Uncertainty quantification guide

The bootstrap produces resampled series; the uq layer turns those into prediction intervals. There are two paths, plus a family of calibrators that control how interval width is computed.

The coverage here is approximate or asymptotic under temporal dependence, not finite-sample distribution-free. Read the per-method note before relying on a number.

Regression prediction intervals: EnbPI

EnbPIEnsemble is a fit/predict object for an sklearn-style regressor. It bootstraps the row indices, fits a clone of the estimator on each resample, and uses the out-of-bag ensemble residuals as the nonconformity scores (Xu and Xie 2021). Because the clones are retained, it can produce intervals for new X as well as in-sample.

from sklearn.linear_model import LinearRegression
from tsbootstrap import EnbPIEnsemble, MovingBlock

ens = EnbPIEnsemble().fit(
    LinearRegression(), X, y, method=MovingBlock(block_length=10),
    n_bootstraps=100, random_state=0,
)
lower, upper, point = ens.predict_interval(alpha=0.1, calibrator="sliding_window")

EnbPI requires an observation-resampling method (the block or IID families); recursive model methods have no out-of-bag set and are rejected. The thin wrappers enbpi_intervals() and fit_predict_oob() cover the simple in-sample, static-width path.

Calibrators: choosing the half-width

The interval half-width is computed from the residual buffer by a calibrator, selected with predict_interval(calibrator=...):

static (static_halfwidths()): one global quantile, the same width everywhere. Use when residuals are stationary.
sliding_window (sliding_window_halfwidths()): a rolling quantile over recent residuals. Use under volatility clustering, where width should track local scale.
aci (aci_halfwidths()): adaptive conformal inference (Gibbs and Candes 2021). Adjusts the target level online from realized coverage errors, so long-run coverage holds under distribution shift. Needs the realized scores and a learning rate.
nexcp (nexcp_quantile()): nonexchangeable conformal (Barber et al. 2023). A recency-weighted quantile, so recent residuals count more; carries a finite-sample guarantee minus a drift-dependent gap.

Forecast intervals

forecast_intervals() simulates a fitted model forward over a horizon and reads per-step empirical quantiles.

from tsbootstrap import AR, forecast_intervals

lower, upper, median = forecast_intervals(
    x, model=AR(order=2), horizon=12, alpha=0.1, random_state=0,
)

It supports the AR model only in this release; ARIMA and VAR forecast intervals are planned for a later release.

Scaling calibration: bootstrap_reduce

For very large numbers of replicates, bootstrap_reduce() evaluates a per-replicate statistic inside the chunk loop and keeps only the reduced values, so peak memory stays proportional to the number of replicates rather than the full path size. It enables large-sample conformal calibration without materializing every path.