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deliverable Β· 120 grounded cards Β· 118 not-covered

All candidates β€” FOSS & provenance

Every grounded candidate with a clickable FOSS implementation reference, an SPDX license badge (vs MIT host), a resolvable paper ID, the git-anchor provenance, and the chronicle-crosscheck coverage verdict.

permissive 64 copyleft (clean-room) 43 unverified 13 crypto-prior 16 forex-dup 2
#CandidateFamilyFOSS implementation @ licensePaper Β· provenanceCoverage
#1 l_skewness_tau3
Robust, parameter-free measure of return/tick-move asymmetry built from linear combinations of order statistics (L-moments) rather than third powers β€”
πŸ“ Distributional shape (L-moment OpenHydrology/lmoments3
GPL-3 (lmoments3); BSD (scipy)
DOI:10.1111/j.2517-6161.1990.t
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#2 l_kurtosis_tau4
Robust, parameter-free tail-peakedness measure from L-moments; concords with goodness-of-fit power and resists outliers far better than classical kurt
πŸ“ Distributional shape (L-moment OpenHydrology/lmoments3
GPL-3 (lmoments3); BSD (scipy)
DOI:10.1111/j.2517-6161.1990.t
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#3 gini_mean_difference
Expected absolute difference between two independent draws of the within-bar return/spread distribution; a robust, distribution-free scale measure equ
πŸ“ Distributional shape (L-moment cran/lmomco
GPL-2.0-or-later
DOI:10.1111/j.2517-6161.1990.t
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#4 bowley_quantile_skewness
Quartile-based (Bowley/Galton) skewness coefficient: a bounded, outlier-robust asymmetry measure built from Q1, median, Q3 with fixed quartile positio
πŸ“ Distributional shape (L-moment scipy/scipy (quantiles) + ~3 lines; robustats reference impl
BSD-3-Clause (scipy)
DOI:10.2307/2987742
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#5 moors_octile_kurtosis
A robust quantile-based peakedness/tail measure built from octiles, capturing how dispersed the distribution is around the +/-sigma shoulders without
πŸ“ Distributional shape (L-moment scipy/scipy
BSD-3-Clause
DOI:10.2307/2348376
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#6 medcouple_skewness
A robust skewness statistic equal to the median of a kernel of pairwise (above-median, below-median) comparisons; 25% breakdown, bounded influence, sc
πŸ“ Distributional shape (L-moment statsmodels/statsmodels
BSD-3-Clause
DOI:10.1198/106186004X12632
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#7 right_quantile_weight_tailweight
A robust right-tail-heaviness descriptor: quartile skewness applied to the upper half of the distribution (above the median), capturing fat-right-tail
πŸ“ Distributional shape (L-moment cran/robustbase
GPL-3.0 (robustbase); reimplementa
DOI:10.1016/j.csda.2004.09.012
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#8 kelly_decile_skewness
A robust asymmetry measure reaching further into the tails than Bowley by using the 10th/50th/90th percentiles instead of quartiles, detecting outer-d
πŸ“ Distributional shape (L-moment numpy/numpy
BSD-3-Clause
DOI:10.1093/biomet/62.1.101
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#9 quartile_coeff_dispersion_intervals
(Q3 βˆ’ Q1)/(Q3 + Q1) of the within-bar inter-quote interval distribution β€” an outlier-robust, scale-free spread index of arrival-gap dispersion that do
πŸ“ Distributional shape (L-moment scipy/scipy
BSD-3-Clause
DOI:10.1016/j.csda.2005.05.007
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#10 sevcik_fd
Maps the bar's price/quote curve into the unit square then estimates fractal dimension from the total point-to-point Euclidean curve length, capturing
πŸͺ’ Fractal & curve-complexity raphaelvallat/antropy
BSD-3-Clause
arXiv:1003.5266
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#11 katz_fd
Fractal dimension of the price path computed from the ratio of total curve length to the path's diameter (max distance from the first point), capturin
πŸͺ’ Fractal & curve-complexity raphaelvallat/antropy
BSD-3-Clause
DOI:10.1016/0010-4825(88)90041
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#12 petrosian_fd
Fast fractal-dimension estimate driven only by the number of sign changes in the first difference of the series, measuring path roughness/zig-zag dens
πŸͺ’ Fractal & curve-complexity raphaelvallat/antropy
BSD-3-Clause
DOI:10.1109/CBMS.1995.465426
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#13 fractal_nld
Normalized Length Density: after amplitude standardization, the mean absolute first difference of the bar's series, mapped through a fixed Weierstrass
πŸͺ’ Fractal & curve-complexity neuropsychology/NeuroKit
MIT
DOI:10.1186/1753-4631-3-8
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#14 cid_ce_arclength
The CID complexity estimate: the amplitude-space arc length of the series, i.e. the square root of the summed squared first differences β€” a single-pas
πŸͺ’ Fractal & curve-complexity pmontman/TSclust
GPL-2.0+
DOI:10.1007/s10618-013-0312-3
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#15 hjorth_complexity
Ratio-of-ratios shape descriptor: how much the rate-of-change of the series departs from a pure sinusoid, i.e. waveform shape irregularity, derived pu
πŸͺ’ Fractal & curve-complexity raphaelvallat/antropy
BSD-3-Clause
DOI:10.1016/0013-4694(70)90143
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#16 intrabar_range_traversal_efficiency
How directly price walked between the high and the low: the bar's high-low range divided by the total absolute tick-to-tick path length traversed insi
πŸͺ’ Fractal & curve-complexity raphaelvallat/antropy
BSD-3-Clause
DOI:10.1016/0010-4825(88)90041
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#17 mean_cosine_turning_angle
Directional persistence of the tick/bar path: the average cosine of the heading change between consecutive segments in the (time, price) plane β€” a sig
