Gaussian Process State-Space Modeling and Particle Filtering for Time Series Decomposition and Nonlinear Signal Extraction
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917115780399104 |
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| author | Kitagawa, Genshiro |
| author_facet | Kitagawa, Genshiro |
| contents | Gaussian-process state-space models (GP-SSMs) provide a flexible nonparametric alternative for modeling time-series dynamics that are nonlinear or difficult to specify parametrically. While the Kalman filter is effective for linear-Gaussian trend and seasonal components, many real-world systems require more expressive representations. GP-SSMs address this need by learning transition functions directly from data, while particle filtering enables Bayesian state estimation even when posterior distributions deviate from Gaussianity. This paper develops a particle-filtering framework for GP-SSM inference and compares its performance with the Kalman filter in trend extraction and seasonal adjustment. We further evaluate nonlinear signal-extraction tasks, demonstrating that GP-SSMs can recover latent states under sharp or asymmetric dynamics. The results highlight the utility of combining GP modeling with sequential Monte Carlo methods for complex time-series analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01162 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gaussian Process State-Space Modeling and Particle Filtering for Time Series Decomposition and Nonlinear Signal Extraction Kitagawa, Genshiro Methodology 62M10(Primary), 62F99(Secondary) Gaussian-process state-space models (GP-SSMs) provide a flexible nonparametric alternative for modeling time-series dynamics that are nonlinear or difficult to specify parametrically. While the Kalman filter is effective for linear-Gaussian trend and seasonal components, many real-world systems require more expressive representations. GP-SSMs address this need by learning transition functions directly from data, while particle filtering enables Bayesian state estimation even when posterior distributions deviate from Gaussianity. This paper develops a particle-filtering framework for GP-SSM inference and compares its performance with the Kalman filter in trend extraction and seasonal adjustment. We further evaluate nonlinear signal-extraction tasks, demonstrating that GP-SSMs can recover latent states under sharp or asymmetric dynamics. The results highlight the utility of combining GP modeling with sequential Monte Carlo methods for complex time-series analysis. |
| title | Gaussian Process State-Space Modeling and Particle Filtering for Time Series Decomposition and Nonlinear Signal Extraction |
| topic | Methodology 62M10(Primary), 62F99(Secondary) |
| url | https://arxiv.org/abs/2512.01162 |