Time Series

Ordinary IID resampling destroys serial dependence. Time-series methods create new series while preserving a chosen dependence structure.

Choose the model you can defend

Method	Dependence model	Parameter
stationary	stationary series, random block lengths	mean_block=
mbb	contiguous fixed-length blocks	block_length=
cbb	fixed blocks with circular wraparound	block_length=
tapered	fixed blocks with softened boundaries	block_length=, taper=
sieve	autoregressive approximation	ar_order=
wild	heteroscedastic residual structure	fitted=, distribution=

Block-bootstrap example

import numpy as np
from bootstrapx import bootstrap

rng = np.random.default_rng(0)
y = np.zeros(500)
for t in range(1, len(y)):
    y[t] = 0.7 * y[t - 1] + rng.normal()

result = bootstrap(
    y,
    np.mean,
    method="stationary",
    mean_block=15,
    n_resamples=4999,
    random_state=42,
)
print(result.confidence_interval)

The method assumes the observed sequence is ordered correctly and a stationary dependence model is scientifically plausible. It does not detect trends, seasonality, structural breaks, or leakage for you.

Check block-length sensitivity

There is no universal block length. Compare a small range and report the choice when endpoints matter:

for mean_block in (10, 15, 20, 30):
    result = bootstrap(
        y,
        np.mean,
        method="stationary",
        mean_block=mean_block,
        n_resamples=4999,
        random_state=42,
    )
    ci = result.confidence_interval
    print(mean_block, ci.low, ci.high)

Large changes are evidence that the inference depends strongly on an unresolved modeling choice; they are not a reason to select the narrowest interval.

For repeated block-bootstrap runs, see the optional Numba acceleration.