πŸͺ’ Fractal & curve-complexity JimMcL/trajr
GPL-3
DOI:10.1016/j.jtbi.2004.03.016
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#18 vonneumann_ratio
Ratio of mean-square successive difference to total variance of the path β€” a parameter-free serial-structure / smoothness statistic; low values = tren
🎲 Randomness & rank tests (runs/ AndriSignorell/DescTools
GPL-2/GPL-3
DOI:10.1214/aoms/1177731677
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#19 bartels_rank_vn_ratio
Rank version of the von Neumann ratio: mean-square successive rank-difference over rank variance; a distribution-free serial-dependence/randomness sta
🎲 Randomness & rank tests (runs/ cran/randtests
GPL-2.0-or-later
DOI:10.1080/01621459.1982.1047
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#20 mann_kendall_s_z
Mann-Kendall monotonic-trend statistic: the normalized sum over all ordered bar pairs of the sign of (later value minus earlier value) β€” a rank-based,
🎲 Randomness & rank tests (runs/ cran/Kendall
GPL-2 (Kendall pkg); pymannkendall
DOI:10.2307/1907187
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#21 turning_point_rate_z
Standardized count of turning points (bars that are a strict local max or local min vs their two neighbors) β€” high values indicate oscillatory/mean-re
🎲 Randomness & rank tests (runs/ cran/randtests
GPL (>= 2)
DOI:10.1111/j.2517-6161.1954.t
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#22 difference_sign_test_z
Standardized count of positive first-differences (number of up-moves) across the lookback β€” a parameter-free sign-balance-of-increments statistic dist
🎲 Randomness & rank tests (runs/ cran/aTSA
GPL (>= 2)
DOI:10.1093/biomet/42.1-2.80
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#23 cox_stuart_trend_z
Cox-Stuart quick sign test for trend: pair the i-th value of the first half with the i-th of the second half, count how often the second exceeds the f
🎲 Randomness & rank tests (runs/ cran/randtests
GPL (>= 2)
DOI:10.1093/biomet/42.1-2.80
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#24 foster_stuart_records_d
Foster-Stuart record-breaking trend statistic: difference between counts of upper-record and lower-record breaks over the lookback β€” distribution-free
🎲 Randomness & rank tests (runs/ JorgeCastilloMateo/RecordTest
GPL (>= 3)
DOI:10.1111/j.2517-6161.1954.t
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#25 pomeau_irreversibility_lag1
The lag-1 time-asymmetric cubic statistic E[x_t^2 * x_{t-1} - x_t * x_{t-1}^2], which is positive/negative when the series rises and falls with differ
⏳ Time-irreversibility & tempora MZanin/irreversibilitytestslibrary
unknown/academic (verify on GitLab
arXiv:0708.4022
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#26 ehlers_increment_asymmetry
Ehlers' time-irreversibility index: the normalized third moment (skewness) of the first-difference series of close prices; zero means time-reversible,
⏳ Time-irreversibility & tempora MZanin/irreversibilitytestslibrary
unknown/academic (verify on GitLab
DOI:10.3390/e23111474
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#27 porta_increment_sign_asymmetry
Porta's index: the fraction of negative first-differences among all nonzero first-differences; a value far from 0.5 indicates acceleration/deceleratio
⏳ Time-irreversibility & tempora MZanin/irreversibilitytestslibrary
unknown/academic (verify on GitLab
DOI:10.3390/e23111474
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#28 guzik_increment_magnitude_asymmetry
Guzik's index: the share of total squared-increment 'energy' that comes from positive increments; differs from Porta by weighting by magnitude rather
⏳ Time-irreversibility & tempora MZanin/irreversibilitytestslibrary
unknown/academic (verify on GitLab
DOI:10.3390/e23111474
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#29 costa_accel_decel_asymmetry
Costa-Goldberger-Peng time-irreversibility index: difference between the rates/energies of consecutive increases vs decreases ('accelerations' vs 'dec
⏳ Time-irreversibility & tempora MZanin/irreversibilitytestslibrary
unknown/academic (verify on GitLab
DOI:10.1103/PhysRevLett.95.198
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#30 dhvg_indegree_outdegree_kld
Lacasa directed-horizontal-visibility-graph irreversibility: map the price series to a directed horizontal visibility graph and measure the Kullback-L
⏳ Time-irreversibility & tempora CarlosBergillos/ts2vg
MIT (ts2vg)
arXiv:1108.1691
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#31 trading_polarity
Net buy-vs-sell trade-count imbalance within the bar, signed and bounded in [-1,+1], using counts of buyer- and seller-initiated ticks rather than the
⚠ forex-roadmap-mentioned (listed as an UNTESTED inventory item in the May Gate extended-inventory; not yet evaluated β€” ve
πŸ”Ž FOREX-MENTIONED-ONLY (roadmap inventory, not evaluated)
🌊 Order-flow & tick intrinsics reimplement from paper
n/a
DOI:10.3390/e22080897
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#32 quote_revision_direction_asymmetry
Imbalance between the count of upward and downward revisions of the best-bid (and symmetrically best-ask) quote across the intra-bar quote stream β€” ca
πŸ”Ž FOREX-COVERED: evaluated on forex_bars in the 2026-05-26/27 Gate campaign
🌊 Order-flow & tick intrinsics reimplement from paper
n/a
DOI:10.1093/rfs/10.4.1035
git-anchor: absent @c803ef96e + @2d308f1c
β›” forex-dup
#33 quote_to_trade_ratio
Ratio of the number of quote updates to the number of executed trades within the bar β€” quoting intensity relative to execution, a market-quality/HFT-a β€” β›” OUT-OF-SCOPE (G5): quote-only substrate, no trades/volume
🌊 Order-flow & tick intrinsics reimplement from paper
n/a
DOI:10.1016/j.jbankfin.2014.09
git-anchor: absent @c803ef96e + @2d308f1c
β›” out-of-scope (G5)
