A0881
Title: On the modelling and prediction of high-dimensional functional time series
Authors: Jinyuan Chang - Southwestern University of Finance and Economics (China)
Qin Fang - the University of Sydney (Australia) [presenting]
Xinghao Qiao - London Schhol of Economics (United Kingdom)
Qiwei Yao - London School of Economics (UK)
Abstract: A two-step procedure is proposed 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 $n$. In the first step, an eigenanalysis of a positive definite matrix is performed, 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 the second step, those groups are handled separately without the loss of information on the overall linear dynamic structure. The second step is devoted to establishing a finite-dimensional dynamical structure for each group's transformed functional time series. Furthermore, the finite-dimensional structure is represented by 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. The theoretical properties of the proposed methods are investigated, and the finite-sample performance is illustrated through both extensive simulation and two real datasets.
