Abstract
In this paper, it is shown that the block circulant matrix decomposition technique makes the multivariate singular spectrum analysis (M-SSA) a well suited tool for detecting of changes of the correlation structure in non-stationary multivariate time series in the presence of high observational noise levels. The major drawback of M-SSA, that it operates on a large covariance matrix and becomes computationally expensive, can be avoided by reordering the Toeplitz-block covariance matrix into a block Toeplitz matrix, embedding this into a block circulant matrix and efficiently block-diagonalizing this by the means of the Fast Fourier Transform (FFT) using the well known algorithm. The overall degree of synchronization among multiple-channel signals is defined by the synchronization index (the S-estimator) of the rearranged and truncated eigenvalue spectrum. Throughout the experiment, the high capability of the proposed algorithm to detect the lag-synchronized state under the influence of strong noise is validated with simulated data—a network of time series generated by autoregressive models (AR) and a network of coupled chaotic Roessler oscillators.
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Appendix
Appendix
A network of time series as a prototypical model of a stochastic dynamical system was generated by an autoregressive model (AR) as a univariate GARCH process simulation with GARCH specification structure spec = garchset(‘C’,0,‘AR’,[0.9 −0.2],‘K’,0.02,‘GARCH’, 0.8, ‘ARCH’,[0.1 0.05]) and applying data smoothing with syntax smooth(x,13,‘rloess’).
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Pukenas, K. Algorithm for the Characterization of the Cross-Correlation Structure in Multivariate Time Series. Circuits Syst Signal Process 33, 1289–1297 (2014). https://doi.org/10.1007/s00034-013-9684-2
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DOI: https://doi.org/10.1007/s00034-013-9684-2