Gaussian Process State-Space Modeling and Particle Filtering for Time Series Decomposition and Nonlinear Signal Extraction

Genshiro Kitagawa

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arXiv · 2512.01162

Gaussian Process State-Space Modeling and Particle Filtering for Time Series Decomposition and Nonlinear Signal Extraction

Genshiro Kitagawa

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Abstract

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.

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Genshiro Kitagawa. 2025-12-01. Gaussian Process State-Space Modeling and Particle Filtering for Time Series Decomposition and Nonlinear Signal Extraction. https://arxiv.org/abs/2512.01162

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