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Principal component analysis for second-order stationary vector time series

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  • Chang, Jinyuan
  • Guo, Bin
  • Yao, Qiwei

Abstract

We extend the principal component analysis (PCA) to secondorder 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 lowerdimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. Therefore those lowerdimensional 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

Suggested Citation

  • Chang, Jinyuan & Guo, Bin & Yao, Qiwei, 2018. "Principal component analysis for second-order stationary vector time series," LSE Research Online Documents on Economics 84106, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:84106
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    File URL: http://eprints.lse.ac.uk/84106/
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    Cited by:

    1. Marc Hallin & Luis K. Hotta & João H. G Mazzeu & Carlos Cesar Trucios-Maza & Pedro L. Valls Pereira & Mauricio Zevallos, 2019. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: a General Dynamic Factor Approach," Working Papers ECARES 2019-14, ULB -- Universite Libre de Bruxelles.
    2. Chang, Jinyuan & Qiu, Yumou & Yao, Qiwei & Zou, Tao, 2018. "Confidence regions for entries of a large precision matrix," LSE Research Online Documents on Economics 87513, London School of Economics and Political Science, LSE Library.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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