# Dynamic Functional Principal Component

### Abstract

In this paper, we address the problem of dimension reduction for time series of functional data ($X_t$: $t$ ∈ $Z$). Such functional time series frequently arise, e.g., when a continuous-time process is segmented into some smaller natural units, such as days. Then each $X_t$ represents one intraday curve. We argue that functional principal component analysis (FPCA), though a key technique in the field and a benchmark for any competitor, does not provide an adequate dimension reduction in a time-series setting. FPCA indeed is a static procedure which ignores the essential information provided by the serial dependence structure of the functional data under study. Therefore, inspired by Brillinger’s theory of dynamic principal components, we propose a dynamic version of FPCA, which is based on a frequency-domain approach. By means of a simulation study and an empirical illustration, we show the considerable improvement the dynamic approach entails when compared to the usual static procedure.

Type
Publication
In Journal of the Royal Statistical Society: Series B (JRSSB)
Date