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Akaike’s information criterion (AIC) is proposed for evaluating statistical models constructed by the maximum likelihood estimators under the situation where the parametric models contain the true mod...el. In order to obtain AIC, it suffices to get a log likelihood function and the maximum likelihood estimator. However, we can not generally derive AIC for discretely observed diffusion processes since the transition densities of diffusion processes do not commonly have explicit forms. This paper presents AIC type of information criterion for discretely observed ergodic diffusion processes. The information criterion is constructed by using an approximate log likelihood function and an asymptotically efficient estimator. The approximate log likelihood function is based on a result of Dacunha-Castelle and Florens-Zmirou (1986). The asymptotically efficient estimator is derived from a contrast function based on a locally Gaussian approximation.続きを見る
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