op

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Axis op on sub-layer L3_A_step_op (layer l3).

Sub-layer

L3_A_step_op

Axis metadata

• Default: 'lag'

• Sweepable: False

• Status: operational

Operational status summary

• Operational: 47 option(s)

• Future: 5 option(s)

Options

adaptive_ma_rf – operational

AlbaMA – RF-driven adaptive moving average smoother for a single time series.

See adaptive_ma_rf function page for full documentation + parameters + standalone usage. Standalone: mf.functions.adaptive_ma_rf_transform.

asymmetric_trim – operational

Albacore-family rank-space transformation (Goulet Coulombe et al. 2024).

See asymmetric_trim function page for full documentation + parameters + standalone usage. Standalone: mf.functions.asymmetric_trim_transform.

boruta_selection – future

(no schema description for boruta_selection)

TBD: option doc not yet authored for this value. The encyclopedia falls back to the bare schema description above. PRs adding a full OptionDoc entry under macroforecast/scaffold/option_docs/l3.py are welcome.

cumsum – operational

Cumulative sum of a series.

See cumsum function page for full documentation + parameters + standalone usage. Standalone: mf.functions.cumsum_transform.

dfm – operational

Dynamic factor model – Kalman state-space factor extraction.

See dfm function page for full documentation + parameters + standalone usage. Standalone: mf.functions.dfm_transform.

diff – operational

First difference: y_t - y_{t-1}.

See diff function page for full documentation + parameters + standalone usage. Standalone: mf.functions.diff_transform.

feature_selection – operational

Filter columns by variance / correlation / lasso pre-screen.

See feature_selection function page for full documentation + parameters + standalone usage. Standalone: mf.functions.feature_selection_transform.

fourier – operational

Fourier basis features – sin/cos at fixed harmonics.

See fourier function page for full documentation + parameters + standalone usage. Standalone: mf.functions.fourier_transform.

genetic_algorithm_selection – future

(no schema description for genetic_algorithm_selection)

TBD: option doc not yet authored for this value. The encyclopedia falls back to the bare schema description above. PRs adding a full OptionDoc entry under macroforecast/scaffold/option_docs/l3.py are welcome.

hamilton_filter – operational

Hamilton (2018) regression-based detrend (HP-filter alternative).

See hamilton_filter function page for full documentation + parameters + standalone usage. Standalone: mf.functions.hamilton_filter_transform.

holiday – operational

Holiday / event dummy variables.

See holiday function page for full documentation + parameters + standalone usage. Standalone: mf.functions.holiday_transform.

hp_filter – operational

Hodrick-Prescott filter – trend / cycle decomposition.

See hp_filter function page for full documentation + parameters + standalone usage. Standalone: mf.functions.hp_filter_transform.

interaction – operational

Pairwise interaction terms only (no pure powers).

See interaction function page for full documentation + parameters + standalone usage. Standalone: mf.functions.interaction_terms_transform.

kernel – operational

Kernel-feature pre-step (Random Fourier / Nyström handle).

Alias – no dedicated function page. See canonical kernel_features (op/kernel_features.md) for full documentation + standalone usage.

Generic handle for an explicit kernel-feature embedding; concrete dispatch is determined by params.kernel (rbf / poly / laplacian). For named variants use kernel_features (RBF Random Fourier) or nystroem.

When to use

Kernel-augmented linear / SVM pipelines.

References

• macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

Related options: kernel_features, nystroem

Last reviewed 2026-05-05 by macroforecast author.

kernel_features – operational

Random Fourier features – approximate RBF kernel via random projection.

See kernel_features function page for full documentation + parameters + standalone usage. Standalone: mf.functions.kernel_features_transform.

l3_feature_bundle – operational

Internal sentinel: bundle column-producing children into the X matrix.

Synthetic node emitted by the runtime to collect the outputs of all leaf transforms into a single X artifact consumed by L4. Authors do not write this node by hand; the cascade builder inserts it.

Surfaced in operational_options so the schema completeness test stays consistent.

When to use

Never authored directly – inserted by the cascade builder.

References

• macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

Related options: l3_metadata_build

Last reviewed 2026-05-05 by macroforecast author.

l3_metadata_build – operational

Internal sentinel: assemble L3 metadata sink (lineage / pipeline definitions).

Synthetic node that produces the column_lineage and pipeline_definitions sinks from the cascade graph. Powers L7 lineage_attribution and transformation_attribution downstream.

When to use

Never authored directly – inserted by the cascade builder when L7 lineage hooks are active.

References

• macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

Related options: l3_feature_bundle

Last reviewed 2026-05-05 by macroforecast author.

lag – operational

Lagged target/predictor block.