#34 buy_sell_duration_asymmetry
Asymmetry between mean inter-trade waiting times following buyer-initiated ticks versus seller-initiated ticks within the bar β€” a signed-time intrinsi β€” β›” OUT-OF-SCOPE (G5): quote-only substrate, no trades/volume
🌊 Order-flow & tick intrinsics reimplement from paper
n/a
arXiv:physics/0608273
git-anchor: absent @c803ef96e + @2d308f1c
β›” out-of-scope (G5)
#35 signed_volume_gini_concentration
Gini concentration of per-tick signed-volume contributions within the bar β€” measures whether directional order flow is dispersed across many ticks or β€” β›” OUT-OF-SCOPE (G5): quote-only substrate, no trades/volume
🌊 Order-flow & tick intrinsics reimplement from paper
n/a
DOI:10.3390/jrfm17080325
git-anchor: absent @c803ef96e + @2d308f1c
β›” out-of-scope (G5)
#36 tick_rule_effective_spread_capture_ratio
Mean signed (price - mid) over the bar's ticks expressed as a fraction of the mean half-spread β€” a parameter-free proxy for how much of the quoted spr β€” β›” OUT-OF-SCOPE (G5): quote-only substrate, no trades/volume
🌊 Order-flow & tick intrinsics mgao6767/frds
MIT (unverified β€” github/pypi fetc
DOI:10.1111/j.1540-6261.1991.t
git-anchor: absent @c803ef96e + @2d308f1c
β›” out-of-scope (G5)
#37 cumulative_residual_entropy
Rao's CDF-based entropy: CRE = -∫ S(x) log S(x) dx, replacing the density in Shannon entropy with the survival function; a parameter-free uncertainty
πŸ”’ Information & negentropy (knob reimplement from paper
none
DOI:10.1109/TIT.2004.828057
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#38 cumulative_residual_extropy
The CDF-based dual of extropy: CREx = -1/2 ∫ S(x)^2 dx where S is the survival function; a knob-free concentration/dispersion measure that replaces th
πŸ”’ Information & negentropy (knob reimplement from paper
none
DOI:10.1017/S0269964819000196
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#39 empirical_cumulative_entropy
Di Crescenzo–Longobardi cumulative entropy: CE = -∫ F(x) log F(x) dx using the CDF (left-tail dual of Rao's CRE); a parameter-free spread/uncertainty
πŸ”’ Information & negentropy (knob reimplement from paper
none
DOI:10.1016/j.jspi.2009.05.038
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#40 lziv_complexity_signs
Lempel-Ziv (1976) complexity of the binary up/down sign sequence of the path: counts distinct sub-patterns produced by recursive copy, an entropy-rate
πŸ”Ž CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable
πŸ”’ Information & negentropy (knob raphaelvallat/antropy
BSD-3-Clause
DOI:10.1109/TIT.1976.1055501
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#41 interval_entropy_dispersion_coeff
Entropy-based (information) dispersion coefficient of the unit-mean-normalized inter-quote interval distribution β€” quantifies arrival-timing randomnes
πŸ”’ Information & negentropy (knob gregversteeg/NPEET
MIT (NPEET); BSD-3-Clause (scipy)
DOI:10.1016/j.ins.2012.12.046
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#42 candle_signed_shoelace_area
Signed (oriented) area enclosed by treating one bar as the closed 4-vertex polyline openβ†’highβ†’lowβ†’closeβ†’open in (ordinal-position, price) space, norma β€” ⚠ paper-ID β‘£ PENDING (G6)
πŸ•―οΈ Single-bar candle geometry shapely/shapely
BSD-3-Clause
no-DOI β€” shoelace / surveyor's-area form
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#43 bid_ask_close_location_divergence
Difference between where the close sits within the BID candle's range versus within the ASK candle's range β€” a spread-geometry asymmetry that mid-pric β€” ⚠ paper-ID β‘£ PENDING (G6)
πŸ•―οΈ Single-bar candle geometry twopirllc/pandas-ta
MIT
no-DOI β€” composed from Williams' Close-L
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#44 ohlc_ordinal_pattern_index
Categorical index naming which of the admissible orderings the four OHLC values realize within the single bar (since H is max and L is min, this resol
πŸ•―οΈ Single-bar candle geometry arsenetar/ordpy
MIT
DOI:10.1103/PhysRevLett.88.174
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#45 heikin_ashi_open_gap_sign
Parameter-free Heikin-Ashi-derived single-bar invariant: the sign/normalized gap between the bar's HA-open ( (prev O + prev C)/2 ) and the bar's true β€” ⚠ paper-ID β‘£ PENDING (G6)
πŸ•―οΈ Single-bar candle geometry twopirllc/pandas-ta
MIT
no-DOI β€” Valcu, 'Using the Heikin-Ashi T
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#46 intrabar_extreme_order_sign
A single sign indicating whether the bar's high or its low occurred first in time within the bar.
πŸ•―οΈ Single-bar candle geometry reimplement from paper
none
arXiv:2509.16137
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#47 local_variation_lv
Mean of 3(Ο„_i βˆ’ Ο„_{i+1})Β² / (Ο„_i + Ο„_{i+1})Β² over consecutive inter-quote intervals β€” a rate-robust local irregularity index where Poisson timing give
⏱️ Inter-quote timing & duration NeuralEnsemble/elephant
BSD-3-Clause (Modified BSD)
DOI:10.1162/089976603322518759
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#48 cv2_consecutive_intervals
Mean of 2|Ο„_{i+1} βˆ’ Ο„_i| / (Ο„_{i+1} + Ο„_i) over consecutive inter-quote intervals β€” a firing-rate-robust local timing-variability index (Poisson = 1).
⏱️ Inter-quote timing & duration NeuralEnsemble/elephant
BSD-3-Clause (Modified BSD)
DOI:10.1152/jn.1996.75.5.1806
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#49 gini_interquote_interval
Gini concentration coefficient of the within-bar inter-quote interval lengths β€” measures how unequally arrival gaps are distributed (Poisson/exponenti
⏱️ Inter-quote timing & duration AndriSignorell/DescTools
GPL-2.0-or-later (DescTools); triv
arXiv:physics/0701008
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#50 rogers_satchell_var_bar
Drift-independent single-bar variance built from high/low/close relative to the bar open, so it is unbiased even when the bar trends.
