Parameter Estimation of Binned Hawkes Processes

Shlomovich, Leigh; Cohen, Edward; Adams, Niall M.; Patel, Lekha

doi:10.1080/10618600.2022.2050247

Cited by 7 publications

(9 citation statements)

References 30 publications

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“…where K = T /Δ and Δ is the bin width. Here we develop and extend the methodology detailed in Shlomovich et al (2022) to handle parameter estimation of multivariate binned Hawkes processes. We do this by considering the superposition of the multivariate count process.…”

Section: N (P) Tmentioning

confidence: 99%

“…In the univariate setting, a method for parameter estimation based on the Whittle likelihood is presented in Cheysson and Lang (2022) and a modified Monte Carlo Expectation Maximisation (MC-EM) approach is presented in Shlomovich et al (2022), termed the Binned Hawkes Expectation Maximisation (BH-EM) algorithm; which is extended here for multivariate data.…”

Section: Multivariate Mcem For Binned Hawkes Processesmentioning

confidence: 99%

“…These are marked time-stamps which are not observed due to practical restrictions. We denote the parameter set to be Θ = {ν, α, β}, where ν is P × 1, and α and β are P × P. The following two steps are as detailed in Shlomovich et al (2022):…”

Section: The Monte Carlo Em Algorithmmentioning

confidence: 99%

“…Generating consistent time-stamps for the latent multivariate process such that the true covariance structure is sufficiently captured is an important problem. We propose the following method for this, which allows us to extend the work in Shlomovich et al (2022) for multivariate count data. Consider N t = [N 1,t , .…”

Section: Multivariate Sampling Via the Superposition Processmentioning

confidence: 99%

“…Additionally Hawkes processes have been considered within cyber-security for modelling of computer network traffic (Mark et al 2019; Price-Williams and Heard 2019) and social media activity, for example in Kobayashi and Lambiotte (2016) where propagation of 'Twitter cascades' is considered. As discussed in Shlomovich et al (2022) practical limitations on storing or recording high resolution data results in an abundance of binned data, that is streams of counts of occurrences per time bin. We can use the counting process representation of a P-variate point process to model this binned data.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A parameter estimation method for multivariate binned Hawkes processes

2022

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It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from limitations on recording capabilities and the expense of storing high volumes of precise data. In order to gain a better understanding of the relationships between processes, we consider modelling the aggregated event data using multivariate Hawkes processes, which offer a description of mutually-exciting behaviour and have found wide applications in areas including seismology and finance. Here we generalise existing methodology on parameter estimation of univariate aggregated Hawkes processes to the multivariate case using a Monte Carlo expectation–maximization (MC-EM) algorithm and through a simulation study illustrate that alternative approaches to this problem can be severely biased, with the multivariate MC-EM method outperforming them in terms of MSE in all considered cases.

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Section: N (P) Tmentioning

confidence: 99%

Section: Multivariate Mcem For Binned Hawkes Processesmentioning

confidence: 99%

Section: The Monte Carlo Em Algorithmmentioning

confidence: 99%

Section: Multivariate Sampling Via the Superposition Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A parameter estimation method for multivariate binned Hawkes processes

2022

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Graph‐based mutually exciting point processes for modelling event times in docked bike‐sharing systems

Sanna Passino,

Che,

Cardoso Correia Perello

2024

Stat

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This paper introduces graph‐based mutually exciting processes (GB‐MEP) to model event times in network point processes, focusing on an application to docked bike‐sharing systems. GB‐MEP incorporates known relationships between nodes in a graph within the intensity function of a node‐based multivariate Hawkes process. This approach reduces the number of parameters to a quantity proportional to the number of nodes in the network, resulting in significant advantages for computational scalability when compared with traditional methods. The model is applied on event data observed on the Santander Cycles network in central London, demonstrating that exploiting network‐wide information related to geographical location of the stations is beneficial to improve the performance of node‐based models for applications in bike‐sharing systems. The proposed GB‐MEP framework is more generally applicable to any network point process where a distance function between nodes is available, demonstrating wider applicability.

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An Inhomogeneous Weibull–Hawkes Process to Model Underdispersed Acoustic Cues

Van Helsdingen,

Marques,

Jones-Todd

2024

JABES

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A Hawkes point process describes self-exciting behaviour where event arrivals are triggered by historic events. These models are increasingly becoming a popular choice in analysing event-type data. Like all other inhomogeneous Poisson point processes, the waiting time between events in a Hawkes process is derived from an exponential distribution with mean one. However, as with many ecological and environmental data, this is an unrealistic assumption. We, therefore, extend and generalise the Hawkes process to account for potential under- or overdispersion in the waiting times between events by assuming the Weibull distribution as the foundation of the waiting times. We apply this model to the acoustic cue production times of sperm whales and show that our Weibull–Hawkes model better captures the inherent underdispersion in the interarrival times of echolocation clicks emitted by these whales.

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Parameter Estimation of Binned Hawkes Processes

Cited by 7 publications

References 30 publications

A parameter estimation method for multivariate binned Hawkes processes

A parameter estimation method for multivariate binned Hawkes processes

Graph‐based mutually exciting point processes for modelling event times in docked bike‐sharing systems

An Inhomogeneous Weibull–Hawkes Process to Model Underdispersed Acoustic Cues

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