### Abstract

In this article, we propose a generalized Akaike's information criterion (AIC) (GAIC), which includes the usual AIC as a special case, for general class of stochastic models (i.e. i.i.d., non-i.i.d., time series models etc.). Then we derive the asymptotic distribution of selected order by GAIC, and show that is inconsistent, i.e. (true order). This is the problem of selection by completely specified models. In practice, it is natural to suppose that the true model g would be incompletely specified by uncertain prior information, and be contiguous to a fundamental parametric model with dimθ _{0}=p _{0}. One plausible parametric description for g is , h=(h _{1},...,h _{K}-p _{0})′ where n is the sample size, and the true order is K. Under this setting, we derive the asymptotic distribution of Then it is shown that GAIC has admissible properties for perturbation of models with order of , where the length {norm of matrix}h{norm of matrix} is large. This observation seems important. Also numerical studies will be given to confirm the results.

Original language | English |
---|---|

Pages (from-to) | 287-297 |

Number of pages | 11 |

Journal | Journal of Time Series Analysis |

Volume | 33 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 Mar |

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### Keywords

- AIC
- Asymptotic theory
- Information criterion
- Model selection
- Spectral distribution

### ASJC Scopus subject areas

- Applied Mathematics
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Time Series Analysis*,

*33*(2), 287-297. https://doi.org/10.1111/j.1467-9892.2011.00759.x

**Generalized information criterion.** / Taniguchi, Masanobu; Hirukawa, Junichi.

Research output: Contribution to journal › Article

*Journal of Time Series Analysis*, vol. 33, no. 2, pp. 287-297. https://doi.org/10.1111/j.1467-9892.2011.00759.x

}

TY - JOUR

T1 - Generalized information criterion

AU - Taniguchi, Masanobu

AU - Hirukawa, Junichi

PY - 2012/3

Y1 - 2012/3

N2 - In this article, we propose a generalized Akaike's information criterion (AIC) (GAIC), which includes the usual AIC as a special case, for general class of stochastic models (i.e. i.i.d., non-i.i.d., time series models etc.). Then we derive the asymptotic distribution of selected order by GAIC, and show that is inconsistent, i.e. (true order). This is the problem of selection by completely specified models. In practice, it is natural to suppose that the true model g would be incompletely specified by uncertain prior information, and be contiguous to a fundamental parametric model with dimθ 0=p 0. One plausible parametric description for g is , h=(h 1,...,h K-p 0)′ where n is the sample size, and the true order is K. Under this setting, we derive the asymptotic distribution of Then it is shown that GAIC has admissible properties for perturbation of models with order of , where the length {norm of matrix}h{norm of matrix} is large. This observation seems important. Also numerical studies will be given to confirm the results.

AB - In this article, we propose a generalized Akaike's information criterion (AIC) (GAIC), which includes the usual AIC as a special case, for general class of stochastic models (i.e. i.i.d., non-i.i.d., time series models etc.). Then we derive the asymptotic distribution of selected order by GAIC, and show that is inconsistent, i.e. (true order). This is the problem of selection by completely specified models. In practice, it is natural to suppose that the true model g would be incompletely specified by uncertain prior information, and be contiguous to a fundamental parametric model with dimθ 0=p 0. One plausible parametric description for g is , h=(h 1,...,h K-p 0)′ where n is the sample size, and the true order is K. Under this setting, we derive the asymptotic distribution of Then it is shown that GAIC has admissible properties for perturbation of models with order of , where the length {norm of matrix}h{norm of matrix} is large. This observation seems important. Also numerical studies will be given to confirm the results.

KW - AIC

KW - Asymptotic theory

KW - Information criterion

KW - Model selection

KW - Spectral distribution

UR - http://www.scopus.com/inward/record.url?scp=84858002747&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858002747&partnerID=8YFLogxK

U2 - 10.1111/j.1467-9892.2011.00759.x

DO - 10.1111/j.1467-9892.2011.00759.x

M3 - Article

VL - 33

SP - 287

EP - 297

JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

SN - 0143-9782

IS - 2

ER -