πŸ”Ž CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable
πŸ“ˆ Range & volatility (drift-inde cran/TTR
GPL-2/3
DOI:10.1214/aoap/1177005835
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#51 overnight_gap_logret_sq
Squared log gap between this bar's open and the previous bar's close β€” the pure close-to-open (overnight/inter-bar) variance component.
πŸ”Ž CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable
πŸ“ˆ Range & volatility (drift-inde jasonstrimpel/volatility-trading
MIT
DOI:10.1086/209650
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#52 edge_spread_bps
Efficient Discrete Generalized Estimator: a single GMM-based effective-spread estimate that combines all four OHLC prices, asymptotically unbiased und
πŸ’§ Effective spread & illiquidity eguidotti/bidask
MIT
DOI:10.1016/j.jfineco.2024.103
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#53 ohlc_generalized_spread_bps
A specific generalized OHLC-combination spread estimator (e.g., OHLC.CHLO or OHL.HLC average) from the same Ardia-Guidotti-Kroencke family, distinct f
πŸ’§ Effective spread & illiquidity eguidotti/bidask
MIT
DOI:10.1016/j.jfineco.2024.103
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#54 hvg_mean_clustering_coefficient_bar
Build the Horizontal Visibility Graph (HVG) of the bar's series (close, or the intra-bar mid-tick stream): each point is a node; nodes i,j connect iff
πŸ•ΈοΈ Visibility-graph topology (par CarlosBergillos/ts2vg
MIT (ts2vg); BSD-3-Clause (network
DOI:10.1103/PhysRevE.80.046103
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#55 hvg_degree_assortativity_coefficient
Build the HVG of the bar-close series (200-bar substrate); report the Pearson degree-degree assortativity coefficient r (correlation of degrees across
πŸ•ΈοΈ Visibility-graph topology (par CarlosBergillos/ts2vg
MIT (ts2vg); BSD-3-Clause (network
arXiv:1012.3850
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#56 hvg_tetradic_motif_profile_entropy
The occurrence-frequency vector of the six distinguishable 4-node (tetradic) motifs in the horizontal visibility graph of the bar series. Each motif e
πŸ•ΈοΈ Visibility-graph topology (par CarlosBergillos/ts2vg
MIT (ts2vg); BSD-3-Clause (network
arXiv:1811.03794
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#57 hvg_mean_shortest_path_length
Mean shortest-path length L of the HVG (average over all node pairs). For i.i.d. random series L scales as ~1.3*log(N)-1.7 (small-world); for high-Hur
πŸ•ΈοΈ Visibility-graph topology (par CarlosBergillos/ts2vg (+ networkx for nx.average_shortest_path_length)
MIT / BSD-3-Clause
arXiv:1002.4526
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#58 hvg_mean_degree_excess
Build the Horizontal Visibility Graph of the 200-bar close (or log-return) series; report the mean node degree <k> = 2*E/N. For any i.i.d. random seri
πŸ•ΈοΈ Visibility-graph topology (par CarlosBergillos/ts2vg
MIT
arXiv:1002.4526
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#59 hvg_forward_visibility_horizon_mean_bar
On the directed HVG, the forward visibility horizon L+(t) at node t is the number of steps until the path first reaches/exceeds x_t (for tie-free seri
πŸ•ΈοΈ Visibility-graph topology (par CarlosBergillos/ts2vg
MIT (ts2vg); reference statistic h
arXiv:2512.02352
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#60 vg_time_directed_clustering_kld
Donges/pyunicorn time-reversal asymmetry of the LOCAL CLUSTERING COEFFICIENT in the visibility graph: decompose each node's local clustering coefficie
⚠ distinct topological aspect vs iter-1 dhvg_indegree_outdegree_kld (clustering not degree)
πŸ•ΈοΈ Visibility-graph topology (par pik-copan/pyunicorn
BSD-3-Clause
arXiv:1507.01571
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#61 bid_ask_intrabar_chatterjee_xi
Chatterjee's xi coefficient between the intra-bar bid tick series and the contemporaneous ask tick series (or between mid and spread). xi in [0,1] mea
πŸ”— Copula-free dependence (intrab scipy/scipy
BSD-3-Clause (scipy); MIT (xicor);
DOI:10.1080/01621459.2020.1758
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#62 bid_ask_intrabar_distance_correlation
Distance correlation (Szekely-Rizzo) between the intra-bar bid and ask tick streams (or mid vs spread). dCor in [0,1], equals 0 iff the two are statis
πŸ”— Copula-free dependence (intrab vnmabus/dcor
MIT
DOI:10.1214/009053607000000505
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#63 hoeffding_d_midreturn_duration
Hoeffding's D measure of dependence between within-bar mid-return magnitude (Y) and inter-quote duration (X). D detects non-monotone/one-to-many depen
πŸ”— Copula-free dependence (intrab chaim-e/independence
GPL-3
DOI:10.1214/aoms/1177730150
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#64 bergsma_dassios_taustar_bidpath_askpath
Bergsma-Dassios tau* (sign covariance generalizing Kendall's tau) between within-bar bid-path and ask-path increments. tau* is 0 iff independent and p
πŸ”— Copula-free dependence (intrab chaim-e/independence
GPL-3
DOI:10.3150/13-BEJ514
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#65 blomqvist_beta_bidpath_askpath
Blomqvist's beta (medial correlation): proportion of within-bar paired (bid-increment, ask-increment) points falling in the concordant quadrants defin
πŸ”— Copula-free dependence (intrab easystats/correlation
GPL-3
DOI:10.1214/aoms/1177729754
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#66 categorical_recurrence_rate_close_ties
Recurrence Rate (RR) of EXACT-EQUAL close prices over the 200-bar substrate: the density of pairs (i,j) with C_i == C_j (price exactly revisited, epsi
πŸ”Ž CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable
♻️ Categorical recurrence quantif morenococo/crqa
GPL-3.0-or-later
DOI:10.3389/fpsyg.2014.00510
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#67 categorical_rqa_determinism_logret_sign
Build a binary recurrence matrix on the discrete symbol stream s_t = sign(close-to-close log return) over the 200-bar substrate, where R_ij = 1 iff s_
⚠ caveat: l_min=2 structural-minimum line length (parameterless-by-convention)
πŸ”Ž CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable
♻️ Categorical recurrence quantif morenococo/crqa
GPL-3.0-or-later
DOI:10.3389/fpsyg.2014.00510
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#68 categorical_rqa_laminarity_tickrule_direction
On the intra-bar tick-rule direction stream d_k in {+1,-1} (Lee-Ready: +1 if trade/quote-mid uptick, -1 if downtick) within each bar, build identity r
⚠ caveat: l_min=2 structural-minimum vertical line
♻️ Categorical recurrence quantif morenococo/crqa
GPL-3.0-or-later
DOI:10.1016/j.physrep.2006.11.