See lag function page for full documentation + parameters + standalone usage. Standalone: mf.functions.lag_matrix.

lasso_path_selection – future

(no schema description for lasso_path_selection)

TBD: option doc not yet authored for this value. The encyclopedia falls back to the bare schema description above. PRs adding a full OptionDoc entry under macroforecast/scaffold/option_docs/l3.py are welcome.

level – operational

Pass-through: keep the series at its original level.

No-op transform; the column flows through unchanged. Used as an explicit anchor in the DAG so downstream ops can reference the level form even when the L2 transform_policy converted to log-differences. Useful when you want both level and diff branches in the same recipe.

When to use

Authoring branches that need the level form alongside a transformed branch.

References

• macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

Related options: diff, log, log_diff, pct_change

Last reviewed 2026-05-05 by macroforecast author.

log – operational

Natural logarithm: ln(y).

See log function page for full documentation + parameters + standalone usage. Standalone: mf.functions.log_transform.

log_diff – operational

Log first difference: ln(y_t) - ln(y_{t-1}).

See log_diff function page for full documentation + parameters + standalone usage. Standalone: mf.functions.log_diff_transform.

ma_increasing_order – operational

MARX – moving averages of increasing order (Coulombe 2024).

See ma_increasing_order function page for full documentation + parameters + standalone usage. Standalone: mf.functions.ma_increasing_order_transform.

ma_window – operational

Trailing moving average over a fixed window.

See ma_window function page for full documentation + parameters + standalone usage. Standalone: mf.functions.ma_window_transform.

maf_per_variable_pca – operational

Per-variable MAF via PCA on lag-panels – Coulombe et al. (2021 IJF) Eq. (7).

See maf_per_variable_pca function page for full documentation + parameters + standalone usage. Standalone: mf.functions.maf_per_variable_pca_transform.

midas – operational

MIDAS Almon / Exp-Almon / Beta weighted lag polynomial (Ghysels-Sinko-Valkanov 2007).

Parametric mixed-frequency aggregation: emits one column per HF predictor whose value is the weighted sum Σ_k ω_k(θ̂) · x_{t·m − k}. The weight kernel ω_k(θ) is fitted by NLS against the LF target_signal input.

Three weighting families:

• almon – polynomial basis ω_k = Σ_q θ_q · k^q of order polynomial_order (default 2). Optional sum-to-one normalisation.

• exp_almon (default) – ω_k ∝ exp(θ_1 k + θ_2 k²); numerically stable and the GSV 2007 §3 default.

• beta – ω_k ∝ k_norm^{θ_1−1} (1 − k_norm)^{θ_2−1} for k_norm = (k+1)/(K+1); flexible monotone / hump kernel.

Defaults: freq_ratio = 3, n_lags_high = 12, sum_to_one = True, max_iter = 200. Optimiser: scipy.optimize.minimize (Nelder-Mead). Per-predictor theta_hat / weights / converged stashed in result.attrs['midas_fit'] for L7 inspection.

Requires a target_signal input port – shares routing with scaled_pca.

When to use

Mixed-frequency nowcasting where parametric lag weights are desired; reproducing GSV 2007 macro / asset-pricing applications.

When NOT to use

High-noise predictors where NLS optimiser diverges (use u_midas + downstream regularised regression instead).

References

• macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

• Ghysels, Sinko & Valkanov (2007) ‘MIDAS Regressions: Further Results and New Directions’, Econometric Reviews 26(1): 53-90.

• Ghysels, Santa-Clara & Valkanov (2004) ‘The MIDAS Touch: Mixed Data Sampling Regression Models’, UCLA / UNC working paper.

Related options: u_midas, scaled_pca, lag

Last reviewed 2026-05-05 by macroforecast author.

nystroem – operational

Nyström kernel approximation – subset-based feature map.

See nystroem function page for full documentation + parameters + standalone usage. Standalone: mf.functions.nystroem_transform.

nystroem_features – operational

Alias for nystroem – explicit feature-stage name.

Alias – no dedicated function page. See canonical nystroem (op/nystroem.md) for full documentation + standalone usage.

Identical to nystroem; preferred when a multi-stage pipeline names its kernel approximation explicitly in the lineage graph.

When to use

Multi-stage pipelines that separate kernel approximation from downstream linear fits.

References

• macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

Related options: nystroem

Last reviewed 2026-05-05 by macroforecast author.

partial_least_squares – operational

Partial least squares regression – supervised factor extraction.

See partial_least_squares function page for full documentation + parameters + standalone usage. Standalone: mf.functions.partial_least_squares_transform.

pca – operational

Principal component analysis – linear factor extraction.

