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Title: Functional autoregressive processes via reproducing kernel Hilbert spaces Authors:  Daren Wang - University of Chicago (China) [presenting]
Abstract: The aim is to study the estimation and prediction of a functional autoregressive (FAR) process, a statistical tool for modeling functional time series data. Due to the infinite-dimensional nature of FAR processes, the existing literature addresses its inference via dimension reduction and theoretical results therein require the assumption of fully observed functional time series. We propose an alternative inference framework via the tools of Reproducing Kernel Hilbert Spaces (RKHS). Specifically, a nuclear norm regularization method is proposed for estimating the transition operators of the FAR process directly from discrete samples of the functional time series. We derive a Representer theorem for the FAR process, which enables infinite-dimensional inference without dimension reduction. Consistent theoretical guarantees are established under the (more realistic) assumption that we only have finite discrete samples of the FAR process.