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#69 categorical_rqa_trapping_time_quote_direction
Trapping Time (TT) on the discrete quote-revision direction stream (best-bid/ask up vs down) = the AVERAGE length of vertical lines (v>=2) in the iden
⚠ caveat: l_min=2 structural-minimum vertical line
♻️ Categorical recurrence quantif morenococo/crqa
GPL-3.0-or-later
DOI:10.1016/j.physrep.2006.11.
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#70 categorical_rqa_diagonal_entropy_logret_sign
Diagonal-line-length entropy (ENTR / L_ENTR) on the identity recurrence matrix of the close-to-close sign stream: Shannon entropy of the probability d
⚠ caveat: l_min=2 structural-minimum diagonal line
♻️ Categorical recurrence quantif morenococo/crqa
GPL-3.0-or-later
DOI:10.1016/j.physrep.2006.11.
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#71 hjorth_mobility_bar
Hjorth Mobility = sqrt( var(first difference of the series) / var(series) ). A scale-free 'mean-frequency' descriptor: the ratio of the standard devia
πŸ”Ž CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable
πŸͺ’ Fractal & curve-complexity neuropsychology/NeuroKit
MIT (NeuroKit2); BSD-3-Clause (ant
DOI:10.1016/0013-4694(70)90143
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#72 psd_wiener_spectral_flatness
Tonality-vs-noise descriptor of a bar's signal: ratio of the geometric mean to the arithmetic mean of the power spectrum of the mean-removed intra-bar
πŸ”Ž CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable
πŸ“‘ Spectral & cepstral shape (par librosa/librosa (librosa.feature.spectral_flatness)
ISC
arXiv:1905.02284
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#73 psd_shannon_spectral_entropy_norm
Normalized Shannon spectral entropy: treat the normalized PSD of the bar's intra-bar tick path (or 200-bar close series) as a probability distribution
πŸ”Ž FOREX-COVERED: evaluated on forex_bars in the 2026-05-26/27 Gate campaign
πŸ“‘ Spectral & cepstral shape (par raphaelvallat/antropy (antropy.spectral_entropy, method='fft', normali
BSD-3-Clause
DOI:10.1016/0013-4694(91)90138
git-anchor: absent @c803ef96e + @2d308f1c
β›” forex-dup
#74 psd_spectral_centroid_normfreq
Spectral center-of-mass ('brightness') of the bar's signal: the power-weighted mean frequency of the intra-bar mid tick path (or 200-bar close series)
⚠ forex-roadmap-mentioned (listed as an UNTESTED inventory item in the May Gate extended-inventory; not yet evaluated β€” ve
πŸ”Ž FOREX-MENTIONED-ONLY (roadmap inventory, not evaluated)
πŸ“‘ Spectral & cepstral shape (par librosa/librosa (librosa.feature.spectral_centroid)
ISC
HAL:hal-00692400
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#75 psd_log_spectral_slope_fullband
Full-band spectral slope: slope of an OLS line fit to log-power vs log-frequency across ALL positive frequency bins (DC excluded) of the bar's intra-b
πŸ“‘ Spectral & cepstral shape (par librosa/librosa (poly_features, order=1, over full band)
ISC
HAL:hal-00692400
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#76 midpath_zero_crossing_rate_meanremoved
Zero-crossing rate of the mean-removed intra-bar mid-price tick path: fraction of consecutive tick pairs where the de-meaned mid changes sign. A time-
πŸ“‘ Spectral & cepstral shape (par librosa/librosa (librosa.feature.zero_crossing_rate, threshold=0
ISC
DOI:10.1109/PROC.1986.13663
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#77 schweizer_wolff_sigma_bidpath_askpath
Schweizer-Wolff sigma: the normalized L1 distance between the empirical copula of (intra-bar bid-tick rank, ask-tick rank) and the independence copula
πŸ”— Copula-free dependence (intrab cran.r-project.org/package=copBasic (wolfCOP)
GPL-2.0
DOI:10.1214/aos/1176345528
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#78 hoeffding_phi_squared_midreturn_duration
Hoeffding's Phi-squared: the normalized L2 distance between the empirical copula of (mid log-return rank, bar-duration rank) and the independence copu
πŸ”— Copula-free dependence (intrab cran.r-project.org/package=copBasic (hoefCOP)
GPL-2.0
DOI:10.1016/j.jmva.2010.06.011
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#79 kendall_taub_signedreturn_spread
Kendall's tau-b: the tie-corrected concordant-minus-discordant rank concordance between signed mid log-return and spread (bps) across the bar substrat
πŸ”— Copula-free dependence (intrab scipy/scipy (scipy.stats.kendalltau, variant='b')
BSD-3-Clause
DOI:10.1093/biomet/33.3.239
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#80 gini_correlation_asymmetry_signedreturn_spread
Schechtman-Yitzhaki Gini correlation ASYMMETRY: the signed difference between the two directional Gini correlations R(return,rank(spread)) and R(sprea
πŸ”— Copula-free dependence (intrab cran/GiniDistance
GPL-2.0
DOI:10.1080/03610928708829359
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#81 energy_distance_bidpath_askpath_distribution
Szekely-Rizzo energy distance between the empirical distribution of intra-bar bid tick increments and the empirical distribution of ask tick increment
πŸ”— Copula-free dependence (intrab vnmabus/dcor
MIT
DOI:10.1016/j.jspi.2013.03.018
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#82 sign_negentropy_logcosh_gap
Hyvarinen robust negentropy of the standardized log-return series: the squared gap between the expected logcosh contrast on the data and on a matched
