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Quasi-likelihood analysis for nonlinear stochastic processes

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  • Yoshida, Nakahiro

Abstract

A brief overview of the theory of quasi-likelihood analysis (QLA) is given and its usefulness is demonstrated with applications to estimation for a volatility parameter of a semimartingale. A simplified version of the QLA is recalled. The role of non-degeneracy of a key index reflecting identifiability is highlighted. In an application of the QLA, the concept of global jump filters is introduced for precise estimation of the volatility parameter from the data contaminated with jumps.

Suggested Citation

  • Yoshida, Nakahiro, 2025. "Quasi-likelihood analysis for nonlinear stochastic processes," Econometrics and Statistics, Elsevier, vol. 33(C), pages 246-257.
    • Handle: RePEc:eee:ecosta:v:33:y:2025:i:c:p:246-257
    DOI: 10.1016/j.ecosta.2022.04.002
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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. 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.
    3. Ioane Muni Toke & Nakahiro Yoshida, 2019. "Analyzing order flows in limit order books with ratios of Cox-type intensities," Working Papers hal-01799398, HAL.
    4. Haruhiko Inatsugu & Nakahiro Yoshida, 2021. "Global jump filters and quasi-likelihood analysis for volatility," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 555-598, June.
    5. Yuta Umezu & Yusuke Shimizu & Hiroki Masuda & Yoshiyuki Ninomiya, 2019. "AIC for the non-concave penalized likelihood method," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 247-274, April.
    6. 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.
    7. 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.
    8. 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.
    9. Ioane Muni Toke & Nakahiro Yoshida, 2022. "Marked point processes and intensity ratios for limit order book modeling," Post-Print hal-02465428, HAL.
    10. Nakahiro Yoshida, 2022. "Quasi-likelihood analysis and its applications," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 43-60, April.
    11. 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.
    12. 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.
    13. 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.
    14. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    15. Ioane Muni Toke & Nakahiro Yoshida, 2018. "Analyzing order flows in limit order books with ratios of Cox-type intensities," Papers 1805.06682, arXiv.org, revised Aug 2019.
    16. 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.
    17. Yoshida, Nakahiro, 2013. "Martingale expansion in mixed normal limit," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 887-933.
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