Principal component analysis for second-order stationary vector time series

By Jinyuan Chang, Bin Guo, Qiwei Yao. Annals of Statistics, 2014

51 citations recorded by the source corpus.

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 analysed 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 analysing 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.

Subfields: Analytical Chemistry, Economics and Econometrics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/591e553edb4eebfea44f13c9a85ec30ef9ced7c0

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Citations in the corpus

Identifying Cointegration by Eigenanalysis (2015, methodology): “the data have been developed, starting from Engle and Granger (1987) and Johansen (1991), in their parametric, unit root vector autoregressive (VAR) setting, and continuing with, for example, Saikkonen and Lütkepohl (2000) and Aznar and Salvador (2002).”
Modelling matrix time series via a tensor CP-decomposition (2021, methodology): “Under some sparsity condition on A and B, applying the technique used to derive Lemma 5 of Chang et al. (2018), we can show that Condition 3(ii) holds for certain (s1, s2).”
Constrained Factor Models for High-Dimensional Matrix-Variate Time Series (2017, unknown): “Diebold & Li (2006) and Diebold et al. (2006) interpret the Nelson-Siegel representation as a dynamic latent factor model where β 1 , β 2 , and β 3 are time-varying latent factors that capture the level (L), slope (S), and curvature (C) of the yield curve at each period t , while the terms that…”