A Unified View of Nonparametric Trend-Cycle Predictors Via Reproducing Kernel Hilbert Spaces
提出统一框架，将多种非参数平滑估计器转化为核函数，推导高阶估计器，并与经典实时分析估计器比较，证明其在信号传递、噪声抑制和收敛速度上的优势。
We provide a common approach for studying several nonparametric estimators used for smoothing functional time series data. Linear filters based on different building assumptions are transformed into kernel functions via reproducing kernel Hilbert spaces. For each estimator, we identify a density function or second order kernel, from which a hierarchy of higher order estimators is derived. These are shown to give excellent representations for the currently applied symmetric filters. In particular, we derive equivalent kernels of smoothing splines in Sobolev and polynomial spaces. The asymmetric weights are obtained by adapting the kernel functions to the length of the various filters, and a theoretical and empirical comparison is made with the classical estimators used in real time analysis. The former are shown to be superior in terms of signal passing, noise suppression and speed of convergence to the symmetric filter.