Expand description
Hannan–Rissanen (1982) recursive ARMA order selection and initial coefficient estimation (their stages 1–2; the efficient third stage is left to the bindings/estimation layer).
Stage 1 fits a long Yule–Walker autoregression (order chosen by AIC, their
practical recommendation) and extracts innovation estimates ε̂. Stage 2
regresses x_t on p lags of x and q lags of ε̂ for every
candidate (p, q) on a common sample and minimises
log σ̃²_{p,q} + (p + q) log T / T (their BIC choice, eq. 1.11).
Their 1983 Biometrika correction (70, p. 303) reports that Theorem 3’s
proof is in error and the stage-2 selection as published can converge to
values larger than (p₀, q₀), typically when the MA polynomial has
zeros near the unit circle; the fix they give — repeating stage 2 with the
residuals ε̃(t) of eq. (1.12) in place of ε̂ — restores convergence and
is applied here by default (erratum_pass). The common-factor degeneracy
makes the stage-2 design matrix singular exactly when p > p₀ and
q > q₀ — such candidates are skipped when the Cholesky fails, which is
itself the paper’s monitoring advice.
Structs§
- HrConfig
- Configuration of
hannan_rissanen. - HrResult
- Output of
hannan_rissanen.
Functions§
- hannan_
rissanen - Hannan–Rissanen stages 1–2: select
(p, q)and return the (consistent, not efficient) stage-2 coefficient estimates.