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Quasi-Bayesian information criterion of SEM for diffusion processes based on high-frequency data

Author

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  • Shogo Kusano

    (Kumamoto University)

  • Masayuki Uchida

    (The University of Osaka
    The University of Osaka
    CREST, Japan Science and Technology Agency)

Abstract

We deal with a model selection problem for structural equation modeling (SEM) for diffusion processes. Based on the asymptotic expansion of the marginal quasi-log likelihood, we propose two types of quasi-Bayesian information criteria of the SEM. It is shown that the information criteria have model selection consistency. Furthermore, we examine the finite-sample performance of the proposed information criteria by numerical experiments.

Suggested Citation

  • Shogo Kusano & Masayuki Uchida, 2025. "Quasi-Bayesian information criterion of SEM for diffusion processes based on high-frequency data," Statistical Inference for Stochastic Processes, Springer, vol. 28(2), pages 1-28, August.
    • Handle: RePEc:spr:sistpr:v:28:y:2025:i:2:d:10.1007_s11203-025-09327-8
    DOI: 10.1007/s11203-025-09327-8
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    References listed on IDEAS

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    1. Po-Hsien Huang, 2017. "Asymptotics of AIC, BIC, and RMSEA for Model Selection in Structural Equation Modeling," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 407-426, June.
    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. 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.
    4. 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.
    5. Aït-Sahalia, Yacine & Xiu, Dacheng, 2017. "Using principal component analysis to estimate a high dimensional factor model with high-frequency data," Journal of Econometrics, Elsevier, vol. 201(2), pages 384-399.
    6. Shoichi Eguchi & Hiroki Masuda, 2024. "Gaussian quasi-information criteria for ergodic Lévy driven SDE," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(1), pages 111-157, February.
    7. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
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