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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.11075 |
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| _version_ | 1866910304277889024 |
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| author | Chen, Feng Kwan, Jeffrey Stindl, Tom |
| author_facet | Chen, Feng Kwan, Jeffrey Stindl, Tom |
| contents | The Hawkes process is a widely used model in many areas, such as
finance, seismology, neuroscience, epidemiology, and social
sciences. Estimation of the Hawkes process from continuous
observations of a sample path is relatively straightforward using
either the maximum likelihood or other methods. However, estimating
the parameters of a Hawkes process from observations of a sample
path at discrete time points only is challenging due to the
intractability of the likelihood with such data. In this work, we
introduce a method to estimate the Hawkes process from a discretely
observed sample path. The method takes advantage of a state-space
representation of the incomplete data problem and use the sequential
Monte Carlo (aka particle filtering) to approximate the likelihood
function. As an estimator of the likelihood function the SMC
approximation is unbiased, and therefore it can be used together
with the Metropolis-Hastings algorithm to construct Markov Chains to
approximate the likelihood distribution, or more generally, the
posterior distribution of model parameters. The performance of the
methodology is assessed using simulation experiments and compared
with other recently published methods. The proposed estimator is
found to have a smaller mean square error than the two benchmark
estimators. The proposed method has the additional advantage that
confidence intervals for the parameters are easily available. We
apply the proposed estimator to the analysis of weekly count data on
measles cases in Tokyo Japan and compare the results to those by
one of the benchmark methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimating the Hawkes process from a discretely observed sample path Chen, Feng Kwan, Jeffrey Stindl, Tom Methodology Computation The Hawkes process is a widely used model in many areas, such as finance, seismology, neuroscience, epidemiology, and social sciences. Estimation of the Hawkes process from continuous observations of a sample path is relatively straightforward using either the maximum likelihood or other methods. However, estimating the parameters of a Hawkes process from observations of a sample path at discrete time points only is challenging due to the intractability of the likelihood with such data. In this work, we introduce a method to estimate the Hawkes process from a discretely observed sample path. The method takes advantage of a state-space representation of the incomplete data problem and use the sequential Monte Carlo (aka particle filtering) to approximate the likelihood function. As an estimator of the likelihood function the SMC approximation is unbiased, and therefore it can be used together with the Metropolis-Hastings algorithm to construct Markov Chains to approximate the likelihood distribution, or more generally, the posterior distribution of model parameters. The performance of the methodology is assessed using simulation experiments and compared with other recently published methods. The proposed estimator is found to have a smaller mean square error than the two benchmark estimators. The proposed method has the additional advantage that confidence intervals for the parameters are easily available. We apply the proposed estimator to the analysis of weekly count data on measles cases in Tokyo Japan and compare the results to those by one of the benchmark methods. |
| title | Estimating the Hawkes process from a discretely observed sample path |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2401.11075 |