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Filtered likelihood for point processes

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  • Giesecke, Kay
  • Schwenkler, Gustavo

Abstract

Point processes are widely used in finance and economics to model the timing of defaults, market transactions, unemployment spells, births, and a range of other events. We develop and analyze likelihood estimators for the parameters of a marked point process and incompletely observed explanatory factors that influence the arrival intensity and mark distribution. We establish an approximation to the likelihood and analyze the convergence and large-sample properties of the associated estimators. Numerical results illustrate the behavior of our estimators.

Suggested Citation

  • Giesecke, Kay & Schwenkler, Gustavo, 2018. "Filtered likelihood for point processes," Journal of Econometrics, Elsevier, vol. 204(1), pages 33-53.
    • Handle: RePEc:eee:econom:v:204:y:2018:i:1:p:33-53
    DOI: 10.1016/j.jeconom.2017.11.011
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    Cited by:

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    2. Areski Cousin & J'er^ome Lelong & Tom Picard, 2021. "Rating transitions forecasting: a filtering approach," Papers 2109.10567, arXiv.org, revised Jun 2023.
    3. Azizpour, S & Giesecke, K. & Schwenkler, G., 2018. "Exploring the sources of default clustering," Journal of Financial Economics, Elsevier, vol. 129(1), pages 154-183.
    4. Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.
    5. Guay, François & Schwenkler, Gustavo, 2021. "Efficient estimation and filtering for multivariate jump–diffusions," Journal of Econometrics, Elsevier, vol. 223(1), pages 251-275.
    6. Areski Cousin & Jérôme Lelong & Tom Picard, 2022. "Rating transitions forecasting: a filtering approach," Working Papers hal-03347521, HAL.
    7. Eymen Errais, 2022. "Pricing insurance premia: a top down approach," Annals of Operations Research, Springer, vol. 313(2), pages 899-914, June.
    8. Xiangdong Liu & Jiahui Wu & Xianglong Li, 2023. "Research on Financial Default Model with Stochastic Intensity Using Filtered Likelihood Method," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    9. Mat'uv{s} Maciak & Ostap Okhrin & Michal Pev{s}ta, 2019. "Infinitely Stochastic Micro Forecasting," Papers 1908.10636, arXiv.org, revised Sep 2019.

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    More about this item

    Keywords

    Point processes; Filtering; Efficient parametric inference; Maximum likelihood; Likelihood approximation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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