Fast, dependence-aware uncertainty for time series and panels

tsbootstrap provides block, model-based, and wild resampling, confidence and prediction intervals, and fused statistics without resampled-path tensors. Typed method specifications and method metadata make the sampling assumptions explicit. The same library handles a single time series or a ragged panel of unequal-length series.

Measured performance

Workload

Result

Boundary and receipt

Four methods shared with arch

Faster in all 16 measured cells; 4.7x to 33x on the longer series

Compiled mean reduction versus arch.apply on eight cores; n=2,000 and B=999 or 10,000. Receipt and methodology.

10,000 series, B=1,000

220x faster

Fused panel mean reduction versus a per-series reduce loop, on the time axis. Panel receipt.

Same panel

141x less peak memory

Fused panel reduction versus materialize-then-reduce, on the memory axis. This is a different baseline from the time comparison.
Capabilities at a glance

Area

tsbootstrap

Comparison boundary

Shared methods

IID, moving block, circular block, stationary block

All four are in arch.bootstrap.

Further resampling

Non-overlapping and tapered blocks; recursive AR, ARIMA, VAR and sieve; wild and block-wild innovations

Outside the four-method benchmark.

Uncertainty

Bootstrap confidence intervals, AR forecast bands, EnbPI and adaptive conformal calibration

Outside the speed comparison.

Scale and tooling

Ragged-panel reduction, diagnostics, method metadata, read-only MCP tools

The panel baselines are two other tsbootstrap workflows.

The headline speed figures apply to the optional compiled named-statistic reducer. The default NumPy backend, arbitrary Python statistics, materialized samples, and one-thread execution have separate performance profiles. See the full benchmark methodology and the engineering deep dive. arch also supports independent-samples bootstrapping and has econometric functionality beyond its bootstrap module; these are outside this comparison.

Start with bootstrap() and a typed method specification:

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()      # shape (999, 200)
oob     = result.get_oob_mask()  # shape (999, 200) boolean out-of-bag mask

User guide

Tutorials

Articles

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

API reference

Indices and tables