Binary versus non-binary information in real time series: empirical results and maximum-entropy matrix models

The dynamics of complex systems, from financial markets to the brain, can be monitored in terms of multiple time series of activity of the constituent units, such as stocks or neurons respectively. While the main focus of time series analysis is on the magnitude of temporal increments, a significant piece of information is encoded into the binary projection (i.e. the sign) of such increments. In this paper we provide further evidence of this by showing strong nonlinear relations between binary and non-binary properties of financial time series. These relations are a novel quantification of the fact that extreme price increments occur more often when most stocks move in the same direction. We then introduce an information-theoretic approach to the analysis of the binary signature of single and multiple time series. Through the definition of maximum-entropy ensembles of binary matrices and their mapping to spin models in statistical physics, we quantify the information encoded into the simplest binary properties of real time series and identify the most informative property given a set of measurements. Our formalism is able to accurately replicate, and mathematically characterize, the observed binary/non-binary relations. We also obtain a phase diagram allowing us to identify, based only on the instantaneous aggregate return of a set of multiple time series, a regime where the so-called `market mode' has an optimal interpretation in terms of collective (endogenous) effects, a regime where it is parsimoniously explained by pure noise, and a regime where it can be regarded as a combination of endogenous and exogenous factors. Our approach allows us to connect spin models, simple stochastic processes, and ensembles of time series inferred from partial information

Enhanced Gravity Model of trade: reconciling macroeconomic and network models

The structure of the International Trade Network (ITN), whose nodes and links represent world countries and their trade relations respectively, affects key economic processes worldwide, including globalization, economic integration, industrial production, and the propagation of shocks and instabilities. Characterizing the ITN via a simple yet accurate model is an open problem. The traditional Gravity Model (GM) successfully reproduces the volume of trade between connected countries, using macroeconomic properties such as GDP, geographic distance, and possibly other factors. However, it predicts a network with complete or homogeneous topology, thus failing to reproduce the highly heterogeneous structure of the ITN. On the other hand, recent maximum-entropy network models successfully reproduce the complex topology of the ITN, but provide no information about trade volumes. Here we integrate these two currently incompatible approaches via the introduction of an Enhanced Gravity Model (EGM) of trade. The EGM is the simplest model combining the GM with the network approach within a maximum-entropy framework. Via a unified and principled mechanism that is transparent enough to be generalized to any economic network, the EGM provides a new econometric framework wherein trade probabilities and trade volumes can be separately controlled by any combination of dyadic and country-specific macroeconomic variables. The model successfully reproduces both the global topology and the local link weights of the ITN, parsimoniously reconciling the conflicting approaches. It also indicates that the probability that any two countries trade a certain volume should follow a geometric or exponential distribution with an additional point mass at zero volume

A GDP-driven model for the binary and weighted structure of the International Trade Network

Recent events such as the global financial crisis have renewed the interest in the topic of economic networks. One of the main channels of shock propagation among countries is the International Trade Network (ITN). Two important models for the ITN structure, the classical gravity model of trade (more popular among economists) and the fitness model (more popular among networks scientists), are both limited to the characterization of only one representation of the ITN. The gravity model satisfactorily predicts the volume of trade between connected countries, but cannot reproduce the observed missing links (i.e. the topology). On the other hand, the fitness model can successfully replicate the topology of the ITN, but cannot predict the volumes. This paper tries to make an important step forward in the unification of those two frameworks, by proposing a new GDP-driven model which can simultaneously reproduce the binary and the weighted properties of the ITN. Specifically, we adopt a maximum-entropy approach where both the degree and the strength of each node is preserved. We then identify strong nonlinear relationships between the GDP and the parameters of the model. This ultimately results in a weighted generalization of the fitness model of trade, where the GDP plays the role of a `macroeconomic fitness' shaping the binary and the weighted structure of the ITN simultaneously. Our model mathematically highlights an important asymmetry in the role of binary and weighted network properties, namely the fact that binary properties can be inferred without the knowledge of weighted ones, while the opposite is not true

Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations

The mesoscopic organization of complex systems, from financial markets to the brain, is an intermediate between the microscopic dynamics of individual units (stocks or neurons, in the mentioned cases), and the macroscopic dynamics of the system as a whole. The organization is determined by "communities" of units whose dynamics, represented by time series of activity, is more strongly correlated internally than with the rest of the system. Recent studies have shown that the binary projections of various financial and neural time series exhibit nontrivial dynamical features that resemble those of the original data. This implies that a significant piece of information is encoded into the binary projection (i.e. the sign) of such increments. Here, we explore whether the binary signatures of multiple time series can replicate the same complex community organization of the financial market, as the original weighted time series. We adopt a method that has been specifically designed to detect communities from cross-correlation matrices of time series data. Our analysis shows that the simpler binary representation leads to a community structure that is almost identical with that obtained using the full weighted representation. These results confirm that binary projections of financial time series contain significant structural information.Comment: 15 pages, 7 figure

