- ReconciledCovariance now takes the base error covariance and returns
P Sigma P^T; the old S A^-1 S^T form was only valid when W equals it.
- RecSpdInverse reports the ridge the normal-equation matrix needed.
- Diebold-Mariano p-value from Student t with n-1 degrees of freedom.
- WeightedDistance added: the metric each projection is orthogonal in.
- Recon_Evidence reports the data span, a per-origin guarantee table and
how far the realised outcome sits from coherent.
- Last-value forecast is no longer described as a random walk.
- README brought in line with the revised article.
CReconciler projects a set of incoherent forecasts onto the column space of a
summing matrix, which cannot increase total squared error under the orthogonal
projection. The engine knows nothing about markets, so the same object serves a
sixty-node temporal hierarchy over twenty-four free hourly returns and a
twenty-one pair currency graph over seven free log prices.
W is never inverted. It is factorised by Cholesky with an escalating ridge, S is
pushed through the same factor, and the only explicit inverse is taken on the
small m x m normal-equation matrix. Five weightings are available, from OLS
through structural and measured WLS to MinT on the sample and Schaefer-Strimmer
shrunk covariances.
Recon_Inspect measures three exact invariants on every run, the last through an
independent projector so it cannot flatter itself. Recon_Evidence walks forward
with residuals entering the error store only after scoring, and compares loss
differentials with a Diebold-Mariano test using a Bartlett kernel and the
Harvey-Leybourne-Newbold correction.
