Prof. Qiwei Yao

Large Segmenting Multiple Time Series by Contemporaneous Linear
Transformation: PCA for Time Series

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 (PCA) 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. 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.

Background

Professor of Statistics at London School of Economics. He is a Fellow of both the Institute of Mathematical Statistics and the American Statistical Association, and also a elected member of the International Statistical Institute.

Research Interests

Time series analysis, Nonparametric regression, Dimension reduction and factor modelling, Spatio-temporal modelling, Financial econometrics
Posted in Speakers2015.