Understanding outputs

MFDRO separates the estimate itself from the evidence that the rolling window was constructed as requested.

Point estimate

MultiFrequencySignal.estimate returns SignalEstimate.

Field	Meaning
rho	Configured non-negative squared cross-frequency dispersion
sqrt_rho	Square root of rho, in the scaled return unit
seed	Effective uint32 seed used by projected calculations
config_digest	SHA-256 identity of the complete SignalConfig
frequency_weights	Normalized dispersion weights, in configured order
frequency_squared_distances	Unweighted squared distance from each frequency to the configured center
barycenter_weights	Normalized center weights, in configured order
sample_sizes	Observation count for every empirical measure
n_assets	Shared multivariate dimension
asset_labels	Canonical labels when DataFrames were supplied
support	Optional free-support center, only when requested and applicable

to_record() flattens the fields into audit-friendly names; to_series() creates a labelled pandas Series.

Walk-forward path

estimate_path returns SignalPath with three tables.

Newly written paths use persistence format version 2.

estimates

One row per successful formation. Alongside rho, sqrt_rho, seed, config identity, and asset count, every frequency contributes:

• distance2_<name>: unweighted squared distance from that frequency to the configured center, before aggregation by lambda_<name>;
• lambda_<name>: normalized dispersion weight;
• barycenter_lambda_<name>: normalized center weight;
• n_<name>: empirical sample size.

The aggregate is recoverable from the component columns:

[ \rho_t = \sum_k \lambda_{k,t}\,d^2_{k,t}. ]

Convenience views return copies:

path.rho
path.sqrt_rho
path.successful_dates
path.dispersion_weights
path.center_weights

audit

One aligned row per successful estimate. It records requested and observed window endpoints, lookback, selected asset count, typed asset-order digest, matrix fullness, no-future-observation status, config digest, seed, and every frequency sample size.

The audit is evidence about package-visible inputs. It does not prove that the source or membership was historically available.

skipped

One row per requested formation omitted under on_insufficient="skip". Machine-readable reasons are:

Reason	Meaning
non_contiguous_months	The complete calendar-month lookback was not represented
reference_calendar_mismatch	Observed dates differ from the supplied authoritative calendar
insufficient_frequency_observations	At least one configured aggregation produced too few usable bins

Malformed configuration, invalid membership, selected missing values, and non-finite values remain hard errors rather than skipped observations.

Empty outputs are stable

All three tables retain their documented columns even if every requested formation is skipped. This makes downstream concatenation and schema checks predictable.

Save and verify a path

destination = path.save("artifacts/path")
restored = SignalPath.load(destination)

The directory contains:

path/
├── audit.json
├── config.json
├── estimates.json
├── manifest.json
└── skipped.json

The manifest records the path-format version, package version, row counts, configuration digest, and a SHA-256 checksum for each payload. Loading verifies checksums, declared row counts, schema, row alignment, and configuration identity before returning an object.

MFDRO 0.2 reads paths written by MFDRO 0.1 in format 1. Those files predate frequency-level distances, so their migrated distance2_<name> values are NaN; the aggregate rho and all historical fields remain unchanged. Saving the loaded object produces format 2. Missing components are never inferred from the aggregate.

The JSON-table format is portable and avoids pickle deserialization. For a long-lived archive, also retain source-data identities and the complete Python environment; JSON persistence does not make upstream data reproducible.