BTCUSDT tick and one-minute data over six years, using common adaptive calibration, eight criteria, and matched-frequency analysis.

  • Results

    Tick advantages are bar-type-specific: tick Renko reaches |VR(4)-1| = 0.020 and AC lag-1 = 0.002, while matched-frequency tick dollar bars lead on all six criteria.

  • Takeaways & Limitations

    Statistical bar quality and directional forecastability are distinct properties, so improved information-bar criteria should not be treated as evidence of superior trading signals.

  • Takeaways & Limitations

    A controlled ablation is needed to isolate activity-based sampling from EMA-induced threshold smoothing.

Abstract

from arXiv · show

This paper provides a controlled comparison of six information bar types (dollar, volume, volatility, range, Renko, and hybrid bars) constructed from both raw Binance aggTrade tick data and one-minute OHLCV bars for the BTCUSDT USDT-margined perpetual futures market over a six-year period spanning January 2020 to December 2025, and evaluated against fixed-interval time-bar baselines. Both pipelines share a common adaptive EMA calibration framework; the tick pipeline additionally uses strictly tick-native activity signals, isolating data resolution as the sole experimental variable. Results across eight statistical quality criteria reveal that the tick advantage is bar-type-specific and most pronounced in bar types whose activity signals are most sensitive to intra-minute price dynamics: tick Renko bars achieve the smallest random-walk deviation recorded ($|\mathrm{VR}(4){-}1| = 0.020$, lag-1 autocorrelation $= 0.002$), and tick volatility bars reduce serial dependence by 69\% relative to the minute baseline ($|\mathrm{VR}(4){-}1|: 0.028$ versus $0.089$). In the multi-regime six-year sample, normality improvements are regime-dependent and secondary: the extreme market events of 2020--2022 inflate fat tails across all bar types, and Ljung-Box independence is rejected for all series at the sample sizes studied. A matched-frequency robustness analysis shows that the apparent tick underperformance on distributional criteria is largely a sampling-frequency artefact: when tick series are coarsened to the minute pipeline's bar count, frequency-matched tick dollar bars lead on all six criteria and matched tick volatility bars attain LB $p = 0.51$, recovering serial independence that the raw oversampled series rejects.

I. INTRODUCTION

Calendar sampling can distort cryptocurrency return properties because market activity is uneven and continuous. This paper addresses the unresolved effect of tick versus minute input resolution through a controlled, multi-bar-type comparison.

  • Motivation: Continuous cryptocurrency trading and uneven order flow make fixed calendar intervals a poor match for information arrival.Quiet periods alternate with rapid bursts of activity, while Bitcoin exhibits fat tails and dependence patterns motivating activity-based sampling.
  • Prior foundation: Activity-based bars close when accumulated market activity reaches a threshold rather than when a clock interval expires.The paper draws on prior work linking activity-based sampling to return distributions and microstructure properties.
  • Research gap: The central gap is whether raw tick trades and pre-aggregated minute OHLCV data materially change the statistical and economic properties of otherwise identical information bars.Minute data loses intra-minute reversals, microstructure events, and partial fills, whereas tick data processes each trade.
  • Study design: The study compares dollar, volume, volatility, range, Renko, and hybrid bars against fixed-interval baselines using common adaptive calibration.Both pipelines are evaluated on BTCUSDT perpetual futures over six years and across eight statistical quality criteria.
  • Study design: A matched-frequency robustness analysis separates genuine resolution effects from sampling-frequency artefacts.The tick series are coarsened to the minute pipeline’s bar count for frequency-matched comparison.
  • Motivation: The intended downstream application is machine learning, where more uniform information content may reduce look-ahead and serial-correlation biases.The paper treats improved statistical bar properties as a proposed training-substrate benefit rather than an established trading outcome.

C. Methodological Considerations

The paper extends activity-based sampling with adaptive thresholds, duration guards, and several noncanonical signal definitions. These choices improve operational control but bound how results should be compared with canonical methods.

