An Outlook on Correlations in Stock Prices

We present an outlook of the studies on correlations in the price timeseries of stocks, discussing the construction and applications of "asset tree". The topic discussed here should illustrate how the complex economic system (financial market) enrichens the list of existing dynamical systems that physicists have been studying for long.Comment: 6 pages, RevTeX format. To appear in the Conference Proceedings of ECONOPHYS-KOLKATA II: International Workshop on Econophysics of Stock Markets and Minority Games", February 14-17, 2006, SINP, Kolkata, as a book chapter in Eds. A. Chatterjee and B.K. Chakrabarti, Econophysics of Stock and other Markets, (Springer-Verlag (Italia), Milan, 2006

Clustering and information in correlation based financial networks

Networks of companies can be constructed by using return correlations. A crucial issue in this approach is to select the relevant correlations from the correlation matrix. In order to study this problem, we start from an empty graph with no edges where the vertices correspond to stocks. Then, one by one, we insert edges between the vertices according to the rank of their correlation strength, resulting in a network called asset graph. We study its properties, such as topologically different growth types, number and size of clusters and clustering coefficient. These properties, calculated from empirical data, are compared against those of a random graph. The growth of the graph can be classified according to the topological role of the newly inserted edge. We find that the type of growth which is responsible for creating cycles in the graph sets in much earlier for the empirical asset graph than for the random graph, and thus reflects the high degree of networking present in the market. We also find the number of clusters in the random graph to be one order of magnitude higher than for the asset graph. At a critical threshold, the random graph undergoes a radical change in topology related to percolation transition and forms a single giant cluster, a phenomenon which is not observed for the asset graph. Differences in mean clustering coefficient lead us to conclude that most information is contained roughly within 10% of the edges.Comment: 11 pages including 14 figures. Uses REVTeX4. To be published in a special volume of EPJ on network

The Spontaneous Emergence of Social Influence in Online Systems

Social influence drives both offline and online human behaviour. It pervades cultural markets, and manifests itself in the adoption of scientific and technical innovations as well as the spread of social practices. Prior empirical work on the diffusion of innovations in spatial regions or social networks has largely focused on the spread of one particular technology among a subset of all potential adopters. It has also been difficult to determine whether the observed collective behaviour is driven by natural influence processes, or whether it follows external signals such as media or marketing campaigns. Here, we choose an online context that allows us to study social influence processes by tracking the popularity of a complete set of applications installed by the user population of a social networking site, thus capturing the behaviour of all individuals who can influence each other in this context. By extending standard fluctuation scaling methods, we analyse the collective behaviour induced by 100 million application installations, and show that two distinct regimes of behaviour emerge in the system. Once applications cross a particular threshold of popularity, social influence processes induce highly correlated adoption behaviour among the users, which propels some of the applications to extraordinary levels of popularity. Below this threshold, the collective effect of social influence appears to vanish almost entirely in a manner that has not been observed in the offline world. Our results demonstrate that even when external signals are absent, social influence can spontaneously assume an on-off nature in a digital environment. It remains to be seen whether a similar outcome could be observed in the offline world if equivalent experimental conditions could be replicated

Dynamic asset trees and Black Monday

The minimum spanning tree, based on the concept of ultrametricity, is constructed from the correlation matrix of stock returns. The dynamics of this asset tree can be characterised by its normalised length and the mean occupation layer, as measured from an appropriately chosen centre called the `central node'. We show how the tree length shrinks during a stock market crisis, Black Monday in this case, and how a strong reconfiguration takes place, resulting in topological shrinking of the tree.Comment: 6 pages, 3 eps figues. Elsevier style. Will appear in Physica A as part of the Bali conference proceedings, in pres

Close relationships: A study of mobile communication records

Mobile phone communication as digital service generates ever-increasing datasets of human communication actions, which in turn allow us to investigate the structure and evolution of social interactions and their networks. These datasets can be used to study the structuring of such egocentric networks with respect to the strength of the relationships by assuming direct dependence of the communication intensity on the strength of the social tie. Recently we have discovered that there are significant differences between the first and further "best friends" from the point of view of age and gender preferences. Here we introduce a control parameter $p_{\rm max}$ based on the statistics of communication with the first and second "best friend" and use it to filter the data. We find that when $p_{\rm max}$ is decreased the identification of the "best friend" becomes less ambiguous and the earlier observed effects get stronger, thus corroborating them.Comment: 11 pages, 7 figure

The evolution of interdisciplinarity in physics research

Science, being a social enterprise, is subject to fragmentation into groups that focus on specialized areas or topics. Often new advances occur through cross-fertilization of ideas between sub-fields that otherwise have little overlap as they study dissimilar phenomena using different techniques. Thus to explore the nature and dynamics of scientific progress one needs to consider the large-scale organization and interactions between different subject areas. Here, we study the relationships between the sub-fields of Physics using the Physics and Astronomy Classification Scheme (PACS) codes employed for self-categorization of articles published over the past 25 years (1985-2009). We observe a clear trend towards increasing interactions between the different sub-fields. The network of sub-fields also exhibits core-periphery organization, the nucleus being dominated by Condensed Matter and General Physics. However, over time Interdisciplinary Physics is steadily increasing its share in the network core, reflecting a shift in the overall trend of Physics research.Comment: Published version, 10 pages, 8 figures + Supplementary Informatio

Community Structure in Time-Dependent, Multiscale, and Multiplex Networks

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly-connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows one to study community structure in a very general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.Comment: 31 pages, 3 figures, 1 table. Includes main text and supporting material. This is the accepted version of the manuscript (the definitive version appeared in Science), with typographical corrections included her

Dynamic asset trees and portfolio analysis

The minimum spanning tree, based on the concept of ultrametricity, is constructed from the correlation matrix of stock returns and provides a meaningful economic taxonomy of the stock market. In order to study the dynamics of this asset tree we characterize it by its normalized length and by the mean occupation layer, as measured from an appropriately chosen center. We show how the tree evolves over time, and how it shrinks particularly strongly during a stock market crisis. We then demonstrate that the assets of the optimal Markowitz portfolio lie practically at all times on the outskirts of the tree. We also show that the normalized tree length and the investment diversification potential are very strongly correlated.Comment: 9 pages, 3 figures (encapsulated postscript

Effects of time window size and placement on the structure of aggregated networks

Complex networks are often constructed by aggregating empirical data over time, such that a link represents the existence of interactions between the endpoint nodes and the link weight represents the intensity of such interactions within the aggregation time window. The resulting networks are then often considered static. More often than not, the aggregation time window is dictated by the availability of data, and the effects of its length on the resulting networks are rarely considered. Here, we address this question by studying the structural features of networks emerging from aggregating empirical data over different time intervals, focussing on networks derived from time-stamped, anonymized mobile telephone call records. Our results show that short aggregation intervals yield networks where strong links associated with dense clusters dominate; the seeds of such clusters or communities become already visible for intervals of around one week. The degree and weight distributions are seen to become stationary around a few days and a few weeks, respectively. An aggregation interval of around 30 days results in the stablest similar networks when consecutive windows are compared. For longer intervals, the effects of weak or random links become increasingly stronger, and the average degree of the network keeps growing even for intervals up to 180 days. The placement of the time window is also seen to affect the outcome: for short windows, different behavioural patterns play a role during weekends and weekdays, and for longer windows it is seen that networks aggregated during holiday periods are significantly different.Comment: 19 pages, 11 figure