Novel method of identifying time series based on network graphs

Abstract

In this article, we propose a novel method for transforming a time series into a complex network graph. The proposed algorithm is based on the spatial distribution of a time series. The characteristics of geometric parameters of a network represent the dynamic characteristics of a time series. Our algorithm transforms, respectively, a constant series into a fully connected graph, periodic time series into a regular graph, linear divergent time series into a tree, and chaotic time series into an approximately power law distribution network graph. We find that when the dimension of reconstructed phase space increases, the corresponding graph for a random time series quickly turns into a completely unconnected graph, while that for a chaotic time series maintains a certain level of connectivity. The characteristics of the generated network, including the total edges, the degree distribution, and the clustering coefficient, reflect the characteristics of the time series, including diverging speed, level of certainty, and level of randomness. This observation allows a chaotic time series to be easily identified from a random time series. The method may be useful for analysis of complex nonlinear systems such as chaos and random systems, by perceiving the differences in the outcomes of the systems-the time series-in the identification of the systemic levels of certainty or randomness.

Multidimensional Time Series Analysis of Financial Markets Based on the Complex Network Approach

“…The method for mapping time series into complex networks that is proposed in this paper is based on expanding the space-distance method proposed in the literature [12] [13] [14].…”

“…The mapping algorithm [12] includes a definition of a node, a definition of distance, and a connecting rule.…”

Stock Price Pattern Prediction Based on Complex Network and Machine Learning

“…The average degree centrality, average strength, average shortest path length, and closeness centrality of each network are calculated using formulas (15), (16), (17), and (19). The evolution of these four network topological characteristics is shown in Figures 4-7.…”

“…Using complex network theory to study stock prices not only allows us to analyze the relationship between different stocks, but also allows us to explore the macroaspects of the comovement characteristics of the market in different periods [9][10][11]. Previous studies have proposed a variety of methods to build complex networks using the time series of stock prices, including visibility graphs [12][13][14], recurrence networks [15][16][17], correlation networks [11,18,19], pattern networks [10,20], and K-neighbors networks [21,22]. Of all the network construction methods, the symbolic pattern network is favored by many scholars because it can more accurately reflect the degree of correlation and direction of the primitive elements in a complex system [10,20,23,24].…”

Data analysis using circular causality in networks

“…We developed a technique to transform large amounts of data into a cause‐and effect relationship graph. The idea of analyzing complex data systems is not new, as precedents to analyze data using systems theory exists: Yi Lin and Sifeng Liu [], motivated by a practical problem of prediction for dry and hot winds, start to develop a theory of systems analysis which can be used to analyse data, Leher Csato et al () analyze probabilistic data models, Ying Li et al [] present a novel method to describe, express, and distinguish a time series by complex network graph. Peter Turchin [] is the driving force behind a field called “cliodynamics,” where scientists and mathematicians analyze history in the hopes of finding patterns they can then use to predict the future.…”