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Conditional minimum density power divergence estimator for self-exciting integer-valued threshold autoregressive models

Author

Listed:
  • Mingyu Sun

    (Changchun University of Technology)

  • Kai Yang

    (Changchun University of Technology)

  • Ang Li

    (Changchun University of Technology)

Abstract

To overcome the sensitivity of maximum likelihood estimation to outliers in integer-valued time series of counts, we develop a conditional version of minimum density power divergence estimator by introducing the structure of the loss function of the original minimum density power divergence estimator. The properties of the proposed estimator, including the strong consistency and asymptotic normality, are obtained. Some simulation studies are conducted to show the performances of the conditional minimum density power divergence estimator. Finally, an application to the quarterly earthquake data is provided and prove that when outliers exist in data set, the proposed estimator has a better performance than the conditional maximum likelihood estimator, showing robustness property.

Suggested Citation

  • Mingyu Sun & Kai Yang & Ang Li, 2025. "Conditional minimum density power divergence estimator for self-exciting integer-valued threshold autoregressive models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(1), pages 198-234, March.
    • Handle: RePEc:spr:testjl:v:34:y:2025:i:1:d:10.1007_s11749-024-00956-4
    DOI: 10.1007/s11749-024-00956-4
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    References listed on IDEAS

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    12. Kai Yang & Yiwei Zhao & Han Li & Dehui Wang, 2023. "On bivariate threshold Poisson integer-valued autoregressive processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 931-963, November.
    13. Han Li & Kai Yang & Dehui Wang, 2017. "Quasi-likelihood inference for self-exciting threshold integer-valued autoregressive processes," Computational Statistics, Springer, vol. 32(4), pages 1597-1620, December.
    14. Alfio Marazzi & Marina Valdora & Victor Yohai & Michael Amiguet, 2019. "A robust conditional maximum likelihood estimator for generalized linear models with a dispersion parameter," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 223-241, March.
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