On the modelling and prediction of high-dimensional functional time series

TL;DR

This paper introduces a two-step method for modeling and predicting high-dimensional functional time series by transforming, grouping, and then applying finite-dimensional vector time series models, supported by theory and real data applications.

Contribution

It presents a novel eigenanalysis-based transformation and grouping approach that simplifies high-dimensional functional time series modeling without losing dynamic information.

Findings

Effective grouping of functional series into uncorrelated clusters

Finite-dimensional vector models accurately predict original series

Method performs well in simulations and real datasets

Abstract

We propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series $p$ is large in relation to the length of time series $n$. Our first step performs an eigenanalysis of a positive definite matrix, which leads to a one-to-one linear transformation for the original high-dimensional functional time series, and the transformed curve series can be segmented into several groups such that any two subseries from any two different groups are uncorrelated both contemporaneously and serially. Consequently in our second step those groups are handled separately without the information loss on the overall linear dynamic structure. The second step is devoted to establishing a finite-dimensional dynamical structure for all the transformed functional time series within each group. Furthermore the finite-dimensional structure is represented by that of a vector time series. Modelling and forecasting for the original high-dimensional functional time series are realized via those for the vector time series in all the groups. We investigate the theoretical properties of our proposed methods, and illustrate the finite-sample performance through both extensive simulation and two real datasets.