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.

Measured proof	Result	Scope and receipt
Four shared methods against arch.apply	Faster in all 16 measured cells; 4.7x to 33x on the longer series	IID, moving, circular, stationary; mean statistic; n=2,000, B=999 or 10,000; optional compiled reducer on eight cores; settled-min receipt and methodology.
Ten thousand series, one fused pass	220x faster than a per-series reduce loop	Time, B=1,000, n=200, MovingBlock(20) mean; panel benchmark.
Same panel, without the resampled-path tensor	141x less peak memory than materialize-then-reduce	Memory, same workload; materialization is a different baseline from the time comparison; panel benchmark.

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

Capability	In tsbootstrap	Comparison boundary
Shared observation bootstrap methods	IID, moving block, circular block, stationary block	All four are also in arch.bootstrap and are covered by the measured comparison.
Additional resampling	Non-overlapping and tapered blocks; recursive AR, ARIMA, VAR and sieve bootstraps; wild and block-wild innovations	Outside the four-method head-to-head benchmark.
Uncertainty workflows	Bootstrap confidence intervals, AR forecast bands, EnbPI and adaptive conformal calibration	These workflows are not part of the speed comparison.
Large panels and tooling	Ragged-panel reducers, method diagnostics and metadata, optional read-only MCP tools	The panel benchmark compares three tsbootstrap workflows, not arch.

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=10000
IID	15x	19x	4.7x	8.6x
MovingBlock	38x	61x	9.8x	26x
CircularBlock	41x	66x	13x	33x
StationaryBlock	19x	24x	6.8x	12x

Read these as sustained gains of roughly 4.7x to 33x on the larger n=2000 workloads; the very large small-n multiples come from arch's per-replicate Python callback in bs.apply, whose overhead dominates its runtime when each resample is cheap, so they measure that overhead as much as the compiled kernel.

The compiled reduce fuses index build, gather, and reduction into one pass, so peak memory stays flat in the number of replicates: at n=2000 the streaming reduce holds about 20 MB at B=50000 where materializing every replicate takes about 1.94 GB (roughly 96x lighter), from benchmarks/results/membench_2026-07-04.json. The multivariate and ragged-panel reduce paths have no equivalent in arch. The panel reduce (bootstrap_reduce_panel) returns the full per-series bootstrap distribution of the statistic (n_bootstraps x num_series), so quantile and tail workflows on an estimator are served directly with no replicate tensor. Use the materializing path only when the workflow consumes the resampled paths themselves. Full methodology, single-thread behavior, and the reproduction script are in benchmarks/README.md.

# install the compiled backend
uv add "tsbootstrap[accel]"
# or
pip install "tsbootstrap[accel]"

📚 Articles

Deep dives on the statistics and engineering behind the library, with worked examples and animations:

• Your bootstrap is lying to you: why the ordinary i.i.d. bootstrap collapses on autocorrelated data (a nominal 90% interval that covers 49.6% of the time) and how block resampling repairs it.
• When your errors aren't equal: the wild bootstrap for heteroskedastic errors, and what a block-wild variant preserves.
• Count the bytes, not the FLOPs: the memory-wall engineering behind the compiled backend, with hardware-counter receipts.
• Ten thousand series, one pass: the panel benchmark, its separate time and memory baselines, and the ragged-panel design.

🧩 Modules

Package layout:

Area	Module(s)	Role
Public API	api.py, methods.py, results.py, errors.py, diagnostics.py	the bootstrap() entry point, typed method specs, structured results, error taxonomy, and diagnose()
Infrastructure	rng.py, validation.py, dispatch.py, metadata.py	deterministic RNG contract, input coercion (incl. the narwhals DataFrame boundary), spec to executor dispatch, method metadata
Block methods	block/	vectorized index kernels, true Politis-Romano stationary, energy-normalized tapering, PWSD block length, OOB primitives
Model methods	model/, engines/	model fitting, stability guards, and recursive AR/ARMA/VAR simulation
Uncertainty quantification	uq/	classical confidence intervals (percentile, basic, studentized, BCa) via conf_int, EnbPI prediction intervals, the static / sliding-window / ACI / AgACI / NexCP calibrators, and AR forecast intervals
Ecosystem	adapters/	skbase / sktime estimator classes over the functional core

🗺 Roadmap

The full, living roadmap is issue #181. Highlights:

Near term:

• Out-of-sample forecast intervals for ARIMA and VAR (currently AR-only).

Candidate methods (good first issues):

• Generalized block (#104), local block (#105), and frequency-domain (#107) bootstraps.
• A GARCH / volatility residual bootstrap, and the smooth-kernel dependent-wild bootstrap.

Distributed execution (Dask / Spark / Ray), an async layer, and a string-keyed factory were considered and deliberately left out. The library is a CPU-bound, single-process toolkit.

