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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.

This paper studies the spillover effect of home mortgage delinquencies using a discrete-choice spatial network model. In our empirical study, a main challenge in estimating this model is that mortgage repayment decisions can only be observed for a sample of all the borrowers in the study region. We show that the nested pseudolikelihood (NPL) algorithm can be readily modified to accommodate this missing data issue. Monte Carlo simulations indicate that the proposed estimator works well in finite samples and ignoring this issue leads to a downward bias in the estimated spillover effect. We estimate the model using data on single-family residential mortgage delinquencies in Clark County of Nevada in 2010, and find strong evidence of spillover effects. We also conduct some counterfactual experiments to illustrate the policy relevance of the spillover effect.

Hall and Marron (1987) introduced kernel estimators of integrals of the squared m -order derivatives of a probability density. Mokkadem and Pelletier (2020) gave recursive versions of their estimators, but the main drawback of these estimators is that their update requires the use of all past data. The aim of this paper is the study of online versions of the estimators introduced by Hall and Marron (1987), that is of estimators which are not only recursive, but which also have the property that their update uses only the last available data. Rates of convergence in mean squared error (MSE) are calculated. Similarly to the estimators of Hall and Marron (1987) and of Mokkadem and Pelletier (2020), our online estimators achieve the parametric rate n − 1 when m = 0 or when higher order kernels are used. For the case when the parametric rate is not obtained, we also study an online version of the estimator proposed by Jones and Sheather (1991). Finally, we provide recursive estimators of the optimal bandwidth in the framework of density estimation.

We study the estimation of dynamic economic models for which some of the state variables are observed only occasionally by the econometrician—a common problem in many fields, ranging from industrial organization to marketing to finance. If such occasional state observations are serially correlated, the likelihood function of the model becomes a potentially high-dimensional integral over a nonstandard domain. We propose a method that generalizes the recursive likelihood function integration procedure (RLI; Reich, 2018) to numerically approximate this integral, and demonstrate its statistical efficiency in several well-understood examples from finance and industrial organization. In extensive Monte Carlo studies, we compare the performance of our approach to a recently suggested method of simulated moments. In all our demonstrations, we consistently and efficiently identify all model parameters, and we find that the additional variance of our estimator when going from full to occasional state observations is small for the parameters of interest.

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.