Parameter Glossary

This page explains the most common parameters you will see in manifest estimators blocks.

Target estimands

Every estimator declares a target_estimand. Truth-based metrics are only computed for an estimator against a record that carries a matching truth (raw/truths.csv).

Estimand	Kind	Model range	Meaning
hurst_scaling_proxy	regression	(0, 1)	Hurst-like scaling exponent H.
long_memory_parameter	regression	(-0.5, 0.5)	Fractional-integration parameter; \(d=H-1/2\) only under compatible stationary finite-variance scaling assumptions.
spectral_exponent_beta	regression	~(-1, 1)	Low-frequency spectral slope \(\beta\), where \(S(f) \propto f^{-\beta}\); \(\beta=2H-1\) for fGn. Other models can have different ranges.
timescale_tau	regression	> 0	Autocorrelation-decay time constant τ₀ in samples. Undefined (None) for power-law LRD.
lrd_class	classification	[0, 1]	Experimental decision score, not necessarily a calibrated probability; lrd_class truth is 0 or 1.

Temporal estimators

Applies to: RS, DFA, DMA, AbsoluteMoment, Variance, VarianceResidual.

Parameter	Type	Default	Description
n_bootstrap	int	200	Number of bootstrap replicates for confidence intervals. Set to 0 to skip bootstrap CIs.
bootstrap_block_len	int	max(4, n//10)	Block length in samples for the circular block bootstrap.
ci_levels	list[float]	[0.95]	Nominal coverage levels for symmetric percentile intervals.
min_scale	int	varies	Minimum block size or scale (in samples) for RS, DFA, DMA, and aggregation estimators. RS defaults to 8.
max_scale	int	varies	Maximum block size or scale (in samples). RS defaults to n//2 so each fitted scale has at least two subseries.
detrend_order	int	1	Polynomial detrending order for DFA and VarianceResidual.
scale_ratio	float	1.5	Geometric spacing factor between consecutive aggregation scales.
use_anis_lloyd_correction	bool	False	(RS only) Divide each scale's average R/S value by the Anis-Lloyd white-noise expectation before fitting the slope.

Spectral estimators

Applies to: GPH, Periodogram, WhittleMLE, ModifiedLocalWhittle.

ModifiedLocalWhittle is the historical registry name for an ordinary Gaussian local Whittle objective. It has no implemented nonstationary correction. Both it and WhittleMLE optimize d within [-0.49, 0.49]; boundary hits are diagnostic warnings. WhittleMLE fits an ARFIMA(0,d,0) spectral shape on the selected frequency band, not an exact time-domain likelihood or the exact fGn spectrum.

Parameter	Type	Default	Description
n_bootstrap	int	200	Number of bootstrap replicates for CIs.
bootstrap_block_len	int	max(4, n//10)	Block length for the circular block bootstrap.
ci_levels	list[float]	[0.95]	Nominal coverage levels.
m	int	varies	Number of low-frequency Fourier frequencies used. GPH and Periodogram default to n^0.5; WhittleMLE defaults to n//8; ModifiedLocalWhittle defaults to n^0.55.
taper	str	"none"	GPH/Periodogram taper. "none" uses the raw periodogram; "cosine" uses a Hann window. WhittleMLE and ModifiedLocalWhittle do not consume this parameter.

Geometric estimators

Applies to: Higuchi, GHE.

Both methods analyse a path. Declare input_representation: increments for fGn records: the adapter constructs a path by prepending zero to their cumulative sum, without demeaning the increments. Declare path for an already integrated path. Omission defaults to path and records a warning. This choice is never inferred from the record's truth. Path-based H proxies are not automatically LRD parameters.

Their candidate circular block bootstrap resamples increments and reconstructs the path for each draw. It does not resample path levels. This procedure still requires method-specific coverage calibration under long memory.

Parameter	Type	Default	Description
input_representation	str	"path"	"path" or "increments"; declare explicitly in research manifests.
k_max	int	max(8, min(64, n//8))	Maximum lag / block size for Higuchi curve-length calculation.
n_scales	int	16	Number of geometrically spaced lags for GHE.
h_min	int	1	Minimum lag for GHE.
h_max	int	n//8	Maximum GHE lag on the analysed path; must exceed h_min and remain below n/2.
q	float	2.0	Positive finite moment order for GHE: mean absolute lagged differences raised to q; report log-log slope divided by q. Use 1.0 for the first absolute moment.
flat_slope_tol	float	0.0	Deprecated; nonzero values are rejected. The former forced H = 0.5 fallback was removed.

Higuchi and GHE report unclipped slopes, with out-of-range diagnostics. GPH, Periodogram and PeriodogramBeta also retain unconstrained regression estimates. The ranges in the estimand table describe model parameters, not enforced estimator bounds. These changes intentionally alter results and require new output bundles.

RS, DFA, DMA, AbsoluteMoment, Variance, VarianceResidual and the WaveletOLS, AbryVeitch and Bardet regressions also retain unconstrained estimates. Their stationary-increment H interpretation requires appropriate inputs. In particular, DFA integrates its input internally; its raw fluctuation slope on an fBm path is not the same target as H on fGn increments. Out-of-range points and bootstrap draws are counted, not silently capped or relabelled as successful memory recovery.

