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Hybrid estimators for stochastic differential equations from reduced data

Author

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  • Yusuke Kaino

    (Osaka University)

  • Masayuki Uchida

    (Osaka University
    Osaka University)

Abstract

We treat parametric inference for unknown parameters of stochastic differential equations from discrete observations from the viewpoint of computational cost. Following Kamatani et al. (Bull Inf Cybern 48:19–35, 2016) and Kaino and Uchida (Hybrid estimators for ergodic diffusion processes from thinned data, 2018), we present the asymptotic results of the multi-step estimators with the initial Bayes type estimators for both ergodic and non-ergodic diffusion type processes. The initial Bayes type estimators are constructed by means of both the reduced data and the thinned data obtained from the full data. Some examples and simulation results are also given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:2:d:10.1007_s11203-018-9184-x
    DOI: 10.1007/s11203-018-9184-x
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Kutoyants, Yu.A., 2017. "On the multi-step MLE-process for ergodic diffusion," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2243-2261.
    5. 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.
    6. 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.
    7. Yasutaka Shimizu, 2006. "M-Estimation for Discretely Observed Ergodic Diffusion Processes with Infinitely Many Jumps," Statistical Inference for Stochastic Processes, Springer, vol. 9(2), pages 179-225, July.
    8. 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.
    9. Ogihara, Teppei & Yoshida, Nakahiro, 2014. "Quasi-likelihood analysis for nonsynchronously observed diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2954-3008.
    10. Yasutaka Shimizu & Nakahiro Yoshida, 2006. "Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations," Statistical Inference for Stochastic Processes, Springer, vol. 9(3), pages 227-277, October.
    11. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    12. 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.
    13. T. Ogihara & N. Yoshida, 2011. "Quasi-likelihood analysis for the stochastic differential equation with jumps," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 189-229, October.
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    Cited by:

    1. 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.
    2. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2023. "Estimation for change point of discretely observed ergodic diffusion processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 142-183, March.
    3. Tonaki, Yozo & Uchida, Masayuki, 2023. "Change point inference in ergodic diffusion processes based on high frequency data," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 1-39.

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