  • Adaptive calibration: EMA thresholds create a path-dependent adaptive pipeline rather than a fixed-threshold rule.The adaptation rate is calibrated from historical coefficient-of-variation and regime-stability measures.
  • Adaptive calibration: A controlled ablation comparing fixed and adaptive thresholds is left for future work.Observed improvements therefore reflect the joint effect of activity sampling and EMA-induced threshold smoothing.
  • Duration constraints: Minimum and maximum duration bounds give the bars a hybrid calendar/activity character.Minimum duration prevents pathologically short bars, while maximum duration forces closure during low activity.
  • Bar definitions: The implemented Renko accumulator uses instantaneous displacement, which can decrease after price reversals.Unlike classical Renko, formed bricks are not held irreversibly, so comparisons with canonical Renko studies require care.
  • Bar definitions: Minute and tick range bars accumulate structurally different signals: summed per-minute ranges versus exact within-bar excursion.The minute approximation systematically underestimates true high-low span in mean-reverting intra-minute environments.
  • Bar definitions: Hybrid bars use OR closure logic because AND logic produces timeout rates exceeding 60% at characteristic Bitcoin threshold correlations.OR logic yields approximately 65% organic close rate at typical correlation levels.

B. Cryptocurrency Market Structure and Statistical Properties

Cryptocurrency’s continuous, order-flow-driven structure makes sampling choices consequential and provides a demanding setting for information bars. The study applies tick-native and minute-based pipelines to Binance BTCUSDT data under a shared framework.

  • Market structure: Continuous trading without session boundaries and documented return dependence make cryptocurrency markets a strong test bed for activity-based sampling.Bitcoin’s statistical properties and frequency-sensitive efficiency measures reinforce the relevance of the sampling question.
  • Market structure: Cryptocurrency price formation is strongly connected to order flow and exchange-level market structure.Prior work documents persistent cross-exchange arbitrage deviations and mechanisms distinct from traditional asset markets.
  • Machine learning: Information bars are motivated as more uniform machine-learning training substrates than calendar-sampled series.The literature links uniform information content to reduced serial-correlation and look-ahead biases.
  • Open problems: Prior work used several bar types with deep learning but did not compare tick-level with minute-level construction or include volatility and hybrid bars systematically.The present study also evaluates the bars against de Prado quality criteria.
  • Evaluation scope: The paper adds timeout percentage and BDS-based nonlinear dependence as explicit evaluation dimensions.Timeout percentage diagnoses calibration failure, while BDS detects dependence structures invisible to standard autocorrelation tests.
  • Data: The dataset is Binance BTCUSDT USDT-margined perpetual futures, with tick records containing trade price, quantity, timestamp, and buyer-maker information.The tick pipeline maintains accumulators continuously across processing batches.
  • Data and calibration: Minute OHLCV dollar volume is approximated as close times volume, discarding intra-minute price paths and introducing systematic bias.Both pipelines otherwise share a common 14-day calibration framework, while tick thresholds are replaced with tick-native activity measures.

B. Calibration Framework

Both pipelines initialize activity thresholds from recent history, then adapt them online with an EMA and duration guards. The tick pipeline replaces minute-derived thresholds with exact tick-native activity measures to isolate resolution.

  • Framework: Static thresholds can become miscalibrated across market regimes, motivating online adaptation to prevailing conditions.The framework uses a two-stage calibration procedure.
  • Historical initialisation: Stage 1 derives initial thresholds, EMA rates, and duration bounds from a 14-day minute-OHLCV calibration window.The initial activity threshold is median daily activity divided by the target bars-per-day.
  • Tick-native replacement: The tick pipeline discards minute-derived thresholds and substitutes median daily tick-native activity divided by the same target bars-per-day.Tick-native measures include exact dollar volume, realized volatility, and running high-low span.
  • Online adaptation: Stage 2 updates the activity threshold after each bar closes using an exponentially weighted moving average.The EMA provides online threshold tracking without requiring a fixed history buffer.
  • Robustness: The capped update min(s_n, 2θ̂_n) prevents one extreme-activity event from permanently inflating the threshold.Without the cap, subsequent bars could become timeout bars after a flash crash or news spike.
  • Estimator choice: The EMA was selected as a computationally practical level estimator for heavy-tailed activity with adaptive tracking speed.Its rate increases under unstable threshold variability and decreases under stable conditions.
  • Duration guards: Minimum and maximum duration bounds hold bars open briefly when activity is insufficient and force-close them when thresholds remain unmet.Force-closed bars are flagged as timeout bars, and timeout percentage is reported as a calibration diagnostic.

C. Evaluation Framework

The evaluation compares information bars with frequency-matched fixed-interval baselines using eight criteria grouped around distributional normality, serial independence, and information density. Primary interpretation emphasizes effect sizes, while supplementary tests characterize and contextualize the results.

