UC San Diego

Functional data objects are usually collected sequentially over time exhibiting forms of dependence. Such data structure is known as functional time series. While there is plentiful literature addressing the topics of linear functional processes, relatively few contributions have dealt with nonparametric functional time series, which is the focus of this dissertation. After introducing some background and basics of functional time series in Chapter 1, I address the topics concerning the applications of kernel methods in the analysis of nonparametric functional time series. Specifically, Chapter 2 investigates the kernel estimation of the autoregressive operator in the nonparametric functional autoregression model. A componentwise bootstrap procedure is proposed in Chapter 3 which can be used for estimating the distribution of the kernel estimation and constructing the prediction regions. Chapter 4 tackles the problem of spectral density estimation of functional time series. A class of higher-order accurate spectral density kernel estimators is proposed based on the notion of flat-top kernel.