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AIC type statistics for discretely observed ergodic diffusion processes

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  • Takayuki Fujii
  • Masayuki Uchida

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. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • Takayuki Fujii & Masayuki Uchida, 2014. "AIC type statistics for discretely observed ergodic diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 17(3), pages 267-282, October.
    • Handle: RePEc:spr:sistpr:v:17:y:2014:i:3:p:267-282
    DOI: 10.1007/s11203-014-9101-x
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    References listed on IDEAS

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    1. Nakahiro Yoshida, 2011. "Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 431-479, June.
    2. Masayuki Uchida, 2010. "Contrast-based information criterion for ergodic diffusion processes from discrete observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 161-187, February.
    3. Masayuki Uchida & Nakahiro Yoshida, 2001. "Information Criteria in Model Selection for Mixing Processes," Statistical Inference for Stochastic Processes, Springer, vol. 4(1), pages 73-98, January.
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    Cited by:

    1. Shoichi Eguchi & Yuma Uehara, 2021. "Schwartz‐type model selection for ergodic stochastic differential equation models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 950-968, September.
    2. Yusuke Kaino & Shogo H. Nakakita & Masayuki Uchida, 2020. "Hybrid estimation for ergodic diffusion processes based on noisy discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 171-198, April.
    3. Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for stochastic differential equations from reduced data," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 435-454, July.

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