Anofox Forecast — Backtesting, CV, Metrics & Conformal Cheat Sheet

Extension: anofox_forecast v0.15.3 | DuckDB: v1.4.5 LTS / v1.5.4+ | Dual naming: ts_* and anofox_fcst_ts_*

Time-series-aware cross-validation, error metrics, and distribution-free intervals.

Critical gotchas

• ts_backtest_auto_by was REMOVED. Use the two-step CV workflow (ts_cv_folds_by → ts_cv_forecast_by) instead. Older docs and tests may still reference the retired one-liner.
• Metric _by table macros (ts_mae_by, ts_rmse_by, …) are deprecated. They're ~2400× slower than the scalar + GROUP BY pattern and don't parallelise. Use scalars.
• Always ORDER BY inside LIST() for temporal correctness: LIST(y ORDER BY ds), not LIST(y).
• ts_cv_forecast_by output renames the target column to y (canonical). Don't try to access the original name.
• Folds must be pre-computed before forecasting. Passing raw data to ts_cv_forecast_by throws a clear error.

The CV two-step workflow (standard)

-- Step 1: Create fold table (train/test rows with actual dates)
CREATE OR REPLACE TABLE cv_folds AS
SELECT * FROM ts_cv_folds_by('data', unique_id, ds, y,
    3,                  -- n_folds
    12,                 -- horizon per fold
    MAP{});             -- optional params

-- Step 2: Forecast per fold's train set, predict its test set
CREATE OR REPLACE TABLE cv_forecasts AS
SELECT * FROM ts_cv_forecast_by('cv_folds', unique_id, ds, y,
    'AutoETS',
    MAP{'seasonal_period': '12'});

-- Step 3: Compute per-series / per-fold metrics
SELECT unique_id, fold_id,
    ts_rmse(LIST(y ORDER BY ds), LIST(yhat ORDER BY ds)) AS rmse,
    ts_mae(LIST(y ORDER BY ds), LIST(yhat ORDER BY ds))  AS mae
FROM cv_forecasts
GROUP BY unique_id, fold_id;

ts_cv_folds_by

ts_cv_folds_by(source VARCHAR, group_col COLUMN, date_col COLUMN, target_col COLUMN,
               n_folds BIGINT, horizon BIGINT, params MAP/STRUCT) → TABLE

Input must be pre-cleaned (no gaps, consistent frequency). Uses position-based indexing so works with all frequencies (including calendar-based monthly / quarterly / yearly).

Params:

Key	Default	Description
gap	0	Periods between train end and test start
embargo	0	Periods excluded from training after previous test
window_type	'expanding'	'expanding', 'fixed', or 'sliding'
min_train_size	1	Min training size (fixed / sliding only)
initial_train_size	auto	Periods before first fold
skip_length	horizon	Periods between folds (1 = dense overlap)
clip_horizon	false	Allow partial test windows near series end

Output: 5 columns — <group_col>, <date_col>, <target_col>, fold_id BIGINT, split VARCHAR ('train' / 'test'). Features NOT passed through — use ts_cv_hydrate_by to join extra columns.

ts_cv_split_by / ts_cv_split_folds_by / ts_cv_split_index_by

Alternate fold-creation entry points for custom cutoffs, pre-computed fold boundaries, or memory-efficient index-only splits. See docs/api/08-cross-validation.md for their param signatures.

ts_cv_forecast_by

ts_cv_forecast_by(cv_folds_table VARCHAR, group_col COLUMN, date_col COLUMN, target_col COLUMN,
                  method VARCHAR, params MAP/STRUCT) → TABLE

Fits method on each fold's train partition, forecasts the test partition.

Output columns: fold_id, <group_col>, <date_col>, y (renamed from target_col), split, yhat, yhat_lower, yhat_upper, model_name.

Params: same shape as ts_forecast_by. All model strings work ('AutoETS', 'Laplace', 'HoltWinters', etc.). See anofox-forecast-models for the full catalogue.

ts_cv_hydrate_by — attach features to fold rows

If your model needs exogenous columns (features, calendar flags, promotions), the folds table lost them. Join them back:

CREATE OR REPLACE TABLE cv_folds_with_features AS
SELECT * FROM ts_cv_hydrate_by('cv_folds', unique_id, ds, y, 'features', ['promo', 'holiday']);

ts_check_leakage

Sanity-check that no test-window rows leaked into training:

SELECT * FROM ts_check_leakage('cv_folds', unique_id, ds, fold_id, split);

Metrics — use scalar functions

Pattern: SELECT group, ts_<metric>(LIST(actual ORDER BY ds), LIST(pred ORDER BY ds)) FROM ... GROUP BY group;

Function	Signature	Description
ts_mae	(DOUBLE[], DOUBLE[]) → DOUBLE	Mean Absolute Error
ts_mse	(DOUBLE[], DOUBLE[]) → DOUBLE	Mean Squared Error
ts_rmse	(DOUBLE[], DOUBLE[]) → DOUBLE	Root MSE
ts_mape	(DOUBLE[], DOUBLE[]) → DOUBLE	Mean Absolute % Error
ts_smape	(DOUBLE[], DOUBLE[]) → DOUBLE	Symmetric MAPE
ts_r2	(DOUBLE[], DOUBLE[]) → DOUBLE	R²
ts_bias	(DOUBLE[], DOUBLE[]) → DOUBLE	Bias (mean error)
ts_mase	(actual, forecast, baseline) → DOUBLE	Scaled by seasonal naive
ts_rmae	(actual, pred1, pred2) → DOUBLE	Relative MAE. < 1 = pred1 better
ts_coverage	(actual, lower, upper) → DOUBLE	Interval coverage rate
ts_quantile_loss	(actual, forecast, q) → DOUBLE	Quantile loss at level q
ts_mqloss	(actual, quantiles[], levels[]) → DOUBLE	Multi-quantile CRPS-adjacent

