tsbootstrap

Fast, dependence-aware uncertainty for one time series or ten thousand. Block, model-based, and wild resampling; confidence and prediction intervals; fused statistics without replicate tensors. Explore the documentation .

tsbootstrap makes the sampling design explicit through typed method specifications, assumption metadata, and replayable run metadata. Its optional compiled reducers calculate statistics while generating resamples, and its panel API supports unequal-length series.

Read the engineering behind these results in Count the bytes, not the FLOPs and Ten thousand series, one pass.

The speed numbers describe the compiled named-statistic reduce path; the default NumPy backend, arbitrary Python statistics, materialized samples, and single-thread execution have distinct performance profiles. See the full benchmark grid for those paths. The arch bootstrap module also offers independent-samples bootstrapping, and the broader arch package includes econometric tools. Neither is covered by this four-method comparison.

📒 Table of Contents

1. 🚀 Getting Started
2. ⚡ Performance
3. 📚 Articles
4. 🧩 Modules
5. 🗺 Roadmap
6. 🤝 Contributing
7. 📄 License
8. 📍 Time Series Bootstrapping Methods intro
9. 👏 Contributors

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🚀 Getting Started

🎮 Using tsbootstrap

tsbootstrap exposes one typed entry point, bootstrap, configured with a method specification. The same call works for every method.

import numpy as np

from tsbootstrap import bootstrap, MovingBlock

rng = np.random.default_rng(0) innovations = rng.standard_normal(200) x = np.empty_like(innovations) x[0] = innovations[0] for t in range(1, len(x)): x[t] = 0.6 * x[t - 1] + innovations[t]

result = bootstrap(x, method=MovingBlock(block_length="auto"), n_bootstraps=999, random_state=0)

samples = result.values() # (n_bootstraps, n) resampled series oob = result.get_oob_mask() # (n_bootstraps, n) out-of-bag mask

Choose a method spec for the structure you need (block lengths default to the automatic Politis-White selection):

from tsbootstrap import StationaryBlock, ResidualBootstrap, SieveAR, AR, ARIMA, diagnose

bootstrap(x, method=StationaryBlock(avg_block_length="auto"))

recursive model-based bootstraps; only ARIMA needs the models extra

bootstrap(x, method=ResidualBootstrap(model=AR(order=2))) bootstrap(x, method=ResidualBootstrap(model=ARIMA(order=(1, 1, 1)))) bootstrap(x, method=SieveAR())

not sure which fits? ask:

print(diagnose(x).recommended_methods)

Inputs can be NumPy arrays, lists, or pandas / Polars DataFrames and Series. The result is a BootstrapResult carrying the samples, provenance metadata, and out-of-bag / in-bag primitives. For the sktime ecosystem, the same methods are also available as estimator classes (MovingBlockBootstrap, ARResidualBootstrap, SieveBootstrap, and the rest) under tsbootstrap.adapters.

Uncertainty quantification

The uq layer turns resampled series into prediction intervals. forecast_intervals gives forward forecast bands for an AR model; EnbPIEnsemble produces out-of-bag prediction intervals for an sklearn-style regressor, with calibrators for stationary, volatility-clustered, and drifting data (static, sliding window, and the adaptive ACI, AgACI, and NexCP schemes); and bootstrap_reduce streams a per-replicate statistic so calibration scales to large replicate counts without holding every path in memory.

from tsbootstrap import AR, forecast_intervals

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

For a confidence interval on a statistic of one series, conf_int runs the bootstrap and reads the interval in one call:

from tsbootstrap import IID, conf_int

lower, upper, point = conf_int(x, "mean", method=IID(), kind="bca", alpha=0.1)

The conformal pieces (EnbPIEnsemble and the calibrators) need the uq extra (scikit-learn). The interactive tutorial gallery works through every method on real and synthetic data, including a "which bootstrap should I use?" decision guide.

MCP server

tsbootstrap ships a read-only Model Context Protocol server so an MCP client (an LLM agent, an IDE) can diagnose a short series and compute a bootstrap confidence interval without writing any Python. Run it with no install step:

uvx --from "tsbootstrap[mcp]" tsbootstrap-mcp

It speaks the stdio transport and exposes exactly two read-only tools:

• diagnose_series: serial-dependence and stationarity diagnostics, a recommended Politis-White block length, and the bootstrap methods the server supports for the series.
• bootstrap_confidence_interval: a percentile confidence interval for the mean, median, std, or variance, using an i.i.d. or block bootstrap.

Both tools accept at most 500 observations and run at most 500 replicates. For larger series, model-based methods, or the uncertainty layer, use the library directly in a local script.

📦 Installation

Requires Python 3.10 or higher.

# with uv (recommended):

uv add tsbootstrap # core: i.i.d. and block methods uv add "tsbootstrap[models]" # adds statsmodels for ARIMA

with pip:

pip install tsbootstrap pip install "tsbootstrap[models]"

AR, VAR, and sieve fitting use the core NumPy implementation. ARIMA imports statsmodels lazily and requires the models extra.

⚡ Performance

*Left: speedup of the compiled reduce path over the arch library on the four overlapping methods. Right: peak memory before and after on the two headline reduce workloads (baseline = materialize every path, then reduce). The figure and the table below are generated from the committed benchmark data in benchmarks/results/; regenerate with python benchmarks/plot_launch.py.*

tsbootstrap ships an optional compiled backend (backend="compiled", via the [accel] extra). On the measured mean-reduction workload it is faster than arch.apply for each of the four shared resampling methods. The table below is the speedup of the streaming reduce path over arch.apply on an 8-core CPU (higher is better), read from benchmarks/results/vs_arch_ccx33_2026-07-11_settled.json (the settled-min statistic; methodology in benchmarks/README.md).

| Method | n=200, B=999 | n=200, B=10000 | n=2000, B=999 | n=2000, B=