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AIC type statistics for discretely observed ergodic diffusion processes

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Abstract

We consider the model selection problem for ergodic diffusion processes based on sampled data. The adaptive estimators for parameters of drift and diffusion coefficients are used in order to construct Akaike’s information criterion (AIC) type model selection statistics. Asymptotic properties of our proposed criteria are given for three kinds of the adaptive estimators.

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Acknowledgments

The authors wish to thank the referee for valuable comments which led to improvements of an earlier version of this paper. Fujii’s research was supported in part by JSPS KAKENHI Grant Number 25730016. Uchida’s research was partially supported by JSPS KAKENHI Grant Numbers 24300107, 24654024, 25245034, and by Cooperative Research Program of the Institute of Statistical Mathematics.

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Authors and Affiliations

  1. Faculty of Economics, Shiga University, 1-1-1 Banba, Hikone, Shiga,  522-8522, Japan

    Takayuki Fujii

  2. CREST, JST, 1-1-1 Banba, Hikone, Shiga, 522-8522, Japan

    Takayuki Fujii

  3. Graduate School of Engineering Science and Center for the Study of Finance and Insurance, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka,  560-8531, Japan

    Masayuki Uchida

  4. CREST, JST, 1-3 Machikaneyama-cho, Toyonaka, Osaka, 560-8531, Japan

    Masayuki Uchida

Authors
  1. Takayuki Fujii
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  2. Masayuki Uchida
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Correspondence to Takayuki Fujii.

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Fujii, T., Uchida, M. AIC type statistics for discretely observed ergodic diffusion processes. Stat Inference Stoch Process 17, 267–282 (2014). https://doi.org/10.1007/s11203-014-9101-x

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  • DOI: https://doi.org/10.1007/s11203-014-9101-x

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