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An unbounded intensity model for point processes

Kim Christensen, Alexei Kolokolov

arXiv 12 Aug 2024 · Econometrics · publishedJournal of Econometrics (2024) · 4 citations (OpenAlex)

arXiv:2408.06519 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We develop a model for point processes on the real line, where the intensity can be locally unbounded without inducing an explosion. In contrast to an orderly point process, for which the probability of observing more than one event over a short time interval is negligible, the bursting intensity causes an extreme clustering of events around the singularity. We propose a nonparametric approach to detect such bursts in the intensity. It relies on a heavy traffic condition, which admits inference for point processes over a finite time interval. With Monte Carlo evidence, we show that our testing procedure exhibits size control under the null, whereas it has high rejection rates under the alternative. We implement our approach on high-frequency data for the EUR/USD spot exchange rate, where the test statistic captures abnormal surges in trading activity. We detect a nontrivial amount of intensity bursts in these data and describe their basic properties. Trading activity during an intensity burst is positively related to volatility, illiquidity, and the probability of observing a drift burst. The latter effect is reinforced if the order flow is imbalanced or the price elasticity of the limit order book is large.

Citation extraction

57
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92
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distinct cited
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appendix boundary found by appendix_command · 57% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Christensen, Oomen, and Renò (2022) The drift burst hypothesis1.00084100%
2Hawkes (1971) Spectra of some self-exciting and mutually exciting point processes0.92844100%
3Jacod and Protter (2012) Discretization of Processes0.8435360%
4Mykland and Zhang (2017) Assessment of uncertainty in high frequency data: The observed asymptotic variance0.84333100%
5Bollerslev, Li, and Xue (2018) Volume, volatility, and public news announcements0.73732100%
6Aït-Sahalia and Jacod (2009) Testing for jumps in a discretely observed process0.64422100%
7Andersen and Bollerslev (1998) Answering the skeptics: Yes, standard volatility models do provide accurate forecasts0.64422100%
8Barndorff-Nielsen and Shephard (2002) Econometric analysis of realized volatility and its use in estimating stochastic volatility models0.64422100%
9Clark (1973) A subordinated stochastic process model with finite variance for speculative prices0.64422100%
10Clinet and Potiron (2018) Statistical inference for the doubly stochastic self-exciting process0.64422100%

Showing the top 10 of 57 scored citations.