See pca function page for full documentation + parameters + standalone usage. Standalone: mf.functions.pca_transform.

pct_change – operational

Period-over-period percentage change: (y_t / y_{t-1}) - 1.

See pct_change function page for full documentation + parameters + standalone usage. Standalone: mf.functions.pct_change_transform.

polynomial – operational

Polynomial basis expansion – degree-d powers of input.

Alias – no dedicated function page. See canonical polynomial_expansion (op/polynomial_expansion.md) for full documentation + standalone usage.

sklearn PolynomialFeatures of degree params.degree. Includes interaction terms by default; set params.interaction_only=True for products without pure powers.

When to use

Capturing low-order non-linearity for linear / kernel models.

When NOT to use

High dimension (degree > 3 with many predictors) – explodes the design matrix; use kernel methods instead.

References

• macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

Related options: interaction, kernel_features, polynomial_expansion

Last reviewed 2026-05-05 by macroforecast author.

polynomial_expansion – operational

Alias for polynomial – explicit expansion node in cascade pipelines.

See polynomial_expansion function page for full documentation + parameters + standalone usage. Standalone: mf.functions.polynomial_expansion_transform.

random_projection – operational

Johnson-Lindenstrauss random Gaussian projection.

See random_projection function page for full documentation + parameters + standalone usage. Standalone: mf.functions.random_projection_transform.

recursive_feature_elimination – future

(no schema description for recursive_feature_elimination)

TBD: option doc not yet authored for this value. The encyclopedia falls back to the bare schema description above. PRs adding a full OptionDoc entry under macroforecast/scaffold/option_docs/l3.py are welcome.

regime_indicator – operational

Discrete regime / state indicator from L1.G.

Lifts the L1.G regime sink (regime_indicator) into the feature panel as a categorical column. Required when L4 is configured for regime_use = predictor or conditional_intercept.

When to use

Regime-conditional forecasts where the model needs explicit access to the state.

References

• macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

Related options: season_dummy, time_trend

Last reviewed 2026-05-05 by macroforecast author.

savitzky_golay_filter – operational

Polynomial-fit smoothing filter (Savitzky & Golay 1964).

See savitzky_golay_filter function page for full documentation + parameters + standalone usage. Standalone: mf.functions.savitzky_golay_transform.

scale – operational

Standardise to zero mean and unit variance.

See scale function page for full documentation + parameters + standalone usage. Standalone: mf.functions.scale_transform.

scaled_pca – operational

Scaled / weighted PCA (target-aware factor extraction).

See scaled_pca function page for full documentation + parameters + standalone usage. Standalone: mf.functions.scaled_pca_transform.

season_dummy – operational

Calendar dummy variables (month-of-year, quarter-of-year).

See season_dummy function page for full documentation + parameters + standalone usage. Standalone: mf.functions.season_dummy_transform.

seasonal_lag – operational

Lag at a seasonal period (e.g. y_{t-12} for monthly data).

See seasonal_lag function page for full documentation + parameters + standalone usage. Standalone: mf.functions.seasonal_lag_matrix.

sliced_inverse_regression – operational

sSUFF / Sliced inverse regression (scaled) – supervised dimension reduction (Huang-Jiang-Li-Tong-Zhou 2022).

See sliced_inverse_regression function page for full documentation + parameters + standalone usage. Standalone: mf.functions.sliced_inverse_regression_transform.

sparse_pca – operational

Sparse PCA – L1-penalised factor loadings (sklearn / Zou-Hastie-Tibshirani 2006).

See sparse_pca function page for full documentation + parameters + standalone usage. Standalone: mf.functions.sparse_pca_transform.

sparse_pca_chen_rohe – operational

Chen-Rohe (2023) Sparse Component Analysis – non-diagonal D variant.

See sparse_pca_chen_rohe function page for full documentation + parameters + standalone usage. Standalone: mf.functions.sparse_pca_chen_rohe_transform.

stability_selection – future

(no schema description for stability_selection)

TBD: option doc not yet authored for this value. The encyclopedia falls back to the bare schema description above. PRs adding a full OptionDoc entry under macroforecast/scaffold/option_docs/l3.py are welcome.

supervised_pca – operational

Supervised PCA (Giglio-Xiu-Zhang 2025) – screen-then-PCA on a target panel.

See supervised_pca function page for full documentation + parameters + standalone usage. Standalone: mf.functions.supervised_pca_transform.

target_construction – operational

Build the supervised target (y) from the panel.