🤝 Contributing

See our good first issues for getting started.

Developer setup

1. Fork the tsbootstrap repository

2. Clone the fork to local:

git clone https://github.com/astrogilda/tsbootstrap

3. In the local repository root, sync the locked development environment with uv:

uv sync --extra dev

4. uv creates an isolated virtual environment from uv.lock and editable-installs the package, so changes to the package are reflected in your environment automatically. Run tools through the environment with uv run (for example uv run pytest).

5. Install the pre-commit hooks:

uv run pre-commit install

The hooks run ruff, formatting, and the other code-quality checks on each commit.

Verifying the Installation

Verify the installation:

python -c "import tsbootstrap; print(tsbootstrap.__version__)"

This prints the installed version.

Contribution workflow

1. Create a new branch with a descriptive name (e.g., new-feature-branch or bugfix-issue-123).

git checkout -b new-feature-branch

2. Make changes to the project's codebase.
3. Commit your changes to your local branch with a clear commit message that explains the changes you've made.

git commit -m 'Implemented new feature.'

4. Push your changes to your forked repository on GitHub using the following command

git push origin new-feature-branch

5. Create a new pull request to the original project repository. In the pull request, describe the changes you've made and why they're necessary.

🧪 Running Tests

To run all tests, in your developer environment, run:

uv run pytest tests/

That runs in a single process. Add the pytest-xdist flags CI uses to run the suite in parallel, which is several times faster on a multi-core machine:

uv run pytest tests/ -n auto --dist loadscope --max-worker-restart 3

The sktime adapter classes can be validated with sktime's estimator checks:

from sktime.utils import check_estimator
from tsbootstrap.adapters import MovingBlockBootstrap

check_estimator(MovingBlockBootstrap)

Contribution guide

See CONTRIBUTING.md for details.

📄 License

This project is licensed under the ℹ️ MIT License. See the LICENSE file for additional info.

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👏 Contributors

Contributors:

This project follows the all-contributors specification. Contributions of any kind welcome!

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📍 Time Series Bootstrapping

tsbootstrap implements bootstrap methods for univariate and multivariate time series. Block methods resample nearby observations together; model-based methods simulate new paths from fitted dynamics.

Overview

An i.i.d. bootstrap breaks serial dependence by resampling individual observations. Block and model-based methods retain aspects of dependence under their stated assumptions. Interval coverage still depends on the data regime, the statistic, and the method choice; see the uncertainty guide.

Bootstrapping methodology

tsbootstrap resamples either the observations directly (i.i.d. and block methods) or the innovations of a fitted model (residual and sieve methods), respecting the chronological order and dependence structure of the data.

Block bootstrap

Block methods resample blocks of consecutive observations to preserve short-range dependence. The block length defaults to the automatic Politis-White (2004) selection.

• Moving block (MovingBlock): overlapping fixed-length blocks (Kunsch 1989).
• Circular block (CircularBlock): blocks wrap around the series end (Politis-Romano 1992).
• Stationary block (StationaryBlock): geometric block lengths with independent uniform restart points (Politis-Romano 1994).
• Non-overlapping block (NonOverlappingBlock): disjoint blocks (Carlstein 1986).
• Tapered block (TaperedBlock(window=...)): blocks weighted by an energy-normalized window (Bartlett, Blackman, Hamming, Hann, or Tukey; Paparoditis-Politis 2001).

Residual bootstrap

For dependent data with a good model fit, ResidualBootstrap(model=...) regenerates the series recursively from the fitted dynamics and resampled, centered innovations (not fitted + residuals). Supported models: AR, ARIMA, and VAR (multivariate). A non-stationary fit is refused (or skipped, per stability_policy) rather than producing explosive paths.

Sieve bootstrap

SieveAR selects an autoregressive order on the original series, then runs the AR recursion; suited to data with autoregressive structure.

Innovation resamplers

The innovation argument on ResidualBootstrap and SieveAR controls how the centered residuals are resampled. It defaults to IID (uniform resampling); two wild resamplers relax the exchangeability that assumes.

• Wild (Wild(distribution=...)): multiplies each residual in place by a mean-zero, unit-variance draw (e*_t = v_t * e_hat_t), keeping its time position and magnitude, so it stays valid under conditional heteroskedasticity (Wu 1986; Liu 1988; Rademacher default per Davidson-Flachaire 2008).
• Block-wild (BlockWild(block_length=...)): holds one multiplier constant across each block of residuals, so serial dependence left by a misspecified mean survives the resampling (piecewise-constant dependent wild bootstrap, Shao 2010).

Both require the host model's burn_in=0 and initial="fixed" defaults so the multipliers align one-to-one with the residuals.

Deferred to a later release

Markov resampling, the distribution bootstrap, GARCH/volatility models, and frequency-domain / seasonal block methods are planned for a future version. The statistic-preserving method has been removed.