Bootstrap inference for Hawkes and general point processes

Cavaliere, Giuseppe; Lü, Ye; Rahbek, Anders; Stærk-Østergaard, Jacob

doi:10.1016/j.jeconom.2022.02.006

Cited by 7 publications

(3 citation statements)

References 45 publications

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“…However, for some point processes that consider additional factors affecting event occurrence rates, we introduce the conditional intensity λ(t|H), where H denotes additional conditional information. As a self-exciting point process, the conditional intensity function of the Hawkes process is defined as [34][35][36]…”

Section: Intensity Functionmentioning

confidence: 99%

HP-LSTM: Hawkes Process–LSTM-Based Detection of DDoS Attack for In-Vehicle Network

Li,

Liu

2024

Future Internet

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Connected and autonomous vehicles (CAVs) are advancing at a fast speed with the improvement of the automotive industry, which opens up new possibilities for different attacks. A Distributed Denial-of-Service (DDoS) attacker floods the in-vehicle network with fake messages, resulting in the failure of driving assistance systems and impairment of vehicle control functionalities, seriously disrupting the normal operation of the vehicle. In this paper, we propose a novel DDoS attack detection method for in-vehicle Ethernet Scalable service-Oriented Middleware over IP (SOME/IP), which integrates the Hawkes process with Long Short-Term Memory networks (LSTMs) to capture the dynamic behavioral features of the attacker. Specifically, we employ the Hawkes process to capture features of the DDoS attack, with its parameters reflecting the dynamism and self-exciting properties of the attack events. Subsequently, we propose a novel deep learning network structure, an HP-LSTM block, inspired by the Hawkes process, while employing a residual attention block to enhance the model’s detection efficiency and accuracy. Additionally, due to the scarcity of publicly available datasets for SOME/IP, we employed a mature SOME/IP generator to create a dataset for evaluating the validity of the proposed detection model. Finally, extensive experiments were conducted to demonstrate the effectiveness of the proposed DDoS attack detection method.

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Section: Intensity Functionmentioning

confidence: 99%

HP-LSTM: Hawkes Process–LSTM-Based Detection of DDoS Attack for In-Vehicle Network

Li,

Liu

2024

Future Internet

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“…Bootstrap inference procedures for Hawkes processes can consist of asymptotic confidence intervals, or in cases where arrival times occur on the interval [0, T ] where T is not sufficiently large, polyhedral confidence sets may be used [10]. There also include resampling techniques such as Fixedor Recursive-Intensity Bootstrap procedures [11].…”

Section: Remarksmentioning

confidence: 99%

A Multivariate Hawkes Process Model for Stablecoin-Cryptocurrency Depegging Event Dynamics

Oxenhorn¹

2022

Preprint

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Stablecoins-digital assets pegged to a specific currency or commodity value-are heavily involved in transactions of major cryptocurrencies [1]. The effects of deviations from their desired fixed values (depeggings) on the cryptocurrencies for which they are frequently used in transactions are therefore of interest to study. We propose a model for this phenomenon using a multivariate mutually-exciting Hawkes process, and present a numerical example applying this model to Tether (USDT) and Bitcoin (BTC).

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“…This is a crucial fact, given that a wide range of tail indices is witnessed in empirical applications on duration data. Thus, for example, Hill estimation of κ yields κ = 2.1 > 2 for the IBM transaction data analyzed in Engle and Russell (1998) and κ = 2.5 > 2 on the durations between tweets in Cavaliere, Lu, Rahbek and Staerk-Østergaard (2022). Moreover, κ = 1.4 ∈ (1, 2) for the DJIA data from Embrechts, Liniger and Lin (2011), while κ = 0.7 < 1 on SPY transaction data over a single trading day (2019:07:31).…”

Section: Introductionmentioning

confidence: 98%

The Econometrics of Financial Duration Modeling

Cavaliere¹,

Mikosch²,

Rahbek³

et al. 2022

Preprint

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We discuss estimation and inference in financial durations models. For the classical autoregressive conditional duration (ACD) models by Engle and Russell (1998, Econometrica 66, 1127-1162, we show the surprising result that the large sample behavior of likelihood estimators depends on the tail behavior of the durations. Even under stationarity, asymptotic normality breaks down for tail indices smaller than one. Instead, estimators are mixed Gaussian with non-standard rates of convergence. We exploit here the crucial fact that for duration data the number of observations within any time span is random. Our results apply to general econometric models where the number of observed events is random.

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Bootstrap inference for Hawkes and general point processes

Cited by 7 publications

References 45 publications

HP-LSTM: Hawkes Process–LSTM-Based Detection of DDoS Attack for In-Vehicle Network

HP-LSTM: Hawkes Process–LSTM-Based Detection of DDoS Attack for In-Vehicle Network

A Multivariate Hawkes Process Model for Stablecoin-Cryptocurrency Depegging Event Dynamics

The Econometrics of Financial Duration Modeling

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