Constructs the regression target according to forecast_strategy (direct / iterated / cumulative_average) and the L1.F horizon set. Outputs the y artifact that L4 fit_model nodes consume.

Required as the leaf of every L3 DAG; the runtime auto-injects it when the user does not.

When to use

Always required – runtime auto-inserts when missing.

References

• macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

Related options: level, diff, log_diff

Last reviewed 2026-05-05 by macroforecast author.

time_trend – operational

Deterministic linear time trend (t = 1, 2, ...).

See time_trend function page for full documentation + parameters + standalone usage. Standalone: mf.functions.time_trend_transform.

u_midas – operational

Unrestricted MIDAS lag stack – mixed-frequency aggregation primitive (Foroni-Marcellino-Schumacher 2015).

Atomic mixed-frequency primitive: stacks K = n_lags_high high-frequency lags of each predictor at low-frequency dates without imposing any weighting structure. For HF column col and LF index position t·m, emits col_lag0, col_lag1, …, col_lag{K-1} where col_lagk[t] = frame[col].iloc[t·m − k].

The downstream L4 OLS estimator recovers data-driven lag coefficients – the unrestricted MIDAS regression (paper §3.2 eq.(20)):

y_{t×k} = μ₀ + μ₁ y_{t×k−k} + ψ₀ x_{t×k−1} + ψ₁ x_{t×k−2} + … + ψ_K x_{t×k−K} + ε_{t×k}

where μ₀, μ₁, and ψ(L) are estimated by OLS (paper §3.2 p.11). Ridge regularisation is available as an explicit opt-in via regularization='ridge' in the paper_methods.u_midas(...) recipe; it deviates from the paper’s estimator choice and is not the default.

Lag-order selection: n_lags_high='bic' (default) runs BIC over K ∈ {1, …, ceil(1.5 × freq_ratio)}, fitting OLS at each candidate and selecting K* = argmin BIC (paper §3.2 p.11 + §3.5). Pass an integer to fix K. 'aic' is also accepted.

AR(1) y-lag: the paper_methods.u_midas(...) helper sets include_y_lag=True by default, prepending the lagged target y_lag1 as the leftmost design-matrix column (μ₁ term of eq.(20)). Set include_y_lag=False to match the simplified §2.3 eq.(14) form with no AR component.

Defaults: freq_ratio = 3 (quarterly target / monthly HF), n_lags_high = 'bic'; target_freq = 'low' subsamples the LF anchor dates. temporal_rule is required and rejects full_sample_once so the aggregation respects walk-forward boundaries.

Surfaces the Borup-Rapach-Schütte (2023) mixed-frequency ML-nowcasting workflow as a 1-line recipe via paper_methods.u_midas(...).

When to use

Macro nowcasting with monthly predictors and quarterly targets; mixed-frequency feature engineering when no parametric weight kernel is desired.

When NOT to use

When n_lags_high · n_HF_columns is large relative to T even after BIC selects a small K – BIC penalises over-parameterisation but cannot reduce the number of predictor columns. Use midas parametric weighting instead, or pair with downstream lasso / ridge (set regularization='ridge') to handle wide design matrices.

References

• macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

• Foroni, Marcellino & Schumacher (2011/2015) ‘Unrestricted Mixed Data Sampling (MIDAS): MIDAS Regressions With Unrestricted Lag Polynomials’. Bundesbank Discussion Paper Series 1, No. 35/2011; published as JRSS-A 178(1): 57-82. DOI 10.1111/rssa.12043.

• Borup, Rapach & Schütte (2023) ‘Mixed-frequency machine learning: Nowcasting and backcasting weekly initial claims with daily internet search-volume data’, International Journal of Forecasting 39(3): 1122-1144.

Related options: midas, lag, ma_window

Last reviewed 2026-05-05 by macroforecast author.

varimax – operational

Varimax-rotated factors (orthogonal rotation for interpretability).

See varimax function page for full documentation + parameters + standalone usage. Standalone: mf.functions.varimax_transform.

varimax_rotation – operational

Alias for varimax – rotation step in a multi-stage factor pipeline.

Alias – no dedicated function page. See canonical varimax (op/varimax.md) for full documentation + standalone usage.

Identical operation to varimax but registered separately so a cascading L3 pipeline can declare pca → varimax_rotation as two visible nodes in its lineage.

When to use

Multi-stage pipelines that explicitly separate factor extraction from rotation.

References

• macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

Related options: varimax, pca

Last reviewed 2026-05-05 by macroforecast author.

wavelet – operational

Discrete wavelet transform – multi-scale time-frequency features.

See wavelet function page for full documentation + parameters + standalone usage. Standalone: mf.functions.wavelet_transform.