Generalized information criterion

Masanobu Taniguchi, Junichi Hirukawa

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    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 languageEnglish
    Pages (from-to)287-297
    Number of pages11
    JournalJournal of Time Series Analysis
    Volume33
    Issue number2
    DOIs
    Publication statusPublished - 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

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