family#

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Axis family on sub-layer L4_A_model_selection (layer l4).

Sub-layer#

L4_A_model_selection

Axis metadata#

  • Default: 'ridge'

  • Sweepable: True

  • Status: operational

Operational status summary#

  • Operational: 42 option(s)

  • Future: 5 option(s)

Options#

ar_p – operational#

Autoregressive AR(p) on the target.

See ar_p function page for full documentation + parameters + standalone usage. Standalone: mf.functions.ar_fit.

ols – operational#

Ordinary least squares – baseline linear regression.

See ols function page for full documentation + parameters + standalone usage. Standalone: mf.functions.ols_fit.

ridge – operational#

Ridge regression (L2-regularised OLS).

See ridge function page for full documentation + parameters + standalone usage. Standalone: mf.functions.ridge_fit.

lasso – operational#

Lasso regression (L1-regularised OLS).

See lasso function page for full documentation + parameters + standalone usage. Standalone: mf.functions.lasso_fit.

elastic_net – operational#

Elastic net (L1 + L2 hybrid).

See elastic_net function page for full documentation + parameters + standalone usage. Standalone: mf.functions.elastic_net_fit.

lasso_path – operational#

Lasso with CV-selected alpha (LassoCV).

See lasso_path function page for full documentation + parameters + standalone usage. Standalone: mf.functions.lasso_path_fit.

bayesian_ridge – operational#

Bayesian ridge with empirical-Bayes prior.

See bayesian_ridge function page for full documentation + parameters + standalone usage. Standalone: mf.functions.bayesian_ridge_fit.

glmboost – operational#

Componentwise L2-boosting with linear base learners.

See glmboost function page for full documentation + parameters + standalone usage. Standalone: mf.functions.glmboost_fit.

huber – operational#

Huber regression (robust to outliers).

See huber function page for full documentation + parameters + standalone usage. Standalone: mf.functions.huber_fit.

var – operational#

Vector autoregression VAR(p).

See var function page for full documentation + parameters + standalone usage. Standalone: mf.functions.var_fit.

factor_augmented_ar – operational#

Factor-augmented AR (PCA factors + AR lags on target).

See factor_augmented_ar function page for full documentation + parameters + standalone usage. Standalone: mf.functions.far_fit.

principal_component_regression – operational#

Principal component regression (PCA → OLS).

See principal_component_regression function page for full documentation + parameters + standalone usage. Standalone: mf.functions.pcr_fit.

decision_tree – operational#

Single decision tree (sklearn) or Slow-Growing Tree (SGT, in-fit shrinkage).

Cheapest non-linear model. Useful as an ablation against random forests / boosting – if a single tree matches RF performance, the ensemble isn’t buying much.

v0.9 sub-axis params.split_shrinkage = η – per-split soft-weight learning rate. 0.0 (default) keeps the standard greedy sklearn CART. Non-zero values activate Slow-Growing Trees (Goulet Coulombe 2024 — operational v0.9.1 dev-stage v0.9.0B-6): a soft-weighted tree where rows on the side that does not satisfy the split rule receive weight (1 − η) instead of 0. Implements Algorithm 1 from the paper exactly: leaf weights propagate multiplicatively through every split, the Herfindahl index H_l = Σ(ω²)/(Σω)² of the leaf weight vector controls stopping, and the leaf prediction is the weighted mean.

Limit cases (verified by tests):

  • η = 1.0 → recovers standard CART (hard splits).

  • η ≈ 0.1, H̄ ≈ 0.05 → SGT regime (‘matches RF on Linear DGP at high R²’ per paper Figure 2).

Sub-axis params (only consulted when split_shrinkage ≠ 0):

  • herfindahl_threshold = H̄ (default 0.25; smaller → deeper tree). Practice: {0.05, 0.1, 0.25} per paper.

  • eta_depth_step – paper rule-of-thumb increases η by eta_depth_step·depth per level (default 0.0 keeps η constant).

  • max_depth – additional safety bound on tree depth.

Note: sklearn DecisionTreeRegressor cannot reproduce SGT via post-fit leaf-multiplication because the splits themselves depend on soft weights (every row, including rule-violators, contributes to the SSE objective). The custom helper _SlowGrowingTree implements the soft-weighted CART from scratch.

When to use

Ablation studies; cheap non-linear baselines; SLOTH single-tree replacement for RF on small samples.

References

  • macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’

  • Breiman, Friedman, Stone & Olshen (1984) ‘Classification and Regression Trees’, CRC Press.

  • Goulet Coulombe (2024) ‘Slow-Growing Trees’, in Machine Learning for Econometrics and Related Topics, Studies in Systems, Decision and Control 508 (Springer). doi:10.1007/978-3-031-43601-7_4.

Related options: random_forest, extra_trees, gradient_boosting

Last reviewed 2026-05-04 by macroforecast author.

random_forest – operational#

Random forest (sklearn).

See random_forest function page for full documentation + parameters + standalone usage. Standalone: mf.functions.random_forest_fit.

extra_trees – operational#

Extremely randomized trees (sklearn).