Enhanced Gravity Model of trade: reconciling macroeconomic and network models

The structure of the International Trade Network (ITN), whose nodes and links represent world countries and their trade relations respectively, affects key economic processes worldwide, including globalization, economic integration, industrial production, and the propagation of shocks and instabilities. Characterizing the ITN via a simple yet accurate model is an open problem. The traditional Gravity Model successfully reproduces the volume of trade between connected countries, using macroeconomic properties such as GDP, geographic distance, and possibly other factors. However, it predicts a network with complete or homogeneous topology, thus failing to reproduce the highly heterogeneous structure of the ITN. On the other hand, recent maximum-entropy network models successfully reproduce the complex topology of the ITN, but provide no information about trade volumes. Here we integrate these two currently incompatible approaches via the introduction of an Enhanced Gravity Model (EGM) of trade. The EGM is the simplest model combining the Gravity Model with the network approach within a maximum-entropy framework. Via a unified and principled mechanism that is transparent enough to be generalized to any economic network, the EGM provides a new econometric framework wherein trade probabilities and trade volumes can be separately controlled by any combination of dyadic and country-specific macroeconomic variables. The model successfully reproduces both the global topology and the local link weights of the ITN, parsimoniously reconciling the conflicting approaches. It also indicates that the probability that any two countries trade a certain volume should follow a geometric or exponential distribution with an additional point mass at zero volume

Enhanced Gravity Model of Trade: Reconciling Macroeconomic and Network Models

The structure of the International Trade Network (ITN), whose nodes and links represent world countries and their trade relations, respectively, affects key economic processes worldwide, including globalization, economic integration, industrial production, and the propagation of shocks and instabilities. Characterizing the ITN via a simple yet accurate model is an open problem. The traditional Gravity Model (GM) successfully reproduces the volume of trade between connected countries, using macroeconomic properties, such as GDP, geographic distance, and possibly other factors. However, it predicts a network with complete or homogeneous topology, thus failing to reproduce the highly heterogeneous structure of the ITN. On the other hand, recent maximum entropy network models successfully reproduce the complex topology of the ITN, but provide no information about trade volumes. Here we integrate these two currently incompatible approaches via the introduction of an Enhanced Gravity Model (EGM) of trade. The EGM is the simplest model combining the GM with the network approach within a maximum-entropy framework. Via a unified and principled mechanism that is transparent enough to be generalized to any economic network, the EGM provides a new econometric framework wherein trade probabilities and trade volumes can be separately controlled by any combination of dyadic and country-specific macroeconomic variables. The model successfully reproduces both the global topology and the local link weights of the ITN, parsimoniously reconciling the conflicting approaches. It also indicates that the probability that any two countries trade a certain volume should follow a geometric or exponential distribution with an additional point mass at zero volume

Uncovering functional brain signature via random matrix theory

The brain is organized in a modular way, serving multiple functionalities. This multiplicity requires that both positive (e.g. excitatory, phase-coherent) and negative (e.g. inhibitory, phase-opposing) interactions take place across brain modules. Unfortunately, most methods to detect modules from time series either neglect or convert to positive any measured negative correlation. This may leave a significant part of the sign-dependent functional structure undetected. Here we present a novel method, based on random matrix theory, for the identification of sign-dependent modules in the brain. Our method filters out the joint effects of local (unit-specific) noise and global (system-wide) dependencies that empirically obfuscate such structure. The method is guaranteed to identify an optimally contrasted functional `signature', i.e. a partition into modules that are positively correlated internally and negatively correlated across. The method is purely data-driven, does not use any arbitrary threshold or network projection, and outputs only statistically significant structure. In measurements of neuronal gene expression in the biological clock of mice, the method systematically uncovers two otherwise undetectable, negatively correlated modules whose relative size and mutual interaction strength are found to depend on photoperiod. The neurons alternating between the two modules define a candidate region of functional plasticity for circadian modulation

Wealth management in Singapore

<p>Each community is labelled with the number of stocks, and the pie chart represents the relative composition of each community based on the industry sectors of the constituent stocks (color legend in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133679#pone.0133679.t001" target="_blank">Table 1</a>). The inter-community link weights are negative, indicating that the communities are all residually anti-correlated.</p