高斯过程时间序列建模
Gaussian Process Modeling of Time Series
- Tokyo University of Marine Science and Technology（东京海洋大学）
- The Institute of Statistical Mathematics（统计数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文介绍高斯过程用于时间序列建模，涵盖核函数选择、回归、超参数估计及模型评估，并展示加性/乘积核分解及GP状态空间模型的应用。
AI中文摘要：
高斯过程（GPs）通过适当选择的核函数，为时间序列建模提供了一个灵活的非参数框架。本章介绍了高斯过程的基本表述、常用核函数、高斯过程回归、超参数估计，以及使用样本内和样本外准则进行模型评估。对平稳、准周期和季节性时间序列的应用，展示了单个核函数和复合核函数如何表示不同形式的时间变化。加性核函数还能提供可解释的分解，将时间序列分解为趋势、平滑局部变化和季节性等潜在成分，而乘积核函数则允许构建更复杂的依赖结构。最后，简要介绍了高斯过程状态空间模型（GP-SSMs），并通过一个非线性示例展示了如何将高斯过程转移模型与粒子滤波和平滑相结合，用于潜在状态估计。
英文摘要：
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.