Model comparison across CV folds

-- Fit two models
CREATE OR REPLACE TABLE cv_naive   AS
SELECT * FROM ts_cv_forecast_by('cv_folds', id, ds, y, 'Naive',   MAP{});
CREATE OR REPLACE TABLE cv_autoets AS
SELECT * FROM ts_cv_forecast_by('cv_folds', id, ds, y, 'AutoETS', MAP{'seasonal_period': '7'});

-- Compare
SELECT 'Naive' AS model,
    ts_mae(LIST(y ORDER BY ds), LIST(yhat ORDER BY ds)) AS mae
FROM cv_naive
UNION ALL
SELECT 'AutoETS',
    ts_mae(LIST(y ORDER BY ds), LIST(yhat ORDER BY ds))
FROM cv_autoets
ORDER BY mae;

Conformal prediction — distribution-free intervals

Attach a coverage-guaranteed prediction interval to forecasts, calibrated from backtest residuals.

Three flavours

Approach	Functions	Use when
One-step	ts_conformal_by	You already have backtest results, want intervals now
Modular	ts_conformal_calibrate + ts_conformal_apply_by	Reuse calibration across multiple forecast rounds
Array-based	ts_conformal_predict, ts_conformal_quantile, etc.	Custom pipelines over LIST(...) arrays

ts_conformal_by (one-step)

ts_conformal_by(backtest_results VARCHAR, group_col COLUMN, actual_col COLUMN,
                forecast_col COLUMN, point_forecast_col COLUMN, params STRUCT) → TABLE

Params:

Key	Default	Description
alpha	0.1	Miscoverage rate (0.1 = 90 %, 0.05 = 95 %)
method	'split'	'split' (symmetric) or 'asymmetric' (skewed residuals)

CREATE OR REPLACE TABLE conformal_bounds AS
SELECT * FROM ts_conformal_by('backtest', unique_id, y, yhat, yhat, {alpha: 0.1});

Modular (ts_conformal_calibrate → ts_conformal_apply_by)

-- Compute calibration once
CREATE OR REPLACE TABLE calib AS
SELECT * FROM ts_conformal_calibrate('backtest', y, yhat, {alpha: 0.1});

-- Apply to any future forecast
SELECT * FROM ts_conformal_apply_by('new_forecasts', unique_id, yhat,
    (SELECT conformity_score FROM calib));

Array-based helpers

• ts_conformal_predict, ts_conformal_predict_asymmetric, ts_conformal_predict_per_step
• ts_conformal_quantile, ts_conformal_intervals
• ts_conformal_learn, ts_conformal_apply
• ts_conformal_coverage, ts_conformal_evaluate

Use these when composing custom pipelines over LIST(residual) arrays.

ts_estimate_backtest_memory

Pre-flight a CV run's memory footprint:

SELECT * FROM ts_estimate_backtest_memory(n_series, avg_length, n_folds, horizon);

Full backtest → conformal pipeline

-- 1. CV folds
CREATE OR REPLACE TABLE folds AS
SELECT * FROM ts_cv_folds_by('clean', product_id, ds, y, 5, 14, MAP{});

-- 2. Model forecast per fold
CREATE OR REPLACE TABLE bt AS
SELECT * FROM ts_cv_forecast_by('folds', product_id, ds, y, 'AutoETS',
    MAP{'seasonal_period': '7'});

-- 3. Per-series metrics
SELECT product_id,
    ts_mae(LIST(y ORDER BY ds), LIST(yhat ORDER BY ds)) AS mae,
    ts_rmse(LIST(y ORDER BY ds), LIST(yhat ORDER BY ds)) AS rmse,
    ts_coverage(LIST(y ORDER BY ds), LIST(yhat_lower ORDER BY ds), LIST(yhat_upper ORDER BY ds)) AS cov
FROM bt GROUP BY product_id;

-- 4. Conformalise → guaranteed 90 % coverage
CREATE OR REPLACE TABLE calib AS
SELECT * FROM ts_conformal_calibrate('bt', y, yhat, {alpha: 0.1});

-- 5. Apply calibration to new forecasts
CREATE OR REPLACE TABLE new_fcst AS
SELECT * FROM ts_forecast_by('clean', product_id, ds, y, 'AutoETS', 14, '1d',
    MAP{'seasonal_period': '7'});

SELECT * FROM ts_conformal_apply_by('new_fcst', product_id, yhat,
    (SELECT conformity_score FROM calib));

See also: anofox-forecast-data-prep (clean input required by ts_cv_folds_by), anofox-forecast-detection (detect seasonal_period before backtesting), anofox-forecast-models (any model string usable in ts_cv_forecast_by).

Reference docs:

• docs/api/08-cross-validation.md
• docs/api/09-evaluation-metrics.md
• docs/api/11-conformal-prediction.md