How to Produce Prediction Intervals¶

This guide shows you how to wrap a point forecaster with SplitConformalForecaster to produce calibrated prediction intervals and evaluate their coverage. Use this when you need uncertainty bounds around your forecasts, for example to size safety stock or flag anomalous observations.

Prerequisites¶

• yohou installed (Installation)
• A fitted or unfitted point forecaster (Getting Started)

Try it interactively¶

1. Wrap a Point Forecaster¶

Pass any point forecaster to SplitConformalForecaster. It applies conformal prediction: it holds out a calibration set from the training data and uses conformity scores measured on that set to size the intervals:

from sklearn.linear_model import Ridge
from yohou.point import PointReductionForecaster
from yohou.interval import SplitConformalForecaster
from yohou.datasets import fetch_electricity_demand
from yohou.model_selection import train_test_split

data = fetch_electricity_demand()
y = data.frame

y_train, y_test = train_test_split(y, test_size=48)

point_forecaster = PointReductionForecaster(estimator=Ridge())

interval_forecaster = SplitConformalForecaster(
    point_forecaster=point_forecaster,
)
interval_forecaster.fit(y_train, forecasting_horizon=24, coverage_rates=[0.90])

coverage_rates is set at fit() time. Multiple rates can be requested at once (coverage_rates=[0.80, 0.90, 0.95]).

If coverage is poor, increase calibration_size (default 100) to give the conformal layer more residuals to learn from. Larger values improve calibration but leave less data for fitting the point forecaster.

2. Predict Intervals¶

Call predict_interval to get a DataFrame with lower and upper bound columns for each requested coverage rate:

y_pred = interval_forecaster.predict_interval()
# columns include: nsw__demand_lower_0.9, nsw__demand_upper_0.9, ...

The column naming pattern is {component}_lower_{rate} and {component}_upper_{rate}. For multiple components or coverage rates, one pair of columns is produced per combination.

3. Score Coverage and Sharpness¶

Use EmpiricalCoverage to check whether the intervals contain the true values at the claimed rate, and IntervalScore to penalize both miscoverage and unnecessarily wide intervals:

from yohou.metrics import EmpiricalCoverage, IntervalScore

coverage = EmpiricalCoverage()
coverage.fit(y_train)
print(coverage.score(y_test, y_pred))

sharpness = IntervalScore()
sharpness.fit(y_train)
print(sharpness.score(y_test, y_pred))

A well-calibrated forecaster has empirical coverage close to the nominal rate (e.g., ~0.90 for a 90% interval). IntervalScore rewards narrow intervals and penalizes observations that fall outside the bounds, so lower is better.

4. Forecast Intervals Directly with Reduction¶

When your estimator already produces quantiles or interval bounds (for example a quantile-capable sklearn regressor or a CatBoost MultiQuantile model), you can skip the conformal wrapper and use IntervalReductionForecaster to fit interval forecasts directly:

from sklearn.linear_model import QuantileRegressor
from yohou.interval import IntervalReductionForecaster

interval_forecaster = IntervalReductionForecaster(
    estimator=QuantileRegressor(solver="highs"),
)
interval_forecaster.fit(y_train, forecasting_horizon=24, coverage_rates=[0.90])
y_pred = interval_forecaster.predict_interval()

The framework fits one quantile model per requested bound and assembles the interval columns using the same {component}_lower_{rate} / {component}_upper_{rate} naming as the conformal path. Use this route when the estimator's own quantile loss is preferable to post-hoc calibration.

See Also¶

• About Interval Forecasting: conformal theory, coverage guarantees, and when to prefer quantile regression over conformal wrapping
• Combine Forecasters with Ensembles: average or envelope bounds from multiple interval forecasters with VotingIntervalForecaster
• Evaluate Forecast Accuracy: point and interval metric overview
• Visualize and Compare Model Scores: plot coverage and interval width over time
• yohou.interval API reference