Estimator Status

This table describes the implementation status of estimators available through the default registry. Status is not a ranking. It tells users how cautiously to interpret results.

The confirmation study now reports point accuracy for its 21 pipelines and interval coverage for selected GPH, Higuchi and GHE procedures. These model- and configuration-specific results do not upgrade any method to reference-grade or establish calibration of every package-default interval.

Status meanings:

• baseline: suitable as a simple comparison method in public examples and smoke benchmarks.
• approximate: useful for research benchmarking, but implemented as a pragmatic approximation rather than a reference implementation.
• experimental: available for exploratory comparison; needs stronger validation before it should anchor public claims.
• reference-grade: validated enough to serve as an implementation reference. No estimator has this status yet.

Estimator	Family	Target estimand	Status	Assumptions	Expected regime	Known failure risks
RS	temporal	hurst_scaling_proxy	baseline	Rescaled-range scaling of stationary increments over selected block sizes.	Clean fGn-style checks with declared block support.	Upward finite-sample bias near H = 0.5 remains. The optional Anis-Lloyd expectation normalization is not a general unbiased correction. Raw slopes are retained; bootstrap calibration is pending.
DFA	temporal	hurst_scaling_proxy	baseline	Power-law residual RMS of a detrended cumulative profile.	Stationary increments with a defensible scale window.	It integrates the input; its slope on an fBm path is not the fGn H target. Out-of-range slopes, scale-window effects and detrending sensitivity remain visible.
DMA	temporal	hurst_scaling_proxy	baseline	Backward moving-average residual RMS of a cumulative profile.	Stationary increments with adequate window support.	Window choices, short records and deterministic trends can distort estimates. Raw slopes are retained.
AbsoluteMoment	temporal	hurst_scaling_proxy	approximate	Absolute first moment of block-aggregated series follows power-law scaling.	Aggregated-variance/moment comparisons on stationary fGn-style records.	Scale-window choices, short records, and centring choices can materially affect the slope.
Variance	temporal	hurst_scaling_proxy	approximate	Variance of block-aggregated series follows power-law scaling.	Classical aggregated variance checks for stationary long-memory-like records.	Bias under trends, level shifts, and poor block-size support.
VarianceResidual	temporal	hurst_scaling_proxy	approximate	Average variance of within-block residuals follows power-law scaling after local detrending.	Residual-variance scaling comparisons on records with enough block support.	Detrending order and scale window can dominate finite-sample estimates.
GPH	spectral	long_memory_parameter	baseline	Low-frequency log-periodogram regression for ARFIMA-style memory.	ARFIMA(0,d,0)-like synthetic regimes with moderate sample sizes.	Bandwidth sensitivity, short-memory leakage, and low-frequency contamination. Optional cosine taper (params.taper: cosine) can reduce periodogram bias from spectral leakage.
Periodogram	spectral	long_memory_parameter	approximate	Log-periodogram slope approximates long-memory parameter.	ARFIMA-style long-memory comparisons.	Bandwidth choices materially affect results; periodogram noise is high. Optional cosine taper (params.taper: cosine) can reduce spectral leakage.
WhittleMLE	spectral	long_memory_parameter	approximate	ARFIMA(0,d,0) Whittle objective over a selected low-frequency band.	Records near the declared spectral model.	It is not exact time-domain Gaussian MLE or exact fGn likelihood. Model misspecification, bandwidth and bounds matter; optimizer boundary hits are reported.
ModifiedLocalWhittle	spectral	long_memory_parameter	approximate	Ordinary Gaussian local Whittle objective under a legacy registry name.	Stationary low-frequency power-law regimes with adequate bandwidth support.	No nonstationary modification is implemented. Bandwidth sensitivity, finite-sample instability and optimizer bounds require validation.
Higuchi	geometric	hurst_scaling_proxy	approximate	H = 2 - D for a suitable self-affine path graph; declare path versus increments explicitly.	Path roughness comparisons on sufficiently long records.	Normalization corrected; estimates are unclipped. Short-memory processes can show apparent persistence over the chosen lags. The confirmation study measures substantial block-percentile undercoverage and fitted-fGn failure on strong AR(1) controls.
GHE	geometric	hurst_scaling_proxy	approximate	Absolute q-th moments of path differences scale as lag raised to qH(q).	Selected-lag moment regression; default q = 2, with q = 1 available explicitly.	Forced H = 0.5 fallback removed; nonzero flat_slope_tol rejected. Declare input representation. Lag range, trends, moment existence and bootstrap calibration require attention.