  • Evaluation criteria: Eight statistical criteria assess distributional normality, serial independence, and information density against fixed-interval time-bar baselines.The criteria are applied across six bar types and three series: minute, tick, and time bar.
  • Primary metrics: |VR(4)−1|, |AC(1)|, and excess kurtosis are primary metrics because they measure random-walk conformance and tail heaviness.Jarque-Bera, Ljung-Box, bar-size CV, Shannon entropy, timeout percentage, BDS, ARCH-LM, KS, and Mann-Whitney are secondary diagnostics.
  • Interpretation: At sample sizes from roughly 30,000 to over 200,000 observations, p-values provide limited discrimination, so comparisons rely on effect-size magnitudes.Ljung-Box and Jarque-Bera return p ≈0 for essentially every series, including economically trivial departures.
  • Interpretation: The tests are used descriptively to characterize cross-bar patterns, without binary accept/reject decisions or multiple-testing correction.The protocol produces 48 primary comparisons across six bar types and three series.
  • Construction: Each bar maintains an activity accumulator and closes when its adaptive threshold is reached, subject to duration bounds.Standard OHLCV fields, bar size, and return are recorded; tick bars additionally provide VWAP, tick count, and buy-sell imbalance.
  • Construction: Tick dollar volume uses exact trade prices and quantities, whereas the minute pipeline approximates dollar volume with closing price times minute volume.The minute accumulator checks threshold crossing only at minute boundaries; the tick accumulator advances with every trade.

B. Volume Bars

Volume bars use cumulative traded quantity as their activity signal in both pipelines. Because minute and tick quantities sum to the same total, their principal difference is when threshold crossings are detected.

  • Volume-bar definition: Volume bars close when cumulative traded quantity reaches the adaptive threshold.This activity signal isolates supply and demand dynamics from price level.
  • Minute pipeline: Minute volume increments use total traded quantity in each one-minute interval.The minute pipeline checks the accumulated quantity at minute boundaries.
  • Tick pipeline: Tick volume increments use the quantity of each individual trade.The tick accumulator advances trade by trade rather than at one-minute boundaries.
  • Pipeline comparison: The minute and tick volume pipelines accumulate arithmetically equivalent total quantities over a bar’s duration.Their practical difference is temporal resolution, not the total quantity accumulated.
  • Pipeline comparison: Tick bars close at the precise trade that first crosses the threshold, while minute bars can incur a detection lag of up to 59 seconds.This lag arises because minute bars can evaluate closure only at one-minute boundaries.

C. Volatility Bars

Volatility bars sample according to accumulated price movement, with the tick pipeline measuring realized trade-level path length and the minute pipeline using close-to-close changes. The two signals diverge most when intra-minute reversals cancel in closing prices.

  • Volatility-bar definition: Volatility bars close when accumulated price movement reaches the adaptive threshold, aligning sampling with the rate of price discovery.This bar type has the largest signal difference between the minute and tick pipelines.
  • Minute pipeline: Minute volatility accumulates absolute close-to-close price movement across one-minute intervals.Each increment compares consecutive minute closing prices.
  • Tick pipeline: Tick volatility accumulates realized volatility from every consecutive trade pair, capturing intra-minute reversals.Three round-trip oscillations of 0.05% contribute 0.15% to the tick accumulator but approximately zero to the minute close-to-close signal.
  • Pipeline comparison: The close-to-close signal is a strict lower bound on true intra-bar path length because cancelling reversals add to tick volatility but not minute volatility.The gap is largest in mean-reverting intra-minute environments and smallest in sustained trends.
  • Range-bar comparison: Range bars use different activity constructions: minute bars sum per-minute high-low spans, while tick bars track the overall band from bar open to the current extreme.The two quantities are not monotonically related because repeated minute ranges and directional drift affect them differently.
  • Range-bar comparison: Tick range displacement advances only when a new trade-price extreme is established; reversals that set no new extreme leave it unchanged.The signal measures the instantaneous excursion from the bar’s opening trade price.

E. Renko Bars

Renko bars close when price reaches an adaptive displacement threshold, but this implementation uses instantaneous displacement rather than classical irreversible brick registration. Tick resolution detects threshold crossings earlier and produces substantially more bars than the minute pipeline.

