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Inference and testing in general point process models such as the Hawkes model is predominantly based on asymptotic approximations for likelihoodbased estimators and tests, as originally developed in Ogata (1978). As an alternative, and to improve finite sample performance, this paper considers bootstrap-based inference for interval estimation and testing. Specifically, 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 'fixed 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 finite samples through a set of detailed Monte Carlo experiments. As far as we are aware, this is the first 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.

International audience; This paper proposes an indirect inference (Gourieroux, Monfort and Renault, 1993; Smith, 1993) estimation method for a large class of dynamic equilibrium models. Our approach is based on the observation that the econometric structure of these systems naturally generates auxiliary equilibria that can serve as building blocks for estimation. We use this insight to develop an accurate estimator for the long-run risk model of Bansal and Yaron (2004). We demonstrate the accuracy of our method by Monte Carlo simulation and estimate the long-run risk model on U.S. data. We also illustrate the good performance of the methodology on an asset pricing model with investor learning.