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

TL;DR

This paper introduces a particle-filtering framework for Gaussian-process state-space models, enabling flexible nonlinear time series decomposition and signal extraction, outperforming traditional methods in complex dynamic scenarios.

Contribution

It develops a novel particle-filtering approach for GP-SSMs and compares its effectiveness with Kalman filters in nonlinear time series analysis.

Findings

GP-SSMs outperform Kalman filters in nonlinear trend extraction.

The framework effectively recovers latent states with sharp or asymmetric dynamics.

Demonstrates the utility of combining GP modeling with Monte Carlo methods.

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.