πŸ”’ Information & negentropy (knob scikit-learn (sklearn.decomposition.FastICA, _gs
BSD-3-Clause
DOI:10.1016/S0893-6080(00)0002
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#83 sign_two_state_entropy_rate
Shannon entropy rate of the return-sign sequence modeled as a two-state (up/down) Markov chain: estimate the up->down and down->up flip probabilities
⚠ lag-1 Markov sign-transition entropy (structural) · forex-roadmap-mentioned (listed as an UNTESTED inventory item in the
πŸ”Ž FOREX-MENTIONED-ONLY (roadmap inventory, not evaluated)
πŸ”’ Information & negentropy (knob github.com/gregversteeg/NPEET (entropy estimator
MIT
DOI:10.3390/e23081046
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#84 empirical_cdf_fisher_rao_arclength
Fisher-Rao (square-root-density / SRVF) arc length of the path traced by the empirical distribution of returns when read as a curve on the unit sphere
πŸ”’ Information & negentropy (knob github.com/jdtuck/fdasrsf_python (fdasrsf)
BSD-3-Clause
arXiv:1103.3817
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#85 updown_magnitude_cumulative_js_divergence
Cumulative Jensen-Shannon divergence (Nguyen-Vreeken CJS) between the empirical distribution of |return| on up-bars and the empirical distribution of
⏳ Time-irreversibility & tempora github.com/eda-rg/cjs (CISPA eda.rg 'cjs' refere
MIT
DOI:10.1007/978-3-319-23525-7_
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#86 interquote_count_fano_factor
Dispersion of the per-second (or per-bar-subinterval) quote counts relative to a Poisson process: variance-of-counts divided by mean-of-counts over th
⏱️ Inter-quote timing & duration elephant-org/elephant (elephant.statistics.fanofactor)
BSD-3-Clause
DOI:10.3389/fncom.2020.569049
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#87 realized_semivariance_signed_ratio
Within-bar decomposition of realized variance into the part from up-ticks vs down-ticks of the mid: RS+ = sum of squared positive mid log-returns, RS-
πŸ“ˆ Range & volatility (drift-inde bashtage/arch Β· cran.r-project.org/package=highfrequency (realized measures); (rSVar)
NCSA (arch) / GPL-2.0-or-later (hi
DOI:10.1162/REST_a_00503
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#88 tickrule_run_length_entropy
Shannon entropy of the run-length distribution of consecutive same-direction tick-rule signs within the bar. Captures whether order flow comes in long
⚠ forex-roadmap-mentioned (listed as an UNTESTED inventory item in the May Gate extended-inventory; not yet evaluated β€” ve
πŸ”Ž FOREX-MENTIONED-ONLY (roadmap inventory, not evaluated)
🌊 Order-flow & tick intrinsics raphaelvallat/antropy (entropy primitives); RLE via numpy
BSD-3-Clause
arXiv:2003.05500
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#89 holden_effective_tick_clustering
Effective-tick (Holden/Goyenko-Holden-Trzcinka) clustering measure: from how often intra-bar prices land on coarse vs fine multiples of the symbol's m
⚠ needs symbol tick size (data constant); GPL bidask ref
πŸ’§ Effective spread & illiquidity eguidotti/bidask (bidask: EDGE + companion low-freq spread proxie
GPL-3.0
DOI:10.1016/j.jfineco.2008.06.
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#90 intrabar_path_straightness_index
The straightness (net-to-gross displacement) index of the intrabar mid-price path: net displacement (close - open in price, or Euclidean endpoint dist
πŸ”Ž CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable
🧭 Intrabar path geometry & topol JimMcL/trajr (TrajStraightness)
GPL-3.0
DOI:10.1016/j.jtbi.2004.03.016
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#91 intrabar_path_total_absolute_turning
Sum of the absolute exterior turning angles at every interior vertex of the intrabar (time,price) tick polyline, normalized by total arc length (total
🧭 Intrabar path geometry & topol JimMcL/trajr · scipy/scipy (TrajAngles / turning angles); (vector algebra)
GPL-3.0
DOI:10.1145/1090122.1090160
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#92 intrabar_gyration_tensor_asphericity
Form the 2x2 radius-of-gyration tensor of the intrabar point cloud {(t_i, p_i)} (tick mids, mean-centered, in normalized time-price coordinates), take
🧭 Intrabar path geometry & topol glotzerlab/freud · plumed/plumed2 (ClusterProperties gyration tensor); (GYRATION
BSD-3-Clause
DOI:10.1063/1.1674820
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#93 intrabar_convex_hull_area_to_pathlength_ratio
Compute the convex hull of the intrabar (time,price) tick point cloud in normalized coordinates; report the dimensionless ratio hull_area / (path_arc_
🧭 Intrabar path geometry & topol scipy/scipy (scipy.spatial.ConvexHull / Qhull)
BSD-3-Clause
DOI:10.3390/ijgi7010014
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#94 intrabar_normalized_levy_area
The LΓ©vy area of the intrabar 2D path lift (e.g. (time, mid) or the (bid, ask) co-path), i.e. the signed area enclosed between the path and the chord
⚠ level-2 path-signature fixed depth (structural)
🧭 Intrabar path geometry & topol bottler/iisignature · datasig-ac-uk/RoughPy
GPL-3.0
arXiv:1603.03788
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#95 intrabar_h0_total_persistence
Sublevel-set persistent homology (H0) of the intrabar mid-price function vs. time: sweep the price level upward, record birth (local minima) and death
πŸ”Ž CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable
