On the validity of Akaike’s identity for random fields

Carsten Jentsch and Marco Meyer

Journal of Econometrics, 2021, vol. 222, issue 1, 676-687

Abstract: For univariate stationary and centered time series (Xt)t∈Z, Akaike’s identity links the inverse of the Yule–Walker matrix Γ(p)=E(XX′), where X=(Xt−1,…,Xt−p)′, to the corresponding finite predictor coefficients. It reads as a Cholesky-type factorization Γ(p)−1=L(p)′Σ(p)−1L(p), where L(p) is lower-triangular and Σ(p)−1 is diagonal. Whereas this Cholesky-type factorization exists whenever Γ(p) is positive definite, Akaike derived a meaningful interpretation of L(p) and Σ(p)−1 in terms of finite predictor coefficients. It is useful in many applications and is particularly crucial to derive asymptotic theory for Berk’s spectral density estimator.

Keywords: Finite predictor coefficients; L2-projection; Random fields; Yule–Walker equations (search for similar items in EconPapers)
JEL-codes: C14 C18 C21 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:222:y:2021:i:1:p:676-687

DOI: 10.1016/j.jeconom.2020.04.044

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