Bundled Estimators

The default estimator registry exposes classical temporal, spectral, geometric, wavelet, and data-driven methods. Discover the installed names with:

lrdbench list-estimators

Estimator entries in manifests use the registry name:

estimators:
  - name: Variance
    family: temporal
    target_estimand: hurst_scaling_proxy
    params:
      min_scale: 2
      max_scale: 256
      scale_ratio: 1.5
      n_bootstrap: 200

Temporal Hurst-Proxy Estimators

These estimators target hurst_scaling_proxy.

Name	Method	Main parameters
RS	Rescaled-range log-log slope over subseries lengths.	min_scale, max_scale, scale_ratio, use_anis_lloyd_correction, bootstrap parameters
DFA	Detrended fluctuation analysis on the cumulative profile.	min_scale, max_scale, detrend_order, bootstrap parameters
DMA	Detrended moving-average fluctuation scaling.	min_scale, max_scale, bootstrap parameters
AbsoluteMoment	Log-log slope of aggregation level versus absolute first moment of block-aggregated series.	min_scale, max_scale, scale_ratio, bootstrap parameters
Variance	Log-log slope of sample variance versus block size for block-aggregated series.	min_scale, max_scale, scale_ratio, bootstrap parameters
VarianceResidual	Half the log-log slope of average sample variance of detrended cumulative-profile residuals versus block size. Closely related to DFA; uses a different scale grid and residual divisor.	min_scale, max_scale, scale_ratio, detrend_order, bootstrap parameters

The aggregation estimators map their fitted slopes onto an unclipped Hurst-style proxy:

• AbsoluteMoment: H = slope + 1
• Variance: H = slope / 2 + 1
• VarianceResidual: H = slope / 2

All three are approximate finite-sample methods. Interpret them with the same caution as other scale-window estimators: the block-size range, scale spacing, detrending order, contamination, and record length can materially change results.

Other Classical Estimators

Spectral estimators target long_memory_parameter:

• GPH
• Periodogram
• WhittleMLE
• ModifiedLocalWhittle

The legacy ModifiedLocalWhittle name implements ordinary Gaussian local Whittle; WhittleMLE fits a band-limited ARFIMA spectral shape rather than exact fGn likelihood. See the parameter glossary for bandwidths and optimizer bounds.

Geometric estimators target hurst_scaling_proxy:

• Higuchi
• GHE

Wavelet estimators target hurst_scaling_proxy:

• WaveletOLS
• WaveletAbryVeitch
• WaveletBardet
• WaveletJensen
• WaveletWhittle

Data-Driven Estimators

The experimental supervised baselines target hurst_scaling_proxy:

• MLRandomForest
• MLSVR
• MLCNN
• MLLSTM

These require a manifest-declared ml_training block unless a model artefact path is supplied. See Data-driven estimators.

Spectral-Exponent and Timescale Estimators

These target spectral slope and an effective exponential ACF timescale. A realisation can carry multiple truths, but only those explicitly declared by its generator: fGn supplies H and β with no finite τ target; fOU supplies driving H and mean-reversion τ, with no β truth. See the estimand tutorial for model restrictions.

Name	Family	Target estimand	Method
PeriodogramBeta	spectral	spectral_exponent_beta	Low-frequency log-periodogram slope, reported as \(\beta\) in \(S(f) \propto f^{-\beta}\); conversion to H requires an appropriate model.
ACFDecay	timescale	timescale_tau	Log-linear fit of the autocorrelation over its leading exponential band; reports the decay constant τ₀ in samples. Correctly specified for AR(1)/OU-type single-timescale dynamics and deliberately misspecified (window-dependent) under true long-range dependence.

LRD Discriminators

These target the decision estimand lrd_class: each emits a score in [0, 1] (higher = stronger evidence of true long-range dependence) as a classification score, and is scored by the classification metrics (roc_auc, balanced_accuracy, true_positive_rate, false_positive_rate) against binary lrd_class companion truths. These experimental methods compare declared LRD models with short-memory controls, including multi_timescale signals that mimic scaling. Their scores are not automatically calibrated probabilities or hypothesis tests; they are outside the confirmation paper's scope.

Name	Method
ThresholdHurstDiscriminator	Naive baseline: a Hurst estimate (base = dfa/gph/rs) squashed through a logistic centred at h0.
LowFreqSpectralDiscriminator	Local-Whittle memory parameter at a shrinking low-frequency band (true LRD keeps d>0 as f→0; a bounded spectrum collapses to d≈0).
ScaleCrossoverDiscriminator	Large-scale DFA slope used as an experimental persistence score; finite-sample behavior depends on scale support and the underlying timescales.
ICModelSelectDiscriminator	Whittle-BIC model comparison of ARFIMA(0,d,0) against short-memory AR(1)/AR(2); favours LRD when the fractional model wins.

Interpretation Notes

Do not mix hurst_scaling_proxy and long_memory_parameter results in a single accuracy ranking unless the benchmark protocol explicitly justifies the comparison. For publication-facing analysis, report estimator name, family, target estimand, parameters, validity rate, and uncertainty support alongside accuracy or robustness metrics.

For maturity and failure-risk labels, see Estimator status.