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. 2017 Sep 5;7(1):10486.
doi: 10.1038/s41598-017-10759-3.

Reconstructing complex network for characterizing the time-varying causality evolution behavior of multivariate time series

Meihui Jiang  1   2   3 , Xiangyun Gao  4   5   6 , Haizhong An  1   2   3 , Huajiao Li  1   2   3 , Bowen Sun  1   2   3
Affiliations

Reconstructing complex network for characterizing the time-varying causality evolution behavior of multivariate time series

Meihui Jiang et al. Sci Rep. .

Abstract

In order to explore the characteristics of the evolution behavior of the time-varying relationships between multivariate time series, this paper proposes an algorithm to transfer this evolution process to a complex network. We take the causality patterns as nodes and the succeeding sequence relations between patterns as edges. We used four time series as sample data. The results of the analysis reveal some statistical evidences that the causalities between time series is in a dynamic process. It implicates that stationary long-term causalities are not suitable for some special situations. Some short-term causalities that our model recognized can be referenced to the dynamic adjustment of the decisions. The results also show that weighted degree of the nodes obeys power law distribution. This implies that a few types of causality patterns play a major role in the process of the transition and that international crude oil market is statistically significantly not random. The clustering effect appears in the transition process and different clusters have different transition characteristics which provide probability information for predicting the evolution of the causality. The approach presents a potential to analyze multivariate time series and provides important information for investors and decision makers.

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Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Figure 1
Figure 1
The definition of the causality patterns.
Figure 2
Figure 2
Schematic illustration of constructing the multivariate time-varying causality transition network.
Figure 3
Figure 3
Sensitivity analysis. (a) Number of nodes and edges for different lengths of sliding window. (b) The density of networks and the average path length for different lengths of sliding window.
Figure 4
Figure 4
The distribution of the weighted degree.
Figure 5
Figure 5
The distribution of weight of edges.
Figure 6
Figure 6
The transition probabilities of the key causality patterns. We choose the edges with weight > 1.
Figure 7
Figure 7
The clustering effect in the multivariate time-varying causality transition network. Note: red-cluster 1(31.3%), yellow-cluster 2(20%), blue-cluster 3(17.39%).
Figure 8
Figure 8
The distribution of transition abilities among the clusters.
Figure 9
Figure 9
The three sub networks formed by three major clusters.
Figure 10
Figure 10
The distribution of the causality patterns in three major clusters over time.
See this image and copyright information in PMC

References

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