  • Renko-bar definition: Renko bars close when price moves a minimum relative distance from the bar’s reference price, filtering short-term oscillations.The implementation is intended to isolate sustained directional moves.
  • Minute pipeline: Minute Renko displacement compares each minute’s closing price with the current bar’s opening reference price.Closure requires the threshold and minimum-duration constraint to be satisfied.
  • Implementation caveat: This implementation uses instantaneous displacement that decreases after partial reversals, unlike classical Renko’s irreversible brick registration.It therefore closes bars less frequently during oscillatory markets and produces higher timeout rates in low-trend regimes.
  • Tick pipeline: Tick Renko applies the same displacement formula to individual trade prices and closes at the first threshold-crossing trade.Trade-level checking detects breaches before the next minute boundary and yields substantially more bars over the same period.
  • Comparability: The tick and minute Renko series operate at fundamentally different resolution scales and are not directly comparable in the same sense as dollar, volume, or volatility bars.The paper interprets their results with this bar-count distinction in mind.
  • Hybrid bars: Hybrid bars close when either dollar-volume or realized-volatility activity first reaches its threshold, subject to duration constraints.Both accumulators advance simultaneously in the tick loop, and the first triggered signal closes the bar.

V. EMPIRICAL RESULTS

Across the six-year multi-regime sample, all return series were stationary, but bar-type comparisons showed different trade-offs between distributional normality and serial independence. Tick pipelines generally improved some dependence measures, while minute pipelines often produced less extreme distributions.

  • ADF rejects the unit-root null at p < 0.001 and KPSS cannot reject stationarity at p = 0.100 for all eighteen series.
  • Dollar Bars: Minute dollar bars lead on five criteria, including excess kurtosis 23.7 versus 50.4 and bar-size CV 0.010 versus 0.399 for tick bars.
  • Dollar Bars: At q = 8, tick dollar bars achieve |VR(8)−1| = 0.059 versus 0.066 for the sixty-minute time baseline, although Ljung-Box rejects independence for all three series.
  • Volume Bars: Minute volume bars lead on entropy, excess kurtosis 7.21 versus 26.98, Jarque-Bera 27,986 versus 1,658,322, and Ljung-Box p-value 0.005 versus 0.000.
  • Volume Bars: Tick volume bars lead on |VR(4)−1| = 0.038 versus 0.062, |AC1| = 0.024 versus 0.026, and timeout rate 0.0% versus 4.8%, while the time baseline has VR deviation 0.012.

C. Volatility Bars

Volatility, range, and Renko bars show that tick-level resolution can improve random-walk conformity, but the gains are bar-type-specific and accompanied by large frequency and distributional differences. Volatility bars favor tick data for dependence measures, whereas range and Renko results expose distinct resolution-scale trade-offs.

  • Volatility Bars: Tick volatility bars produce 164,591 bars versus 8,624 minute bars, a 19-fold difference caused by faster realised-volatility accumulation at tick resolution.
  • Volatility Bars: Tick volatility bars reduce |VR(4)−1| from 0.089 to 0.028, a 69% reduction and the largest relative improvement across bar types.Tick volatility bars also have |AC1| = 0.013 versus 0.044 for minute bars.
  • Range Bars: Minute range bars lead on six of eight criteria, including excess kurtosis 8.19 versus 150.7 and |VR(4)−1| = 0.037 versus 0.107 for tick bars.The eight-hour time baseline achieves the lowest VR deviation, 0.028.
  • Renko Bars: Tick and minute Renko bars differ by 26-fold in bar count because tick displacement is checked per trade while minute displacement is checked only at minute boundaries.
  • Renko Bars: Tick Renko returns have standard deviation 0.0034 versus 0.0170 for minute Renko returns, producing a narrower, taller density on the shared return axis.The figure note attributes this visual contrast directly to resolution-scale mismatch.
  • Renko Bars: Tick Renko bars achieve |VR(4)−1| = 0.020 and |AC1| = 0.002, the lowest values across all bar types and pipelines.Ljung-Box still rejects independence at the studied sample size, so the result reflects reduced effect size rather than exact independence.
  • Renko Bars: Minute Renko bars lead on distributional normality, with excess kurtosis 2.31 versus 24.92 and Jarque-Bera 2,015 versus 6,116,039.Their timeout rate is 12.3%, above the 10% calibration warning threshold.
  • Renko Bars: Renko results are interpreted as establishing resolution limits for displacement-based bars, not uniform superiority of either pipeline.

