8. The approach for complexity analysis of multivariate time series

Kazimieras Pukenas

Lithuanian Sports University, Kaunas, Lithuania

E-mail: kazimieras.pukenas@lsu.lt

(Received 15 June 2015; received in revised form 1 August 2015; accepted 11 August 2015)

Abstract. This paper proposes to estimate the complexity of a multivariate time series by the spatio‑temporal entropy based on multivariate singular spectrum analysis (M-SSA). In order to account for both within- and cross-component dependencies in multiple data channels the high dimensional block Toeplitz covariance matrix is decomposed as a Kronecker product of a spatial and a temporal covariance matrix and the multivariate spatio‑temporal entropy is defined in terms of modulus and angle of the complex quantity constructed from the spatial and temporal components of the multivariate entropy. The benefits of the proposed approach are illustrated by simulations on complexity analysis of multivariate deterministic and stochastic processes.

Keywords: multivariate time series analysis, multivariate entropy, multivariate singular spectrum analysis, Kronecker product expansion.

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Cite this article

Pukenas Kazimieras The approach for complexity analysis of multivariate time series. Mathematical Models in Engineering, Vol. 1, Issue 2, 2015, p. 61‑66.

 

Mathematical Models in Engineering. December 2015, Volume 1, Issue 2

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