Functional Autoregression for Sparsely Sampled Data
提出一种层次高斯过程模型，专门处理稀疏或不规则采样且存在测量误差的函数型时间序列，通过函数自回归和吉布斯采样实现预测与推断，并在美国收益率曲线数据上验证了有效性。
We develop a hierarchical Gaussian process model for forecasting and\ninference of functional time series data. Unlike existing methods, our approach\nis especially suited for sparsely or irregularly sampled curves and for curves\nsampled with non-negligible measurement error. The latent process is\ndynamically modeled as a functional autoregression (FAR) with Gaussian process\ninnovations. We propose a fully nonparametric dynamic functional factor model\nfor the dynamic innovation process, with broader applicability and improved\ncomputational efficiency over standard Gaussian process models. We prove\nfinite-sample forecasting and interpolation optimality properties of the\nproposed model, which remain valid with the Gaussian assumption relaxed. An\nefficient Gibbs sampling algorithm is developed for estimation, inference, and\nforecasting, with extensions for FAR(p) models with model averaging over the\nlag p. Extensive simulations demonstrate substantial improvements in\nforecasting performance and recovery of the autoregressive surface over\ncompeting methods, especially under sparse designs. We apply the proposed\nmethods to forecast nominal and real yield curves using daily U.S. data. Real\nyields are observed more sparsely than nominal yields, yet the proposed methods\nare highly competitive in both settings.\n