F. Hybrid Bars

Hybrid bars close on dollar-volume or realised-volatility activity signals, with tick and minute pipelines producing different frequencies and statistical profiles. Tick hybrid bars lead on several distributional and variance-ratio criteria, while minute hybrids provide better bar-size uniformity and slightly stronger Ljung–Box results.

  • Construction and frequency: 90,856 tick hybrid bars versus 28,738 minute hybrid bars were produced, with timeout rates of 0.2% and 0.0%, respectively.Both pipelines therefore closed on genuine activity signals rather than frequent calibration failures.
  • Distributional quality: 6.77 tick excess kurtosis versus 20.88 minute and 57.12 time-bar excess kurtosis made tick hybrid the strongest normality result among tick bar types.The six-year sample nevertheless strongly rejected normality for both pipelines.
  • Cross-bar comparison: 0.020 on |VR(4)−1| and 0.002 on lag-1 autocorrelation made tick Renko the best random-walk-conforming series across all reported series.Its 26-fold bar-count difference reflects different resolution scales, so Renko cross-pipeline comparisons are resolution-specific.
  • Serial-dependence criteria: 0.023 versus 0.029 on |VR(4)−1| gave tick hybrids the better variance-ratio result, with the tick advantage persisting at q = 8: 0.028 versus 0.042.Tick hybrids also led on Shannon entropy, 2.60 versus 2.39.
  • Serial-dependence criteria: 0.059 versus 0.041 on Ljung–Box p-values favored minute hybrids, while bar-size CV favored minute hybrids by 0.010 versus 0.583.Lag-1 autocorrelation was marginally lower for minute hybrids, 0.008 versus 0.010.
  • Interpretation and limitations: All bar types rejected serial independence and normality in the 2020–2025 multi-regime sample, limiting claims of blanket tick-data superiority.The paper recommends selecting the pipeline by bar type and the downstream criterion that matters most.

A. Experimental Design

The paper tests whether data resolution changes information-bar quality and downstream prediction by comparing common-protocol pipelines on statistical and machine-learning evaluations. It finds near-chance directional predictability, no systematic link between statistical quality and AUC, and important limitations from feature selection and backtest interpretation.

  • Objective: The downstream experiment tests whether statistical quality advantages translate into superior out-of-sample directional prediction.This directly evaluates the paper’s stated machine-learning motivation.
  • Labeling: Each bar receives a +1 or −1 label according to whether its close rises over the next three calendar days.The horizon exceeds every bar’s minimum duration and remains within a regime of measurable price memory.
  • Features: A unified 28-feature stationary set is constructed for every bar type to ensure fair cross-bar comparison.Features remove price-level dependence that could inflate apparent in-sample skill.
  • Models: Three default classifiers—Random Forest, Gradient Boosting, and SVM—are evaluated without cross-bar hyperparameter tuning.Datasets over 15,000 events are subsampled only for SVM because of its quadratic memory and compute scaling.
  • Evaluation protocol: Five-split walk-forward cross-validation uses an expanding training window and a 1% embargo to limit leakage from overlapping return windows.Out-of-sample predictions from all folds are concatenated for evaluation.
  • Prediction results: 0.498–0.596 AUC-ROC across all bar types and data sources indicates near-chance directional predictability; minute Renko’s 0.596 was the highest.The differences are small relative to liquid-market directional-prediction noise and should not be treated as a meaningful ranking.
  • Prediction results: No single statistical criterion systematically predicted AUC: minute volatility combined |AC1| = 0.044 with AUC 0.498, while minute hybrid combined 0.008 with 0.529.The paper characterizes statistical conditioning and directional predictability as largely orthogonal in this dataset.
  • Limitations: The unified feature set may disadvantage tick information bars by excluding native variables such as VWAP, buy-sell imbalance, tick count, and realised-volatility accumulators.Adding bar-type-specific native features is identified as a follow-up direction.

VII. DISCUSSION

The tick-level advantage is signal-dependent: it grows when minute aggregation loses intra-minute activity information, while calibration and regime differences constrain interpretation.

