Module levinson 

Levinson–Durbin recursion: Yule–Walker AR fits of every order 1..=K in O(K²), yielding the PACF and the innovation variance of each order.

This single recursion feeds both estimator families: the information criteria need sigma2[k] for every k; the Fine–Hwang estimators need the PACF (reflection[k]) or the long-AR coefficients (phi_last).

Structs

Levinson

Output of levinson.

Functions

burg_from_series

Burg’s method (Burg 1967; Kay & Marple 1981): each reflection coefficient is chosen to minimise the sum of forward and backward prediction error power, so the fitted AR is always stationary and behaves better than Yule–Walker near the unit circle. Returns the same shape as levinson; sigma2[0] is the biased sample variance and sigma2[k] = sigma2[k-1] (1 - κ_k²).

levinson

Run Levinson–Durbin on autocovariances r[0..=K].

levinson_from_series

Convenience: autocovariance + Levinson in one call.