WaveletOLS	wavelet	hurst_scaling_proxy	approximate	Log detail variances scale linearly across levels under the fGn convention.	Stationary increments with at least three retained levels.	Scale-band selection, symmetric-extension boundaries and short signals. Raw slopes are retained; the conservative db4 pilot band is unavailable at n = 256.
WaveletAbryVeitch	wavelet	hurst_scaling_proxy	experimental	Abry-Veitch-style wavelet log-scale regression approximation.	Exploratory wavelet comparison on long enough records.	Needs stronger validation; sensitive to wavelet family and usable levels.
WaveletBardet	wavelet	hurst_scaling_proxy	experimental	Weighted wavelet log-scale regression approximation.	Exploratory wavelet comparison on long enough records.	Weighting and level selection can drive results; short signals are invalid.
WaveletJensen	wavelet	hurst_scaling_proxy	experimental	Two-band wavelet slope extrapolation.	Exploratory comparison where fine and coarse bands are both populated.	Band definitions can be fragile; short or narrow-band records fail.
WaveletWhittle	wavelet	hurst_scaling_proxy	experimental	Wavelet-domain Whittle-type fit to detail variances.	Exploratory wavelet comparison on long enough records.	Numerical fit and level support remain experimental.
MLRandomForest	data-driven	hurst_scaling_proxy	experimental	Supervised synthetic training distribution declared in ml_training.	Contaminated synthetic Hurst-proxy comparisons where train/eval provenance is explicit.	Distribution shift, training-grid leakage, and optional dependency availability.
MLSVR	data-driven	hurst_scaling_proxy	experimental	Supervised synthetic training distribution declared in ml_training.	Feature-based nonlinear baseline against classical estimators.	Feature design and hyperparameters can dominate results; no estimator-level CI.
MLCNN	data-driven	hurst_scaling_proxy	experimental	Supervised synthetic training distribution declared in ml_training; requires lrdbench[nn].	Sequence baseline for exploratory neural comparisons.	Small training grids can overfit; distribution shift and stochastic training affect results.
MLLSTM	data-driven	hurst_scaling_proxy	experimental	Supervised synthetic training distribution declared in ml_training; requires lrdbench[nn].	Sequential neural baseline for exploratory comparisons.	Slow training, overfitting, and weak extrapolation outside the manifest training grid.
PeriodogramBeta	spectral	spectral_exponent_beta	approximate	Low-frequency log-periodogram slope, reported as β = 2d under the fractional-noise model.	Spectral-exponent comparisons alongside compatible Hurst estimators.	GPH slope conversion corrected; old results halved d. Bandwidth trades variance against short-memory contamination and approximation bias; wider is not universally better.
ACFDecay	timescale	timescale_tau	approximate	Log-linear fit of the leading exponential band of the autocorrelation.	Single-timescale (AR(1)/OU) recovery; a diagnostic contrast under true LRD.	Deliberately misspecified for power-law LRD (window-dependent τ); reciprocal-of-slope skew inflates the mean.
ThresholdHurstDiscriminator	discrimination	lrd_class	baseline	Logistic squash of a point Hurst estimate.	Naive LRD-vs-short-memory decision floor.	No power against apparent LRD (multi-timescale) — near-chance on that adversary by design.
LowFreqSpectralDiscriminator	discrimination	lrd_class	experimental	Local-Whittle memory parameter at a shrinking low-frequency band.	Distinguishing true LRD from short-memory nulls.	Low-frequency estimate is noisy; bandwidth choice (m_power) affects separation.
ScaleCrossoverDiscriminator	discrimination	lrd_class	experimental	Large-scale DFA slope (scale-invariance of the exponent).	Detecting the crossover that short-memory processes show at large scales.	Weaker/noisier signal than the spectral and likelihood discriminators.
ICModelSelectDiscriminator	discrimination	lrd_class	experimental	Whittle-BIC comparison of ARFIMA(0,d,0) vs AR(1)/AR(2).	Principled LRD-vs-short-memory model selection.	Depends on the AR-order set and the fitted spectral models; BIC scale (scale) sets score calibration.

Interpretation Rules

Do not mix estimator targets casually. hurst_scaling_proxy and long_memory_parameter are related in some model families but are not identical public-contract quantities.

Leaderboard results are summaries of declared component metrics. They are not universal estimator rankings and should always be reported with the underlying metrics.

For publication-facing analysis, prefer reporting estimator families, target estimands, parameter settings, and failure/missing-uncertainty rates alongside any accuracy or robustness summaries.

Data-driven estimators are run-local supervised baselines. Interpret them relative to the manifest-declared ml_training distribution, not as distribution-free LRD estimators.