  • Resolution Advantage and Its Structural Determinants: Tick-level quality gains are proportional to information lost when minute aggregation approximates the underlying activity signal.The paper distinguishes structural mismatch from regime mismatch as the two main sources of calibration challenge.
  • Resolution Advantage and Its Structural Determinants: Tick hybrid bars achieve excess kurtosis 6.77 and JB = 174,557, the lowest values among tick-source pipelines.The OR rule closes when tick-native dollar volume or realised volatility first reaches its threshold, aligning boundaries with elevated activity.
  • Resolution Advantage and Its Structural Determinants: Tick volatility bars reduce |VR(4)−1| by 69% versus minute bars, achieving 0.028 versus 0.089 despite producing more observations.Minute volatility uses close-to-close displacement, whereas tick volatility captures total intra-minute price-path length.
  • Resolution Advantage and Its Structural Determinants: Minute volume bars lead on four of eight criteria, with LB p = 0.005 versus 0.000 for tick volume bars.The minute and tick volume signals are arithmetically equivalent, while smoother minute closure timing yields lower residual serial correlation.
  • Resolution Advantage and Its Structural Determinants: Minute range bars lead on five of eight criteria, including entropy 3.245 versus 1.388, kurtosis 8.19 versus 150.70, and LB p = 0.540 versus 0.000.The result is consistent with structural differences between cumulative per-minute spans and tick-level displacement accumulation.
  • Calibration and Regime Effects: The calibration window covers 1–14 January 2020, while later shocks and regime transitions produced substantially different dollar volumes and realised volatilities.EMA adaptation updates thresholds continuously; the paper recommends multi-regime calibration windows or regime-detection procedures for future work.
  • Calibration and Regime Effects: Tick Renko produces 236,098 bars versus 8,985 minute bars, a 26-fold difference, with tick entropy of 2.984.The result reflects microstructure-level displacement detection and indicates concentrated bar sizes inconsistent with diverse information-event sampling.
  • Calibration and Regime Effects: Hybrid calibration sets each threshold to 2× the desired frequency, while timeout rates remain 0.0% for minute and 0.1% for tick pipelines.The combined OR firing rate targets the intended bars-per-day under the observed dollar-volume/volatility correlation.

C. Matched-Frequency Robustness Analysis

Raw tick comparisons are confounded by higher sampling frequency, so coarsening tick series to the minute bar count tests whether apparent distributional disadvantages persist at matched frequency.

  • Frequency Mismatch: Tick pipelines sample 2.8–26.6× more frequently than minute counterparts, mechanically inflating excess kurtosis and altering per-bar return scaling.Examples include dollar bars at 37.9 versus 13.7 bars/day and Renko bars at 109.7 versus 4.1 bars/day.
  • Matched-Frequency Design: Table VII compares phase-averaged 1:k-coarsened tick bars with minute bars and calendar baselines on six criteria.The criteria are |kurtosis|, |AC1|, JB, LB p(10), |VR(4)−1|, and |VR(8)−1|; wins count the criteria where matched tick is best.
  • Matched-Frequency Design: For additive signals, aggregating k threshold bars is nearly equivalent to using a k× threshold, but equivalence is only approximate for path-dependent range and Renko rules.Matched-frequency results for range and Renko should therefore be treated as indicative rather than exact.
  • Matched-Frequency Results: Matched tick dollar bars lead on all six criteria, with kurtosis 20.8 versus 23.7 minute and LB p = 0.052 versus the minute pipeline.Their |VR(4)−1| is 0.029 versus 0.051 for minute and 0.041 for the time bar.
  • Matched-Frequency Results: Matched tick hybrid bars lead on five of six criteria, with kurtosis 3.09, JB = 12,775, and LB p = 0.245.The result supports a tick advantage after frequency is controlled for hybrid activity signals.
  • Overall Findings: The paper compares six bar types across raw Binance tick data, one-minute OHLCV data, and fixed-interval time bars using eight statistical criteria over six years.The study covers BTCUSDT perpetual futures from 1 January 2020 to 31 December 2025.
  • Overall Findings: Tick quality advantages are bar-type-specific: hybrid and selected Renko criteria favour ticks, while dollar, volume, volatility, and range generally favour minute bars before matching frequency.For Renko, tick AC lag-1 is −0.002 versus −0.028 minute, and |VR(4)−1| is 0.020 versus 0.070.
  • Overall Findings: Tick hybrid bars have the lowest tail risk among tick pipelines, with kurtosis 6.77 and JB = 174,557.They also achieve |VR(4)−1| = 0.023 and LB p = 0.041 among tick-source series.
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