A System-Theoretic Approach to Hawkes Process Identification with Guaranteed Positivity and Stability
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910224305094656 |
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| author | Rong, Xinhui Nair, Girish N. |
| author_facet | Rong, Xinhui Nair, Girish N. |
| contents | The Hawkes process models self-exciting event streams, requiring a strictly non-negative and stable stochastic intensity. Standard identification methods enforce these properties using non-negative causal bases, yielding conservative parameter constraints and severely ill-conditioned least-squares Gram matrices at higher model orders. To overcome this, we introduce a system-theoretic identification framework utilizing the sign-indefinite orthonormal Laguerre basis, which guarantees a well-conditioned asymptotic Gram matrix independent of model order. We formulate a constrained least-squares problem enforcing the necessary and sufficient conditions for positivity and stability. By constructing the empirical Gram matrix via a Lyapunov equation and representing the constraints through a sum-of-squares trace equivalence, the proposed estimator is efficiently computed via semidefinite programming. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14942 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A System-Theoretic Approach to Hawkes Process Identification with Guaranteed Positivity and Stability Rong, Xinhui Nair, Girish N. Systems and Control Methodology The Hawkes process models self-exciting event streams, requiring a strictly non-negative and stable stochastic intensity. Standard identification methods enforce these properties using non-negative causal bases, yielding conservative parameter constraints and severely ill-conditioned least-squares Gram matrices at higher model orders. To overcome this, we introduce a system-theoretic identification framework utilizing the sign-indefinite orthonormal Laguerre basis, which guarantees a well-conditioned asymptotic Gram matrix independent of model order. We formulate a constrained least-squares problem enforcing the necessary and sufficient conditions for positivity and stability. By constructing the empirical Gram matrix via a Lyapunov equation and representing the constraints through a sum-of-squares trace equivalence, the proposed estimator is efficiently computed via semidefinite programming. |
| title | A System-Theoretic Approach to Hawkes Process Identification with Guaranteed Positivity and Stability |
| topic | Systems and Control Methodology |
| url | https://arxiv.org/abs/2603.14942 |