Enum Criterion 

pub enum Criterion {
    Aic,
    Aicc,
    Bic,
    Hq,
    Fpe,
    Cat,
    Mdl,
}

Penalised-likelihood criteria (all “smaller is better”).

Variants

Aic

Akaike (1973): n log σ̂² + 2k. Not consistent; prediction-efficient (Shibata 1980).

Aicc

Hurvich & Tsai (1989) small-sample correction: AIC + 2K(K+1)/(n-K-1) with K = k + 1 free parameters (the k AR coefficients plus the innovation variance), the convention of forecast::Arima without constant. The series is demeaned before fitting but the mean is not counted (same as R’s ar()).

Bic

Schwarz (1978): n log σ̂² + k log n. Strongly consistent (Hannan 1980).

Hq

Hannan & Quinn (1979): n log σ̂² + 2 c k log log n, c = 1 here. Minimal consistent penalty.

Fpe

Akaike (1969) final prediction error: σ̂² (n+k)/(n-k). Not consistent.

Cat

Parzen (1974, 1977) criterion autoregressive transfer function: CAT(k) = (1/n) Σ_{j=1..k} 1/σ̄²_j − 1/σ̄²_k with the unbiased-adjusted relative variances σ̄²_j = n (σ̂²_j/σ̂²_0) / (n − j) (innovation variance divided by the sample variance, as in the ACF-based recursion Parzen uses), and CAT(0) = −(1 + 1/n). The normalisation makes the value dimensionless and the argmin scale-invariant. Asymptotically equivalent to AIC; not consistent.

Mdl

Rissanen (1978) two-part minimum description length: (n/2) log σ̂² + (k/2) log n. In this AR form every value is exactly BIC/2, so the argmin coincides with BIC’s; included so the benchmark can report it under its own name.

Implementations

impl Criterion

pub const ALL: [Criterion; 7]

pub fn name(self) -> &'static str

pub fn n_params(k: usize) -> usize

Number of free parameters counted by the penalty for an AR(k) fit: the k coefficients plus the innovation variance. For AIC/BIC/HQ the variance term is a constant shift that does not affect the argmin, so they use k directly as in the textbook formulas; AICc’s correction is nonlinear in K, so there it matters.

pub fn value(self, sigma2: &[f64], k: usize, n: usize) -> f64

Criterion value for an AR(k) fit on n observations. sigma2[j] must hold the innovation variance of the AR(j) fit for j = 0..=k; every criterion except CAT reads only sigma2[k], but CAT accumulates over the whole nested path.

Trait Implementations

impl Clone for Criterion

fn clone(&self) -> Criterion

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for Criterion

impl Debug for Criterion

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Eq for Criterion

impl Hash for Criterion

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl PartialEq for Criterion

fn eq(&self, other: &Criterion) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for Criterion