Segmenting Multiple Time Series by Contemporaneous Linear Transformation

• Activity Number: 625
• Type: Invited
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: International Chinese Statistical Association
• Author(s): Jinyuan Chang* and Bin Guo and Qiwei Yao
• Companies: The University of Melbourne and Peking University and London School of Economics
• Keywords: Autocorrelation ; Cross-correlation ; Dimension reduction ; Eigenanalysis ; High-dimensional time series ; Weak stationarity

Abstract

We seek for a contemporaneous linear transformation for a p-variate time series such that the transformed series is segmented into several lower-dimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. The method may be viewed as an extension of principal component analysis for multiple time series. Technically it also boils down to an eigenanalysis for a positive definite matrix. When $p$ is large, an additional step is required to perform a permutation in terms of either maximum cross-correlations or FDR based on multiple tests. The asymptotic theory is established for both fixed $p$ and diverging $p$ when the sample size $n$ tends to infinity, reflecting the fact that the method also applies when the dimension $p$ is large in relation to $n$. Numerical experiments with both simulated and real datasets indicate that the proposed method is an effective initial step in analysing multiple time series data, which leads to substantial dimension-reduction in modelling and forecasting high-dimensional linear dynamical structures. The method can also be adapted to segment multiple volatility processes.