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.

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	Self-similar scaling over selected block sizes.	Clean fGn/fBm-style synthetic checks and simple public smoke suites.	Finite-sample bias: the classical estimator systematically over-estimates H near 0.5 and for small n. An opt-in Anis-Lloyd correction is available via params.use_anis_lloyd_correction. Short signals, nonstationary trends, and contamination can also bias the slope; bootstrap intervals are approximate.
DFA	temporal	hurst_scaling_proxy	baseline	Power-law fluctuation scaling after polynomial detrending.	fGn/fBm-style signals with a defensible scale window.	Scale-window and detrending-order choices can dominate finite-sample results.
DMA	temporal	hurst_scaling_proxy	baseline	Moving-average fluctuation scaling over selected windows.	fGn/fBm-style signals where window range avoids edge effects.	Window choices, short records, and deterministic trends can distort estimates.
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	Gaussian ARFIMA(0,d,0) spectral likelihood approximation.	Clean ARFIMA-style records near the fitted model family.	Model misspecification, numerical bounds, and short samples.
ModifiedLocalWhittle	spectral	long_memory_parameter	approximate	Local low-frequency Whittle objective captures fractional memory.	ARFIMA-style long-memory regimes with adequate low-frequency support.	Bandwidth sensitivity and finite-sample instability.
Higuchi	geometric	hurst_scaling_proxy	approximate	Graph dimension maps to a Hurst-style proxy.	Geometry-based comparator on sufficiently long records.	It is indirect LRD evidence and can fail under short or highly noisy signals.
GHE	geometric	hurst_scaling_proxy	approximate	Increment moments scale across selected lags.	Multiscale increment-variance comparisons.	Arbitrary heuristic: when the absolute log-log slope is below flat_slope_tol (default 0.08), the estimate is clamped to 0.5. This guard is empiric, not theoretically derived; set flat_slope_tol: 0.0 to disable it. Also sensitive to lag-grid choices and short samples.
WaveletOLS	wavelet	hurst_scaling_proxy	approximate	Wavelet detail variances scale linearly across selected levels.	fGn/fBm-style records with adequate wavelet levels.	Scale-band selection, boundary effects, and short signals.
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.

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.