Bootstrap Inference for Hawkes and General Point Processes
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Hawkes 及一般点过程的 Bootstrap 推断
- 研究问题
- 对 Hawkes 等点过程进行区间估计和检验时，如何构造易于实施的 Bootstrap，并检验其有效性与有限样本表现？
- 方法与思路
- 作者提出各次重抽样保持条件强度固定的 FIB，与递归强度 RIB 比较，并研究对原始等待时间的时间变换结果进行重抽样。
- 材料陈述的贡献
- 摘要称，两类方案均获得新的渐近理论，文章还建立与自回归条件持续期模型的联系，并用蒙特卡洛及金融、社交媒体数据展示方法。
- 阅读关注点
- 应核对固定强度与递归强度的生成步骤、有效性条件和等待时间重抽样规则，以及模拟中区间覆盖率与检验表现的比较。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审与期刊接收未核实；摘要未给出允许的点过程条件、数值表现或各方案优劣成立的具体范围。
原文摘要
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 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, 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, we provide new bootstrap (asymptotic) theory which allows to assess bootstrap validity, and propose a 'non-parametric' approach based on resampling time-changed transformations of the original waiting times. We also establish the link between the proposed bootstraps for point process models and the related autoregressive conditional duration (ACD) models. Lastly, we show effectiveness of the different bootstrap schemes in finite samples through a set of detailed Monte Carlo experiments, and provide applications to both financial data and social media data to illustrate the proposed methodology.