期刊
JOURNAL OF TIME SERIES ANALYSIS
卷 33, 期 2, 页码 287-297出版社
WILEY-BLACKWELL
DOI: 10.1111/j.1467-9892.2011.00759.x
关键词
AIC; information criterion; asymptotic theory; spectral distribution; model selection; Primary 62M10; 62M99; 62F99; Secondary 62B10
资金
- Grants-in-Aid for Scientific Research [23244011] Funding Source: KAKEN
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 dim 0 = p0. One plausible parametric description for g is , h = (h1, ... ,hK - p0) 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 h is large. This observation seems important. Also numerical studies will be given to confirm the results.
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