On selection of the order of the spectral density model for a stationary process

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Let {X(t)} be a stationary process with mean zero and spectral density g(x). We shall use a kth order parametric spectral model f τ(k) (x) for this process. Without Gaussianity we can obtain an estiamte of τ(k), say ĝt(k), by maximizing the quasi-Gaussian likelihood of this model. We can then construct the best linear predictor of X(t), which is computed on the basis of the estimated spectral density f ĝt(k) (x). An asymptotic lower bound of the mean square error of the estimated predictor is obtained. The bound is attained if k is selected by Akaike's information criterion.

Original languageEnglish
Pages (from-to)401-419
Number of pages19
JournalAnnals of the Institute of Statistical Mathematics
Volume32
Issue number1
DOIs
Publication statusPublished - 1980 Dec
Externally publishedYes

Fingerprint

Spectral Density
Stationary Process
Predictors
Akaike Information Criterion
Mean square error
Likelihood
Lower bound
Zero
Model

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)

Cite this

@article{5c990481e0324402b93e64c1d411827a,
title = "On selection of the order of the spectral density model for a stationary process",
abstract = "Let {X(t)} be a stationary process with mean zero and spectral density g(x). We shall use a kth order parametric spectral model f τ(k) (x) for this process. Without Gaussianity we can obtain an estiamte of τ(k), say ĝt(k), by maximizing the quasi-Gaussian likelihood of this model. We can then construct the best linear predictor of X(t), which is computed on the basis of the estimated spectral density f ĝt(k) (x). An asymptotic lower bound of the mean square error of the estimated predictor is obtained. The bound is attained if k is selected by Akaike's information criterion.",
author = "Masanobu Taniguchi",
year = "1980",
month = "12",
doi = "10.1007/BF02480345",
language = "English",
volume = "32",
pages = "401--419",
journal = "Annals of the Institute of Statistical Mathematics",
issn = "0020-3157",
publisher = "Springer Netherlands",
number = "1",

}

TY - JOUR

T1 - On selection of the order of the spectral density model for a stationary process

AU - Taniguchi, Masanobu

PY - 1980/12

Y1 - 1980/12

N2 - Let {X(t)} be a stationary process with mean zero and spectral density g(x). We shall use a kth order parametric spectral model f τ(k) (x) for this process. Without Gaussianity we can obtain an estiamte of τ(k), say ĝt(k), by maximizing the quasi-Gaussian likelihood of this model. We can then construct the best linear predictor of X(t), which is computed on the basis of the estimated spectral density f ĝt(k) (x). An asymptotic lower bound of the mean square error of the estimated predictor is obtained. The bound is attained if k is selected by Akaike's information criterion.

AB - Let {X(t)} be a stationary process with mean zero and spectral density g(x). We shall use a kth order parametric spectral model f τ(k) (x) for this process. Without Gaussianity we can obtain an estiamte of τ(k), say ĝt(k), by maximizing the quasi-Gaussian likelihood of this model. We can then construct the best linear predictor of X(t), which is computed on the basis of the estimated spectral density f ĝt(k) (x). An asymptotic lower bound of the mean square error of the estimated predictor is obtained. The bound is attained if k is selected by Akaike's information criterion.

UR - http://www.scopus.com/inward/record.url?scp=51249182457&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249182457&partnerID=8YFLogxK

U2 - 10.1007/BF02480345

DO - 10.1007/BF02480345

M3 - Article

VL - 32

SP - 401

EP - 419

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 1

ER -