The RS use_anis_lloyd_correction option divides by the Gaussian white-noise expectation before regression and adds 0.5. This is an implementation-specific normalization using that expectation, not a general unbiased estimator.

Wavelet estimators

Applies to: WaveletOLS, WaveletAbryVeitch, WaveletBardet, WaveletJensen, WaveletWhittle.

Parameter	Type	Default	Description
n_bootstrap	int	200	Number of bootstrap replicates for CIs.
bootstrap_block_len	int	max(4, n//10)	Block length for the circular block bootstrap.
ci_levels	list[float]	[0.95]	Nominal coverage levels.
wavelet	str	"db4"	Wavelet family passed to pywt.wavedec.
j_drop_high	int	AbryVeitch: 2; OLS/Bardet/Whittle: 1	Number of finest (highest-frequency) levels removed.
j_drop_low	int	AbryVeitch/Bardet: 2; OLS/Whittle: 1	Number of coarsest (lowest-frequency) levels removed.
fine_band, coarse_band	pair[int, int]	[2, 4], [4, 6]	Jensen level bands.

Maximum DWT depth is computed from record length and the wavelet filter. max_level is not a consumed estimator parameter. At least three retained detail levels are required by the regression helpers; length alone does not guarantee a fit.

Data-driven estimators

Applies to: MLRandomForest, MLSVR, MLCNN, MLLSTM.

Parameter	Type	Default	Description
model_path	str	None	Path to a pre-trained model artefact. If absent, the estimator trains from the manifest's ml_training block.
max_lag	int	16	(MLRandomForest, MLSVR) Number of autocorrelation lags included in the feature vector. Changing this from the value used during training will raise a max_lag_mismatch error instead of silently producing garbage.
n_estimators	int	100	(MLRandomForest) Number of trees in the random forest.
max_depth	int	None	(MLRandomForest) Maximum depth of each tree. None means fully grown.
min_samples_leaf	int	1	(MLRandomForest) Minimum samples per leaf.
C	float	10.0	(MLSVR) SVR regularization parameter.
epsilon	float	0.03	(MLSVR) SVR epsilon-tube margin.
kernel	str	"rbf"	(MLSVR) Kernel type.
sequence_length	int	256	(MLCNN, MLLSTM) Length every input series is resampled to before being fed to the network. Values smaller than 8 raise an error.
conv1_channels	int	16	(MLCNN) First convolution channel count.
conv2_channels	int	32	(MLCNN) Second convolution channel count.
hidden_size	int	32	(MLLSTM) LSTM hidden size per layer.
num_layers	int	1	(MLLSTM) Number of stacked LSTM layers. Values >1 trigger inter-layer dropout.
dropout	float	0.2	(MLCNN, MLLSTM) Dropout probability applied after conv/LSTM layers and in the MLP head. Set to 0.0 to disable (LSTM will still use 0.2 when num_layers > 1 because the implementation uses a fallback at that setting).
learning_rate	float	0.001	(MLCNN, MLLSTM) Adam learning rate.
weight_decay	float	1e-4	(MLCNN, MLLSTM) Adam weight-decay (L2 regularization).
batch_size	int	16	(MLCNN, MLLSTM) Training mini-batch size.
epochs	int	8	(MLCNN, MLLSTM) Number of training epochs.

Spectral-exponent and timescale estimators

Applies to: PeriodogramBeta, ACFDecay.

Parameter	Type	Default	Description
m	int	n^0.5	(PeriodogramBeta) Number of low-frequency Fourier frequencies for the slope fit.
taper	str	"none"	(PeriodogramBeta) Spectral taper ("none" or "cosine").
max_lag	int	automatic, capped at n//4	(ACFDecay) Automatic fitting stops before the first ACF value below rho_floor. An explicit cap instead retains positive ACF values above 1e-6 within that cap.
rho_floor	float	0.1	(ACFDecay) Threshold used to end the automatic leading ACF band; an explicit max_lag overrides this stopping rule.
n_bootstrap, bootstrap_block_len, ci_levels			Shared block-bootstrap CI parameters (see temporal estimators).

LRD discriminators

Applies to: ThresholdHurst / LowFreqSpectral / ScaleCrossover / ICModelSelect.

All target lrd_class and emit a [0, 1] score.

Parameter	Type	Default	Description
base	str	"dfa"	(ThresholdHurst) Underlying Hurst estimator: "dfa", "gph", or "rs".
h0	float	0.55	(ThresholdHurst, ScaleCrossover) Logistic decision centre on the Hurst / large-scale-slope axis.
width	float	0.05	Logistic scale.
m_power	float	0.45	(LowFreqSpectral) Low-frequency bandwidth as m = n^m_power.
d0	float	0.075	(LowFreqSpectral) Logistic centre on the memory-parameter axis.
ar_orders	list[int]	[1, 2]	(ICModelSelect) Short-memory AR orders compared against ARFIMA(0,d,0).
scale	float	4.0	(ICModelSelect) Logistic scale on the ΔBIC axis.

Execution block

Parameter	Type	Default	Description
max_workers	int	1	Thread-pool size for parallel estimator fits.
estimate_cache_dir	str	None	Directory for on-disk estimate caches.
cache_read	bool	True	Allow reading from the estimate cache.
cache_write	bool	True	Allow writing to the estimate cache.