See extra_trees function page for full documentation + parameters + standalone usage. Standalone: mf.functions.extra_trees_fit.

gradient_boosting – operational#

Gradient-boosted regression trees (sklearn).

See gradient_boosting function page for full documentation + parameters + standalone usage. Standalone: mf.functions.gradient_boosting_fit.

xgboost – operational#

XGBoost gradient-boosted trees (optional dependency).

See xgboost function page for full documentation + parameters + standalone usage. Standalone: mf.functions.xgboost_fit.

lightgbm – operational#

LightGBM gradient-boosted trees (optional dependency).

See lightgbm function page for full documentation + parameters + standalone usage. Standalone: mf.functions.lightgbm_fit.

catboost – operational#

CatBoost gradient-boosted trees (optional dependency).

See catboost function page for full documentation + parameters + standalone usage. Standalone: mf.functions.catboost_fit.

svr_linear – operational#

Support vector regression with linear kernel.

See svr_linear function page for full documentation + parameters + standalone usage. Standalone: mf.functions.svr_linear_fit.

svr_rbf – operational#

Support vector regression with RBF kernel.

See svr_rbf function page for full documentation + parameters + standalone usage. Standalone: mf.functions.svr_rbf_fit.

svr_poly – operational#

Support vector regression with polynomial kernel.

See svr_poly function page for full documentation + parameters + standalone usage. Standalone: mf.functions.svr_poly_fit.

kernel_ridge – operational#

Kernel Ridge Regression – closed-form non-linear ridge in the dual.

See kernel_ridge function page for full documentation + parameters + standalone usage. Standalone: mf.functions.kernel_ridge_fit.

mlp – operational#

Multi-layer perceptron (sklearn).

See mlp function page for full documentation + parameters + standalone usage. Standalone: mf.functions.mlp_fit.

lstm – operational#

Long short-term memory recurrent NN (torch, optional).

See lstm function page for full documentation + parameters + standalone usage. Standalone: mf.functions.lstm_fit.

gru – operational#

Gated recurrent unit RNN (torch, optional).

See gru function page for full documentation + parameters + standalone usage. Standalone: mf.functions.gru_fit.

transformer – operational#

Transformer encoder regressor (torch, optional).

See transformer function page for full documentation + parameters + standalone usage. Standalone: mf.functions.transformer_fit.

knn – operational#

k-nearest-neighbours regression.

See knn function page for full documentation + parameters + standalone usage. Standalone: mf.functions.knn_fit.

bvar_minnesota – operational#

Bayesian VAR with Minnesota prior shrinkage.

See bvar_minnesota function page for full documentation + parameters + standalone usage. Standalone: mf.functions.bvar_minnesota_fit.

bvar_normal_inverse_wishart – operational#

Bayesian VAR with Normal-Inverse-Wishart prior.

See bvar_normal_inverse_wishart function page for full documentation + parameters + standalone usage. Standalone: mf.functions.bvar_niw_fit.

factor_augmented_var – operational#

Factor-augmented VAR (Bernanke-Boivin-Eliasz 2005).

See factor_augmented_var function page for full documentation + parameters + standalone usage. Standalone: mf.functions.favar_fit.

macroeconomic_random_forest – operational#

Goulet Coulombe (2024) MRF: random walk regularised forest with per-leaf local linear regression and Block Bayesian Bootstrap forecast ensembles.

Macroeconomic Random Forest. Each leaf fits a local linear regression of y on the state vector S; coefficient series are smoothed via random-walk regularisation (rw_regul parameter); forecast ensembles use the Block Bayesian Bootstrap (Taddy 2015 extension). Surfaces Generalised Time-Varying Parameters (GTVPs) via the L7 mrf_gtvp op.

Backed by Ryan Lucas’s reference implementation, vendored under macroforecast/_vendor/macro_random_forest/ with surgical numpy 2.x / pandas 2.x compatibility patches (no algorithmic changes). Upstream: https://github.com/RyanLucas3/MacroRandomForest. No extra required – the family works out of the box.

Citation requirement: research using this family must cite Goulet Coulombe (2024) ‘The Macroeconomy as a Random Forest’, Journal of Applied Econometrics (arXiv:2006.12724) and acknowledge the upstream implementation by Ryan Lucas (https://github.com/RyanLucas3/MacroRandomForest).

Tunable params: B (bootstrap iterations, default 50), ridge_lambda (default 0.1), rw_regul (RW penalty 0..1, default 0.75), mtry_frac (default 1/3), trend_push (default 1), quantile_rate (default 0.3), fast_rw (default True), parallelise (default False), n_cores (default 1).

When to use

Macro forecasting with non-stationary parameter dynamics; alternative to switching models.

References

  • macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’

  • Goulet Coulombe, P. (2024) ‘The Macroeconomy as a Random Forest’, Journal of Applied Econometrics. arXiv:2006.12724.

  • Lucas, R. (2022) ‘MacroRandomForest’ (Python implementation). https://github.com/RyanLucas3/MacroRandomForest. MIT licence.

Related options: random_forest, bvar_minnesota

Last reviewed 2026-05-04 by macroforecast author.

dfm_mixed_mariano_murasawa – operational#

Mariano-Murasawa-style mixed-frequency dynamic factor model.

