### 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 language | English |
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Pages (from-to) | 401-419 |

Number of pages | 19 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 32 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1980 Dec |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistics and Probability
- Mathematics(all)

### Cite this

**On selection of the order of the spectral density model for a stationary process.** / Taniguchi, Masanobu.

Research output: Contribution to journal › Article

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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 -