Giuseppe Cavaliere, Ye Lu, Anders Rahbek, Jacob Stærk-Østergaard
arXiv 7 Apr 2021 · Econometrics · publishedJournal of Econometrics (2022) · 11 citations (OpenAlex)
arXiv:2104.03122 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Embrechts, P., T. Liniger, and L. Lin (2011) Multivariate Hawkes processes: an application to financial data | 1.000 | 9 | 4 | 100% |
| 2 | Ogata, Y (1978) The asymptotic behavior of maximum likelihood estimators for stationary point processes | 0.836 | 12 | 6 | 58% |
| 3 | Daley, D. J. and D. Vere-Jones (2003) An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods | 0.737 | 3 | 2 | 100% |
| 4 | Engle, R.F. and J. Russell (1998) Autoregressive Conditional Duration: a new model for irregularly spaced transaction data | 0.737 | 3 | 2 | 100% |
| 5 | Billingsley, P (1968) Convergence of Probability Measures | 0.644 | 2 | 2 | 100% |
| 6 | Clements, A. E., R. Herrera, and A. S. Hurn (2015) Modelling interregional links in electricity price spikes | 0.644 | 2 | 2 | 100% |
| 7 | Cavaliere, G., R. S. Pedersen, and A. Rahbek (2018) The fixed volatility bootstrap for a class of ARCH($q$) models self | 0.644 | 2 | 2 | 100% |
| 8 | Perera, I. and M. J. Silvapulle (2021) Bootstrap based probability forecasting in multiplicative error models | 0.644 | 2 | 2 | 100% |
| 9 | Rizoiu, M. A., Y. Lee, S. Mishra, and L. Xie (2017) A tutorial on Hawkes processes for events in social media | 0.644 | 2 | 2 | 100% |
| 10 | Sarma, S. V., D. P. Nguyen, G. Czanner, S. Wirth, M. A. Wilson, W. S… (2011) Computing confidence intervals for point process models | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 43 scored citations.