[bashtage]

Target 9.1: merge after v9.0.0 is tagged. Closes #617.

Adds arch.bootstrap.LocalBlockBootstrap(block_size, locality, *args, seed=None, **kwargs), the local block bootstrap of Paparoditis and Politis (2002), C. R. Acad. Sci.
Paris, Ser. I 335(11), 959-962, for locally stationary series.

Design:

• Each block's start is drawn uniformly on [max(0, m·b − K), min(n − b, m·b + K)], with K
  the locality in observations (the paper's nB). The blocks are concatenated and
  truncated to n.
• update_indices is vectorised NumPy (independent draws per block), with no compiled
  sampler.
• It subclasses CircularBlockBootstrap. locality is a read-only property like
  block_size, and clone keeps both. _check_sampling requires block_size <= n.
• With K >= n, every start is allowed, which is the moving block bootstrap.
• apply, cov, var, every conf_int method, and seed and state handling work
  unchanged.
• It is not offered in SPA, StepM or MCS. Their null assumes stationarity, and a test
  checks that "local" is rejected there.
• The docs cover the purpose, the reference and the 0-based convention (the paper is
  1-based). The caveats are:
  • BCa's jackknife is heuristic;
  • the studentized interval reuses b and K, and std_err_func is the alternative;
  • choosing b and K is left to the user.

Validation:

• No package implements the method; all 25,424 CRAN packages were searched. The reference
  is an independent base-R implementation of the paper: the indices are identical on 8
  cases, which are stored in the tests.
• A Python loop reference agrees on 20 cases, with both Generator and RandomState draws.
• For a trend plus noise (n = 600, b = 10, K = 40), the standard error of the mean is
  0.0424 against the true 0.0408. The circular block bootstrap gives 0.11-0.12.

Tests:

• test_local_block_bootstrap.py (186): exact support on edge cases; chi-square
  uniformity of the starts; the trend check; clone, seed, state and the read-only
  properties; every conf_int method, including the nested studentized interval; pandas
  and keyword inputs.
• test_validation_local_block_bootstrap.py (232 rows).
• Deliberate bugs are each caught: an exclusive upper end (the prototype's bug), the
  literal 1-based window, no truncation, and clone dropping the locality.
• Fast suite 27,385 passed. The tests pass in random orders and without matplotlib.
  numpydoc lint 0, and the docs build has no new warnings.

Thanks to @yngvem for the proposal and the prototype.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.97%. Comparing base (d2c90b4) to head (207aa90).
⚠️ Report is 6 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #967      +/-   ##
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+ Coverage   98.95%   98.97%   +0.02%     
==========================================
  Files         136      138       +2     
  Lines       30043    30713     +670     
  Branches     2331     2375      +44     
==========================================
+ Hits        29729    30399     +670     
  Misses        256      256              
  Partials       58       58              

Flag	Coverage Δ
adder	98.92% <100.00%> (+0.02%)	⬆️
subtractor	98.92% <100.00%> (+0.02%)	⬆️

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