Iteration 1

Robust, parameter-free measure of return/tick-move asymmetry built from linear combinations of order statistics (L-moments) rather than third powers —

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Robust, parameter-free tail-peakedness measure from L-moments; concords with goodness-of-fit power and resists outliers far better than classical kurt

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Expected absolute difference between two independent draws of the within-bar return/spread distribution; a robust, distribution-free scale measure equ

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Quartile-based (Bowley/Galton) skewness coefficient: a bounded, outlier-robust asymmetry measure built from Q1, median, Q3 with fixed quartile positio

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A robust quantile-based peakedness/tail measure built from octiles, capturing how dispersed the distribution is around the +/-sigma shoulders without

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A robust skewness statistic equal to the median of a kernel of pairwise (above-median, below-median) comparisons; 25% breakdown, bounded influence, sc

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A robust right-tail-heaviness descriptor: quartile skewness applied to the upper half of the distribution (above the median), capturing fat-right-tail

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A robust asymmetry measure reaching further into the tails than Bowley by using the 10th/50th/90th percentiles instead of quartiles, detecting outer-d

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(Q3 − Q1)/(Q3 + Q1) of the within-bar inter-quote interval distribution — an outlier-robust, scale-free spread index of arrival-gap dispersion that do

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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

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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

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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

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Normalized Length Density: after amplitude standardization, the mean absolute first difference of the bar's series, mapped through a fixed Weierstrass

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The CID complexity estimate: the amplitude-space arc length of the series, i.e. the square root of the summed squared first differences — a single-pas

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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

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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

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Directional persistence of the tick/bar path: the average cosine of the heading change between consecutive segments in the (time, price) plane — a sig

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Ratio of mean-square successive difference to total variance of the path — a parameter-free serial-structure / smoothness statistic; low values = tren

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Rank version of the von Neumann ratio: mean-square successive rank-difference over rank variance; a distribution-free serial-dependence/randomness sta

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Mann-Kendall monotonic-trend statistic: the normalized sum over all ordered bar pairs of the sign of (later value minus earlier value) — a rank-based,

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Standardized count of turning points (bars that are a strict local max or local min vs their two neighbors) — high values indicate oscillatory/mean-re

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Standardized count of positive first-differences (number of up-moves) across the lookback — a parameter-free sign-balance-of-increments statistic dist

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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

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Foster-Stuart record-breaking trend statistic: difference between counts of upper-record and lower-record breaks over the lookback — distribution-free

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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

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Ehlers' time-irreversibility index: the normalized third moment (skewness) of the first-difference series of close prices; zero means time-reversible,

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Porta's index: the fraction of negative first-differences among all nonzero first-differences; a value far from 0.5 indicates acceleration/deceleratio

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Guzik's index: the share of total squared-increment 'energy' that comes from positive increments; differs from Porta by weighting by magnitude rather

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Costa-Goldberger-Peng time-irreversibility index: difference between the rates/energies of consecutive increases vs decreases ('accelerations' vs 'dec

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Lacasa directed-horizontal-visibility-graph irreversibility: map the price series to a directed horizontal visibility graph and measure the Kullback-L

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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-MENTIONED-ONLY (roadmap inventory, not evaluated)

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Imbalance between the count of upward and downward revisions of the best-bid (and symmetrically best-ask) quote across the intra-bar quote stream — ca

🔎 FOREX-COVERED: evaluated on forex_bars in the 2026-05-26/27 Gate campaign

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Ratio of the number of quote updates to the number of executed trades within the bar — quoting intensity relative to execution, a market-quality/HFT-a

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Asymmetry between mean inter-trade waiting times following buyer-initiated ticks versus seller-initiated ticks within the bar — a signed-time intrinsi

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Gini concentration of per-tick signed-volume contributions within the bar — measures whether directional order flow is dispersed across many ticks or

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Mean signed (price - mid) over the bar's ticks expressed as a fraction of the mean half-spread — a parameter-free proxy for how much of the quoted spr

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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

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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

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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

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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

🔎 CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable

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Entropy-based (information) dispersion coefficient of the unit-mean-normalized inter-quote interval distribution — quantifies arrival-timing randomnes

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Signed (oriented) area enclosed by treating one bar as the closed 4-vertex polyline open→high→low→close→open in (ordinal-position, price) space, norma

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Difference between where the close sits within the BID candle's range versus within the ASK candle's range — a spread-geometry asymmetry that mid-pric

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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

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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

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A single sign indicating whether the bar's high or its low occurred first in time within the bar.

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Mean of 3(τ_i − τ_{i+1})² / (τ_i + τ_{i+1})² over consecutive inter-quote intervals — a rate-robust local irregularity index where Poisson timing give

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Mean of 2|τ_{i+1} − τ_i| / (τ_{i+1} + τ_i) over consecutive inter-quote intervals — a firing-rate-robust local timing-variability index (Poisson = 1).

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Gini concentration coefficient of the within-bar inter-quote interval lengths — measures how unequally arrival gaps are distributed (Poisson/exponenti

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Drift-independent single-bar variance built from high/low/close relative to the bar open, so it is unbiased even when the bar trends.

🔎 CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable

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Squared log gap between this bar's open and the previous bar's close — the pure close-to-open (overnight/inter-bar) variance component.

🔎 CRYPTO-PRIOR: present in patterns/crypto lit-scan (provenance only; still forex-proposable

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Efficient Discrete Generalized Estimator: a single GMM-based effective-spread estimate that combines all four OHLC prices, asymptotically unbiased und

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A specific generalized OHLC-combination spread estimator (e.g., OHLC.CHLO or OHL.HLC average) from the same Ardia-Guidotti-Kroencke family, distinct f

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