IDEAS home Printed from https://ideas.repec.org/a/spr/sistpr/v17y2014i3p267-282.html
   My bibliography  Save this article

AIC type statistics for discretely observed ergodic diffusion processes

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11203-014-9101-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11203-014-9101-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kengo Kamatani & Masayuki Uchida, 2015. "Hybrid multi-step estimators for stochastic differential equations based on sampled data," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 177-204, July.
    2. Shoichi Eguchi & Hiroki Masuda, 2019. "Data driven time scale in Gaussian quasi-likelihood inference," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 383-430, October.
    3. Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for small diffusion processes based on reduced data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 745-773, October.
    4. 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.
    5. Masayuki Uchida & Nakahiro Yoshida, 2014. "Adaptive Bayes type estimators of ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 181-219, July.
    6. Nakahiro Yoshida, 2022. "Quasi-likelihood analysis and its applications," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 43-60, April.
    7. Clinet, Simon & Yoshida, Nakahiro, 2017. "Statistical inference for ergodic point processes and application to Limit Order Book," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1800-1839.
    8. Uchida, Masayuki & Yoshida, Nakahiro, 2013. "Quasi likelihood analysis of volatility and nondegeneracy of statistical random field," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2851-2876.
    9. Yoshida, Nakahiro, 2013. "Martingale expansion in mixed normal limit," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 887-933.
    10. Yusuke Shimizu, 2017. "Moment convergence of regularized least-squares estimator for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1141-1154, October.
    11. 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.
    12. Shogo H. Nakakita & Yusuke Kaino & Masayuki Uchida, 2021. "Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 177-225, February.
    13. Jean Jacod & Michael Sørensen, 2018. "A review of asymptotic theory of estimating functions," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 415-434, July.
    14. Yuji Sakamoto & Nakahiro Yoshida, 2009. "Third-order asymptotic expansion of M-estimators for diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 629-661, September.
    15. Masuda, Hiroki, 2007. "Ergodicity and exponential [beta]-mixing bounds for multidimensional diffusions with jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 35-56, January.
    16. Yoshida, Nakahiro, 2023. "Asymptotic expansion and estimates of Wiener functionals," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 176-248.
    17. Masatoshi Goda, 2023. "Sparse estimation for generalized exponential marked Hawkes process," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 139-169, April.
    18. Masayuki Uchida & Nakahiro Yoshida, 2004. "Information Criteria for Small Diffusions via the Theory of Malliavin–Watanabe," Statistical Inference for Stochastic Processes, Springer, vol. 7(1), pages 35-67, March.
    19. Kou Fujimori, 2019. "The Dantzig selector for a linear model of diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 475-498, October.
    20. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2022. "Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 397-430, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sistpr:v:17:y:2014:i:3:p:267-282. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.