🧭 Intrabar path geometry & topol scikit-tda/ripser.py · giotto-ai/giotto-tda (CubicalPersistence/lower-star)
MIT
arXiv:2311.01115
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#96 sign_markov_entropy_production_rate_threestate
Markov-chain entropy-production (time-irreversibility) rate of the 3-state sign transition matrix: the Kullback-Leibler divergence rate between the fo
⚠ lag-1 3-state sign Markov chain (structural alphabet) · forex-roadmap-mentioned (listed as an UNTESTED inventory item in
πŸ”Ž FOREX-MENTIONED-ONLY (roadmap inventory, not evaluated)
⏳ Time-irreversibility & tempora github.com/networkx/networkx (graph build) + clo
BSD-3-Clause
arXiv:1201.5613
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#97 sign_markov_slem_spectral_gap_mixing_threestate
Second-largest-eigenvalue-modulus (SLEM) / spectral-gap mixing rate of the 3-state sign transition matrix: |lambda_2| where lambda_2 is the eigenvalue
⚠ lag-1 sign Markov chain
🎲 Randomness & rank tests (runs/ github.com/TommasoBelluzzo/PyDTMC (MarkovChain.m
MIT
DOI:10.1137/S0036144503423264
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#98 sign_markov_inout_strength_asymmetry_flux
Net stationary-flux asymmetry of the 3-state sign transition graph: for each directed sign-pair the antisymmetric current J_ij = pi_i P_ij - pi_j P_ji
⚠ lag-1 sign Markov chain
⏳ Time-irreversibility & tempora github.com/networkx/networkx + numpy closed-form
BSD-3-Clause
arXiv:2404.01978
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#99 groeneveld_meeden_b3_skewness
Groeneveld-Meeden global skewness b3 = (mean - median)/E|X - median| = (mean-median)/MAD-from-median. The mean-median location gap normalized by the m
πŸ“ Distributional shape (L-moment scipy/scipy (mean, median, median_abs_deviation primitives)
BSD-3-Clause
DOI:10.2307/2987742
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#100 hl_pseudomedian_minus_median_gap
Location-shape gap between the Hodges-Lehmann pseudomedian (median of all Walsh pairwise averages (xi+xj)/2) and the ordinary median, normalized by a
πŸ“ Distributional shape (L-moment scipy/scipy (median primitive) + numpy Walsh-average constru
BSD-3-Clause
DOI:10.1214/aoms/1177704172
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#101 bickel_halfsample_mode_skewness
Bickel modal skewness = (mean - mode)/scale, where the mode is the robust Half-Sample Mode (HSM): recursively keep the shortest half-interval containi
⚠ half-sample-mode structural (dense ticks needed)
πŸ“ Distributional shape (L-moment cran/modeest (paulponcet/modeest mirror) hsm() + skewness
GPL-3
DOI:10.1016/S0167-9473(01)0005
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#102 left_medcouple_lower_tailweight
Brys-Hubert-Struyf Left Medcouple (LMC): the medcouple skewness kernel evaluated on the lower structural half {x <= median}, i.e. LMC = -mc(x[x<=media
πŸ“ Distributional shape (L-moment cran/robustbase lmc()
GPL-2.0-or-later
DOI:10.1016/j.csda.2004.09.012
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#103 right_medcouple_upper_tailweight
Brys-Hubert-Struyf Right Medcouple (RMC): medcouple kernel on the upper structural half {x >= median}, RMC = mc(x[x>=median]). Robust per-tail kurtosi
πŸ“ Distributional shape (L-moment cran/robustbase rmc()
GPL-2.0-or-later
DOI:10.1016/j.csda.2004.09.012
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#104 l_correlation_serfling_xiao_bidpath_askpath
Serfling-Xiao L-correlation: the 2nd-order L-comoment ratio ρ_L(X|Y)=λ2[12]/λ2[11], built from the concomitants of one intra-bar series (bid mid-price
πŸ”— Copula-free dependence (intrab cran.r-project.org/package=lmomco (Lcomoment.matrix + Lcomoment.correlation, Willi
GPL-2.0-or-later
DOI:10.1016/j.jmva.2007.01.008
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#105 l_comoment_directional_asymmetry_bidpath_askpath
The Serfling-Xiao directional gap Ξ” = Ξ»2[12] - Ξ»2[21]: the difference between the 2nd L-comoment of bid-path-given-ask-path and ask-path-given-bid-pat
πŸ”— Copula-free dependence (intrab cran.r-project.org/package=lmomco (Lcomoment.matrix off-diagonal entries [12] vs [
GPL-2.0-or-later
DOI:10.1016/j.jmva.2007.01.008
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#106 symmetric_gini_covariance_jointrank_bidpath_askpath
Sang-Dang-Sang symmetric Gini covariance/correlation: a rank-based bivariate dependence built from the JOINT rank function (spatial-rank) rather than
πŸ”— Copula-free dependence (intrab xdang/SymmetricGini (Ole Miss Xin Dang reference code; also reimplem
GPL-3.0-or-later
DOI:10.1002/cjs.11287
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#107 etc_effort_to_compress_logret_sign
Effort-To-Compress complexity of the per-bar log-return sign string {+,0,-}: run Non-Sequential Recursive Pair Substitution (NSRPS) β€” at each step rep
πŸ”’ Information & negentropy (knob pranaysy/ETCPy
Apache-2.0
DOI:10.1140/epjst/e2013-01888-
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#108 sequitur_grammar_compression_ratio_logret_sign
Run the Sequitur (Nevill-Manning–Witten) online grammar-inference algorithm on the log-return sign string. Sequitur is fully deterministic β€” it enforc
πŸ”’ Information & negentropy (knob markomanninen/pysequitur
MIT
arXiv:cs/9709102 (Nevill-Manning & Witte
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#109 intrabar_h0_persistent_entropy
