Moment Matching and Interval Censored Inference

Patrick J. Laub, Young Lee and Thomas Taimre
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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

Chapter Chapter 7 in The Elements of Hawkes Processes, 2021, pp 57-69 from Springer

Abstract: 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.

Date: 2021
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DOI: 10.1007/978-3-030-84639-8_7

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