Unraveling chaotic attractors by complex networks and measurements of stock market complexity

Abstract

We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel-Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process.

Lempel-Ziv Complexity and Crises of Cryptocurrency Market

“…However, a completely different picture emerges when the high-frequency stock index data are used. H. Cao and Y. Li [32] present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index, which can potentially be exploited for prediction, has a similar meaning to the Lempel-Ziv complexity, and is an appropriate measure of a series' complexity.…”

“…Because of the simplicity of the LZC method, the entropy rate can be estimated from a single discrete sequence of measurements with a low computational cost [19]. Methods of the complex networks theory [20] proceed from the possibility of representing the time series in the form of a graph and the subsequent analysis of the spectral and topological properties of the latter from the standpoint of complexity theory [21] In the conditions of volatile, environmentally dependent financial markets, it is important to take measures of complexity that allow the early stages to identify critical phenomena that manifest themselves in the form of crises and that cause significant damage to the global and country economies [21][22][23][24]. In this paper, we show that the LZC measure can be just such a measure of complexity, which is an early precursor of crisis phenomena in the cryptocurrency market.…”

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].…”

Topology Universality and Dissimilarity in a Class of Scale-Free Networks

“…External control factors are expressed in many ways, such as determinacy [15], controllability [16] and stability [17]. Except that, researchers also put forward complexity [18, 19] and trade-off relationship [20] to study the topology characters for complex networks.…”

“…In this paper, we still consider the factors of growth, preferential attachment, competition, aging, resource balance and control [11, 16, 17, 19–22] in order to evolve real world and find the key factors of the universality and dissimilarity for evolving networks. We evolve the complex network models by adjusting the deterministic or random factors and discuss the effect of determinacy and randomness on topology characters of SF networks based on our previous model [24].…”