BOOTSTRAP INFERENCE FOR HAWKES AND GENERAL POINT PROCESSES

Giuseppe Cavaliere, Ye Lu, Anders Rahbek and J Staerk-Ostergaard

No 2021-05, Working Papers from University of Sydney, School of Economics

Abstract: Inference and testing in general point process models such as the Hawkes model is predominantly based on asymptotic approximations for likelihood based estimators and tests, as originally developed in Ogata (1978). As an alternative, and to improve fi nite sample performance, this paper considers bootstrap-based inference for interval estimation and testing. Specifi cally, for a wide class of point process models we consider a novel bootstrap scheme labeled ` fixed intensity bootstrap' (FIB), where the conditional intensity is kept fixed across bootstrap repetitions. The FIB, which is very simple to implement and fast in practice, naturally extends previous ideas from the bootstrap literature on time series in discrete time, where the so-called `fi xed design' and ` fixed volatility' bootstrap schemes have shown to be particularly useful and effective. We compare the FIB with the classic recursive bootstrap, which is here labeled `recursive intensity bootstrap' (RIB). In RIB algorithms, the intensity is stochastic in the bootstrap world and implementation of the bootstrap is more involved, due to its sequential structure. For both bootstrap schemes, no asymptotic theory is available; we therefore provide here a new bootstrap (asymptotic) theory, which allows to assess bootstrap validity. We also introduce novel `nonparametric' FIB and RIB schemes, which are based on resampling time-changed transformations of the original waiting times. We show effectiveness of the different bootstrap schemes in fi nite samples through a set of detailed Monte Carlo experiments. As far as we are aware, this is the fi rst detailed Monte Carlo study of bootstrap implementations for Hawkes-type processes. Finally, in order to illustrate, we provide applications of the bootstrap to both financial data and social media data.

Keywords: Self-exciting point processes; conditional intensity; bootstrap inference; Hawkes process. (search for similar items in EconPapers)
Date: 2021-03
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http://econ-wpseries.com/2021/202105.pdf

Related works:
Journal Article: Bootstrap inference for Hawkes and general point processes (2023)
Working Paper: Bootstrap Inference for Hawkes and General Point Processes (2021)
Working Paper: Bootstrap inference for Hawkes and general point processes (2021)
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