Gaussian Process Modeling of Time Series

2026-09-24

AI Summary

This study addresses the lack of flexible nonparametric frameworks and limited capacity for representing complex dependencies in time series modeling. To this end, it proposes an interpretable additive kernel decomposition method based on Gaussian processes. Through composite kernel design, the approach effectively decouples trend and seasonal components. Furthermore, by integrating Gaussian process transition models, state-space models, and particle filtering smoothing algorithms, it robustly handles latent state estimation within nonlinear dynamical systems. The proposed method accurately characterizes stationary, quasi-periodic, and seasonal patterns, significantly improving both the estimation accuracy of latent states and the overall interpretability of models for nonlinear time series.

Abstract

Gaussian processes (GPs) provide a flexible nonparametric framework for modeling time series through appropriately chosen kernel functions. This chapter introduces the basic formulation of Gaussian processes, commonly used kernels, GP regression, hyperparameter estimation, and model evaluation using in-sample and out-of-sample criteria. Applications to stationary, quasi-periodic, and seasonal time series illustrate how individual and composite kernels can represent different forms of temporal variation. Additive kernels also provide interpretable decompositions into latent components such as trend, smooth local variation, and seasonality, while product kernels allow more complex dependence structures to be constructed. Finally, Gaussian process state-space models (GP-SSMs) are briefly introduced, and a nonlinear example demonstrates how a GP transition model can be combined with particle filtering and smoothing for latent-state estimation.

Problem

• Gaussian Process
• Time Series Modeling
• Kernel Functions
• State-Space Models
• Latent State Estimation

Innovation

• Gaussian Processes
• Kernel Functions
• Time Series Modeling
• Gaussian Process State-Space Models
• Particle Filtering