tsorder

Order selection for time-series models — classical information criteria and Fine–Hwang threshold estimators with pluggable statistics — in a dependency-free Rust core with R and Python bindings (bindings: planned).

Site & API reference: https://castlaboratory.github.io/tsorder/

tsorder/
├── crates/tsorder-core/   Rust core (dependency-free)
├── bindings/r/            R package (extendr, pkgdown) — planned
├── bindings/python/       Python package (PyO3/maturin) — planned
├── benchmark/             benchmark runner and (future) results
└── site/                  landing page; rustdoc is published under /api by CI

Idea in one paragraph

Fine & Hwang (1979) proved the first consistent estimator of system order: fit a model whose memory p_n grows with n, zero every coefficient below a vanishing threshold η_n, and report the last surviving lag. It needs no likelihood, no Gaussianity and no maximum order. It was never studied empirically. We found that the original threshold is not scale-invariant and degrades with n, that studentizing fixes it, that the PACF is the natural self-studentized statistic for AR (matching BIC, and beating it on subset AR in small samples), and that the same recipe extends to MA (Bartlett-studentized ACF) and — in principle, calibration still open — to ARMA via canonical correlations. For the AR case the rigorous theory (Gumbel-calibrated bands over a growing Yule–Walker fit, consistent order selection) is Jirak (2012, Ann. Statist.); tsorder builds on it rather than competing with it. tsorder packages all of this next to AIC/AICc/BIC/HQ/FPE so the two families can be compared on equal footing.

Quick start (Rust)

use tsorder_core::*;

let x: Vec<f64> = /* your series */;

// Classical
let bic = ic_order(&x, Criterion::Bic, None)?;
println!("BIC order = {}", bic.order);

// Fine–Hwang with the recommended statistic (PACF) and threshold
let fh = fh_order(&x, FhConfig::default())?;
println!("FH order = {} (p_n = {}, tau = {:.2})", fh.order, fh.p_n, fh.tau);

// MA order via Bartlett-studentized ACF
let ma = fh_order(&x, FhConfig { statistic: Statistic::AcfBartlett, ..Default::default() })?;

// Ensemble
let e = ensemble_order(&x, &[
    FhConfig { statistic: Statistic::Pacf, ..Default::default() },
    FhConfig { statistic: Statistic::LongArOls, ..Default::default() },
], EnsembleRule::Majority)?;

Where things stand (2026-10-23)

• Core: AIC/AICc/BIC/HQ/FPE/CAT/MDL over Yule–Walker, Burg or conditional-OLS fits (IcMethod); Fine–Hwang thresholding with Pacf, LongArYw, LongArOls, Acf, AcfBartlett, InversePacf (Cleveland's inverse ACF route), JirakBand (exact Jirak-2012 studentization) and the experimental PacfRobust (Ma–Genton Q_n autocorrelations, 25 % breakdown); thresholds BicLike, Lil, MaxOfK, Gumbel, Fixed; memory ⌈2 log n⌉ (the default, picked by the benchmark) or ⌊n^0.4⌋; autocovariance by FFT for large lags; the Q_n scale estimator (O(n log n), matches R's robustbase::Qn); a sim feature with the benchmark's ARMA generator (t innovations, outliers, observation noise); McMillan-degree estimators: svc_order (Bauer's 2001 SVC via past×future canonical correlations, his Table 1 reproduced as a regression test), hankel_svt_order (calibrated singular-value thresholding) and hankel_rank_order (Robin–Smith's rank test on the autocovariance Hankel, weighted-χ² null by exact Imhof inversion, vanishing level); ARMA (p, q) identification by eacf (Tsay–Tiao's table, matching R's TSA::eacf digit for digit, with an automated triangle-vertex reading) and hannan_rissanen (stages 1–2). Clippy-clean, no dependencies, MSRV 1.81.
• Theory positioning: AR thresholding is Jirak (2012); canonical correlations with growing window is Bauer (2001); Hankel rank tests are Robin & Smith (2000) and Camba-Méndez & Kapetanios (2001). tsorder implements all of them under one umbrella; the open questions it targets are MA, robustness and Bauer's calibration problem.
• Pre-alpha. The API will still change.

License

MIT. Authors: André Leite, Raydonal Ospina, Cristiano Ferraz, Hugo Vasconcelos, Diogo Bezerra (CASTLab/UFPE) and Paulo Renato Alves Firmino, with Claude. See CITATION.cff for how to cite.