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Moment Matching and Interval Censored Inference

In: The Elements of Hawkes Processes

Author

Listed:
  • Patrick J. Laub

    (University of Melbourne, Faculty of Business and Economics)

  • Young Lee

    (Harvard University, Faculty of Arts and Sciences)

  • Thomas Taimre

    (The University of Queensland, School of Mathematics and Physics)

Abstract

In this chapter, we focus on the problem of drawing inferences from Hawkes processes using the GMM. Differently from evaluating the maximum likelihood estimates as explained in Chap. 5 , the generalised method of moments (GMM) is a method for constructing estimators that uses assumptions regarding the specific moments of the random variables instead of assumptions with regards to the entirety of the distribution. These assumptions are known as moment conditions. We will first introduce the GMM and then detail how it can be used for Hawkes processes with exponential excitation function. Furthermore, we explain how to use the GMM to infer parameters of a class of generalised Hawkes processes with exponential excitation function but this time with random jump sizes.

Suggested Citation

  • Patrick J. Laub & Young Lee & Thomas Taimre, 2021. "Moment Matching and Interval Censored Inference," Springer Books, in: The Elements of Hawkes Processes, chapter 0, pages 57-69, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-84639-8_7
    DOI: 10.1007/978-3-030-84639-8_7
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