pub fn hankel_rank_order(
x: &[f64],
config: HankelRankConfig,
) -> Result<HankelRankResult>Expand description
Sequential rank test on the autocovariance Hankel: Robin & Smith’s (2000)
characteristic-root statistic CRT_r = n Σ_{i>r} σ̂_i² (their Wald form,
with identity weighting, so the roots are the squared singular values of
the Hankel), with the null law Σ λ_i χ²₁ of their Theorem 3.2. The
weights are the eigenvalues of (D ⊗ C)' Ω (D ⊗ C) with C, D the
null-space singular vectors; the Hankel’s duplication structure reduces
this to the small matrix (L' W)' (L' W) where Ξ = L L' is the
Bartlett (Gaussian) covariance of the distinct sample autocovariances and
W[ℓ, (a,b)] = Σ_{i+j+1=ℓ} C[i,a] D[j,b]. Stops at the first
non-rejection (Camba-Méndez & Kapetanios’s sequence, started at r = 0);
with RankAlpha::LogDecay the estimate is consistent (Hosoya 1989).
Combining Robin–Smith’s statistic with the autocovariance Hankel is this crate’s assembly of published pieces (CK use Cragg–Donald’s test instead); the lineage is Baram & Porat (1988) → Robin & Smith (2000).