See dfm_mixed_mariano_murasawa function page for full documentation + parameters + standalone usage. Standalone: mf.functions.dfm_fit.

quantile_regression_forest – operational#

Meinshausen (2006) quantile regression forest.

Records the per-leaf empirical training-target distribution and forecasts arbitrary quantiles by averaging leaf-conditional CDFs. Surfaces forecast_intervals directly without a Gaussian shortcut. Pairs with forecast_object: quantile.

When to use

Growth-at-risk / VaR studies; density forecasting.

References

  • macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’

  • Meinshausen (2006) ‘Quantile Regression Forests’, JMLR 7.

Related options: random_forest, bagging

Last reviewed 2026-05-04 by macroforecast author.

bagging – operational#

Bootstrap-aggregating wrapper around any base family; supports Booging.

params.base_family selects the base estimator; params.n_estimators (default 50) bootstrap resamples are fit; predict averages. predict_quantiles surfaces empirical bag-quantiles.

v0.9 sub-axis params.strategy – bag composition strategy:

  • standard (default) – plain Breiman (1996) bagging; i.i.d. bootstrap with replacement.

  • block (operational v0.8.9) – circular moving-block bootstrap (Künsch 1989 variant: block starts wrap at n via modulo) for serially-correlated panels (Taddy 2015 ext. used in MRF).

  • booging (operational v0.9.1) – Goulet Coulombe (2024) ‘To Bag is to Prune’. Outer B bags of (intentionally over-fitted) inner Stochastic Gradient Boosted Trees + Data Augmentation: each predictor column is duplicated as X̃_k = X_k + N(0, (σ_k · da_noise_frac)²); per-bag column-drop of rate da_drop_rate (default 0.2); inner SGB at inner_n_estimators=500, inner_learning_rate=0.1, inner_max_depth=4, inner_subsample=0.5. Sampling without replacement at max_samples=0.75. Outer n_estimators=B (default 100) replaces tuning the boosting depth S – the bag-prune theorem (paper §2) lets us over-fit the inner SGB and let the bag average prune. Helper _BoogingWrapper.

  • sequential_residual – legacy alias for booging retained for back-compat. Pre-2026-05-07 plan sketch (“K rounds bag-on-residuals”) was an inaccurate description of the same paper’s algorithm; the option now routes to the outer-bagging-of-inner-SGB construction.

When to use

Variance reduction on noisy series; quantile bands without quantile regression; Booging / block-bootstrap recipes; over-fit-then-bag pruning.

References

  • macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’

  • Breiman (1996) ‘Bagging Predictors’, Machine Learning 24(2).

  • Künsch (1989) ‘The jackknife and the bootstrap for general stationary observations’, Annals of Statistics 17(3) – moving-block variant.

  • Goulet Coulombe (2024) ‘To Bag is to Prune’, arXiv:2008.07063 – Booging algorithm.

Related options: random_forest, extra_trees, quantile_regression_forest, gradient_boosting

Last reviewed 2026-05-04 by macroforecast author.

mars – operational#

Multivariate Adaptive Regression Splines (Friedman 1991).

See mars function page for full documentation + parameters + standalone usage. Standalone: mf.functions.mars_fit.

garch11 – operational#

GARCH(1,1) univariate conditional-variance model (Bollerslev 1986).

See garch11 function page for full documentation + parameters + standalone usage. Standalone: mf.functions.garch11_fit.

egarch – operational#

Exponential GARCH with leverage asymmetry (Nelson 1991).

See egarch function page for full documentation + parameters + standalone usage. Standalone: mf.functions.egarch_fit.

realized_garch_with_rv_exog – operational#

GARCH(1,1) with realised-variance series fed as the exogenous regressor (NOT Hansen-Huang-Shek 2012 joint MLE).

See realized_garch_with_rv_exog function page for full documentation + parameters + standalone usage. Standalone: mf.functions.realized_garch_fit.

ets – operational#

Exponential Smoothing State-Space (Hyndman-Koehler-Ord-Snyder 2008) – ETS family.

See ets function page for full documentation + parameters + standalone usage. Standalone: mf.functions.ets_fit.

theta_method – operational#

Theta method (Assimakopoulos-Nikolopoulos 2000) – M3-competition winning baseline.

See theta_method function page for full documentation + parameters + standalone usage. Standalone: mf.functions.theta_fit.

holt_winters – operational#

Holt-Winters additive / multiplicative seasonal exponential smoothing.

See holt_winters function page for full documentation + parameters + standalone usage. Standalone: mf.functions.holt_winters_fit.

midas_almon – future#

(no schema description for midas_almon)

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/l4.py are welcome.

midas_beta – future#

(no schema description for midas_beta)

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/l4.py are welcome.

midas_step – future#

(no schema description for midas_step)

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/l4.py are welcome.

dfm_unrestricted_midas – future#

(no schema description for dfm_unrestricted_midas)

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/l4.py are welcome.

realized_garch – future#

(no schema description for realized_garch)

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/l4.py are welcome.