Shannon entropy of the normalized H0 lifetime distribution from the single sublevel-set filtration of the intrabar mid-price-vs-time function. Take th
⚠ single natural sublevel filtration (structural)
πŸ”Ž CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable
🧭 Intrabar path geometry & topol GUDHI/gudhi-devel · giotto-ai/giotto-tda (CubicalComplex sublevel persistence + entropy);
GUDHI: MIT (core; some modules pul
arXiv:1803.08304
git-anchor: absent @c803ef96e + @2d308f1c
crypto-prior
#110 anderson_darling_a2_vs_gaussian_fit_logret
Anderson-Darling goodness-of-fit statistic AΒ² measuring the squared distance between the empirical CDF of the bar's intra-bar mid log-returns and the
πŸ“ Distributional shape (L-moment statsmodels/statsmodels (statsmodels.stats.diagnostic.normal_ad β†’ return
BSD-3-Clause
DOI:10.1214/aoms/1177729437
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#111 spread_increment_sign_reversal_rate
Per-bar fraction of consecutive intra-bar spread increments that reverse direction. Build the per-tick spread s_t = ask_t - bid_t, take first differen
🌊 Order-flow & tick intrinsics github.com/blue-yonder/tsfresh (number_crossing_
MIT
DOI:10.1111/j.1540-6261.1984.t
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#112 theil_t_index_interquote_durations
Theil's T entropy inequality index (generalized-entropy GE(1)) computed on the set of intra-bar interquote durations: T = (1/n)Β·Ξ£ (dα΅’/dΜ„)Β·ln(dα΅’/dΜ„), w
⚠ GE(1) order Ξ± fixed at 1 (structural); dense duration-inequality family β€” |r| screen vs interval_entropy_dispersion_coef
⏱️ Inter-quote timing & duration pysal/inequality (class inequality.theil.Theil)
BSD-3-Clause
DOI:10.1007/978-0-387-72796-7_
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#113 ramsey_rothman_bicovariance_gamma21_lag1_midlogret
Ramsey–Rothman symmetric-bicovariance time-reversal-asymmetry statistic at lag 1 on the zero-mean mid log-return series: Ξ³β‚‚,₁ = E[Yβ‚œΒ²Β·Yβ‚œβ‚‹β‚] βˆ’ E[Yβ‚œΒ·Yβ‚œβ‚‹
⚠ lag-1 + orders (2,1) structural; use the σ³-normalized point estimate, NOT the p-value test form (which needs a finite 6
⏳ Time-irreversibility & tempora MZanin/irreversibility (Zanin 2025; PMC12650947)
MIT (unverified β€” confirm on repo;
DOI:10.2307/2077963
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#114 intrabar_positive_occupation_fraction_above_open_us_weighted
Microsecond-weighted fraction of intra-bar time the mid (or bid/ask) path spends STRICTLY ABOVE the bar's opening mid. This is LΓ©vy's first arcsine la
⚠ β€˜above open’ is a fixed structural reference (parameterless-by-convention), not a tuned level.
πŸŒ“ Intrabar occupation-time & arc scipy/scipy (scipy.stats.arcsine for the null CDF; numpy for
BSD-3-Clause
arXiv:1706.01675
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#115 intrabar_time_weighted_occupation_above_twap
Fraction of the bar's wall-clock duration that the mid-price spends strictly above the bar's own time-weighted average price (TWAP), computed by integ
⚠ Centered (above own TWAP) companion to the above-open occupation; check mutual Spearman vs above-open tomorrow.
πŸŒ“ Intrabar occupation-time & arc scipy/scipy
BSD-3-Clause
arXiv:1712.00795
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#116 intrabar_normalized_time_of_maximum
Normalized timestamp of the intra-bar HIGH: (t_argmax(high) - t_start)/duration, in [0,1]. LΓ©vy's third arcsine law functional. Encodes WHEN the extre
πŸŒ“ Intrabar occupation-time & arc numpy/numpy (argmax + normalization)
BSD-3-Clause
arXiv:1706.01675
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#117 intrabar_signed_normalized_time_lead_of_high_over_low
Signed temporal lead of the extremes: (t_argmax(high) - t_argmin(low))/duration, in [-1,1]. Positive => the high occurred AFTER the low (down-then-up β€” claim narrowed to the |Ξ”T| magnitude (sign = #46)
⚠ Its SIGN duplicates intrabar_extreme_order_sign; only the |Ξ”T| MAGNITUDE (temporal separation of the extremes) is the no
πŸŒ“ Intrabar occupation-time & arc numpy/numpy
BSD-3-Clause
arXiv:1706.01675
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#118 critical_exponent_sign_word
The critical exponent of the per-bar sign(Ξ”mid) word over the 200-bar window: the supremum, taken over ALL factors of the word, of (factor length / it β€” ⚠ paper-ID β‘£ PENDING (G6)
⚠ lag-1 sign word (199 symbols) is the structural-minimum substrate.
πŸ”€ Combinatorics-on-words symboli sagemath/sage
GPL-3.0-or-later
arXiv:1406.0263
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#119 palindromic_defect_sign_word
The palindromic defect of the sign(Ξ”mid) word: D(w) = (|w| + 1) βˆ’ (number of DISTINCT palindromic factors of w, including the empty word). By the Drou
⚠ lag-1 sign word; DJP empty-word+singletons counted by fixed convention, not a knob.
πŸ”€ Combinatorics-on-words symboli sagemath/sage
GPL-3.0-or-later
DOI:10.1142/S012905410400242X
git-anchor: absent @c803ef96e + @2d308f1c
not-covered
#120 pietra_hoover_index_interquote_durations
The Pietra index (a.k.a. Hoover / Schutz / Robin-Hood index) of the intra-bar inter-quote interval durations: the maximum vertical gap between the Lor
⚠ L1 max-Lorenz-gap (=Β½ relative MAD); distinct interior ranking from the Gini/Theil duration items β€” confirm orthogonalit
⏱️ Inter-quote timing & duration numpy/numpy
BSD-3-Clause
DOI:10.1016/j.csda.2020.106974
git-anchor: absent @c803ef96e + @2d308f1c
not-covered