An unbounded intensity model for point processes

TL;DR

This paper introduces a novel unbounded intensity model for point processes that captures extreme clustering of events, develops a nonparametric detection method for bursts, and applies it to high-frequency financial data revealing significant insights.

Contribution

It proposes a new unbounded intensity model for point processes, along with a nonparametric burst detection approach applicable to finite intervals, validated through Monte Carlo simulations and real data.

Findings

Detected intensity bursts in EUR/USD data correlating with market volatility.

Burst periods are associated with increased illiquidity and drift probability.

The method controls size under the null hypothesis and effectively detects bursts.

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.