Mapping coupled time-series onto a complex network

Ardalankia, Jamshid; Askari, Jafar; Sheykhali, Somaye; Haven, Emmanuel; Jafari, G. R.

doi:10.1209/0295-5075/132/58002

Cited by 5 publications

(3 citation statements)

References 41 publications

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“…In the real world, finding a process in isolation from other processes is challenging. As a result, a process can be not only influenced by its own past but also by the past of other processes [18][19][20] . For example, historical oil prices directly impact specific commodities' costs and even some countries' GDPs 21 .…”

Section: Introductionmentioning

confidence: 99%

Generalization of Chapman-Kolmogorov equation to two coupled processes

Motahari,

Noudehi,

Jamali

et al. 2024

Preprint

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Real-world processes often display a prolonged memory, which extends beyond the single-step dependency characteristic of Markov processes. In addition, the current state of an empirical process is often not only influenced by its own past but also by the past states of other dependent processes. This study introduces the generalized version of the Chapman-Kolmogorov equation (CKE) to estimate the memory size in such scenarios. To assess the applicability of our approach, we generate coupled time series with predetermined memory lengths using the autoregressive model. The results show a high degree of accuracy in measuring memory lengths. Subsequently, we employ the generalized CKE to analyze cryptocurrency data as a real-world case study. Our results indicate that the past dynamics of cryptocurrencies significantly impact their current states, thereby highlighting interdependencies among them. The method proposed in this study can be also utilized in forecasting coupled time series.

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Section: Introductionmentioning

confidence: 99%

Generalization of Chapman-Kolmogorov equation to two coupled processes

Motahari,

Noudehi,

Jamali

et al. 2024

Preprint

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“…Numerous properties in the time series can be revealed by the family of visibility graphs, for example, estimating the Hurst exponent of fractal stochastic processes [ 62 , 63 ], proving the relationship between the power-law degree distribution and fractality in series [ 57 ], analyzing multifractal properties of time series [ 64 ], and measuring the irreversibility of real-valued time series [ 65 – 67 ]. In addition, it has been applied in different fields to address practical problems, including studying the dynamics of a passive scalar plume [ 68 ], planning long-voyage routes [ 69 ], analyzing electroencephalogram signals [ 70 ], extracting hidden information in coupled timessss series [ 71 , 72 ], and aggregating data in complex systems [ 73 ].…”

Section: Introductionmentioning

confidence: 99%

Visibility graph for time series prediction and image classification: a review

2022

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The analysis of time series and images is significant across different fields due to their widespread applications. In the past few decades, many approaches have been developed, including data-driven artificial intelligence methods, mechanism-driven physical methods, and hybrid mechanism and data-driven models. Complex networks have been used to model numerous complex systems due to its characteristics, including time series prediction and image classification. In order to map time series and images into complex networks, many visibility graph algorithms have been developed, such as horizontal visibility graph, limited penetrable visibility graph, multiplex visibility graph, and image visibility graph. The family of visibility graph algorithms will construct different types of complex networks, including (un-) weighted, (un-) directed, and (single-) multi-layered networks, thereby focusing on different kinds of properties. Different types of visibility graph algorithms will be reviewed in this paper. Through exploring the topological structure and information in the network based on statistical physics, the property of time series and images can be discovered. In order to forecast (multivariate) time series, several variations of local random walk algorithms and different information fusion approaches are applied to measure the similarity between nodes in the network. Different forecasting frameworks are also proposed to consider the information in the time series based on the similarity. In order to classify the image, several machine learning models (such as support vector machine and linear discriminant) are used to classify images based on global features, local features, and multiplex features. Through various simulations on a variety of datasets, researchers have found that the visibility graph algorithm outperformed existing algorithms, both in time series prediction and image classification. Clearly, complex networks are closely connected with time series and images by visibility graph algorithms, rendering complex networks to be an important tool for understanding the characteristics of time series and images. Finally, we conclude in the last section with future outlooks for the visibility graph.

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“…The sign and weight of each link show the type and strength of the two connected companies. The constructed network can be analyzed by different models such as percolation [ 3 ] and random theory [ 11 , 12 ]. These models can help us to find new features and reveal hidden patterns in data.…”

Section: Introductionmentioning

confidence: 99%

Financial crisis in the framework of non-zero temperature balance theory

et al. 2022

Self Cite

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In financial crises, assets see a deep loss of value, and the financial markets experience liquidity shortages. Although they are not uncommon, they may cause by multiple contributing factors which makes them hard to study. To discover features of the financial network, the pairwise interaction of stocks has been considered in many pieces of research, but the existence of the strong correlation between stocks and their collective behavior in crisis made us address higher-order interactions. Hence, in this study, we investigate financial networks by triplet interaction in the framework of balance theory. Due to detecting the contribution of higher-order interactions in understanding the complex behavior of stocks we take the advantage of the order parameter of the higher-order interactions. Looking at real data of the financial market obtained from S&P500 index(SPX) through the lens of balance theory for the quest of network structure in different periods (on and off-crisis) faces us with the existence of a structural difference of networks corresponding to the periods. Addressing two well-known crises the Great regression (2008) and the Covid-19 recession (2020), our results show an ordered structure forms in the on-crisis period in the financial network while stocks behave independently far from a crisis. The formation of the ordered structure of stocks in crisis makes the network more resilient to disorder (thermal fluctuations). The resistance of the ordered structure against applying the disorder measure the crisis strength and determine the temperature at which the network transits. There is a critical temperature, Tc, in the language of statistical mechanics and mean-field approach which above, the ordered structure destroys abruptly and a first-order phase transition occurs. The stronger the crisis, the higher the critical temperature.

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Mapping coupled time-series onto a complex network

Cited by 5 publications

References 41 publications

Generalization of Chapman-Kolmogorov equation to two coupled processes

Generalization of Chapman-Kolmogorov equation to two coupled processes

Visibility graph for time series prediction and image classification: a review

Financial crisis in the framework of non-zero temperature balance theory

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