2014/10/31 by Jinyuan Chang, Bin Guo, Qiwei Yao · 1 citation
Chemistry · Computer Science · Economics, Econometrics and Finance · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Blind Source Separation Techniques #Combinatorics #Complex Systems and Time Series Analysis #Computer science #Diagonal #Dimension (graph theory) #Dimensionality reduction #Econometrics #Mathematical analysis #Mathematics #Order of integration (calculus) #Principal component analysis #Series (stratigraphy) #Spectroscopy and Chemometric Analyses #Statistics #Time series #Transformation (genetics) #Volatility (finance) #stat.ME
paper · pdf · doi:10.1214/17-aos1613
published as Annals of Statistics 2018, Vol. 46, No. 5, 2094-2124 · The original title dated back to October 2014 is "Segmenting Multiple Time Series by Contemporaneous Linear Transformation: PCA for Time Series"
arxiv created 2017/04/12 · openalex publication_date 2018/08/17 · arxiv updated 2018/12/21 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that 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. Therefore, those lower-dimensional series can be analyzed separately as far as the linear dynamic structure is concerned. Technically, it 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 data sets indicate that the proposed method is an effective initial step in analyzing multiple time series data, which leads to substantial dimension reduction in modelling and forecasting high-dimensional linear dynamical structures. Unlike PCA for independent data, there is no guarantee that the required linear transformation exists. When it does not, the proposed method provides an approximate segmentation which leads to the advantages in, for example, forecasting for future values. The method can also be adapted to segment multiple volatility processes.