Applying complexity science to air traffic management

Versión aceptada obtenida del archivo digital en línea WestminsterResearch de la Universidad de Westminster. Complexity science is the multidisciplinary study of complex systems. Its marked network orientation lends itself well to transport contexts. Key features of complexity science are introduced and defined, with a specific focus on the application to air traffic management. An overview of complex network theory is presented, with examples of its corresponding metrics and multiple scales. Complexity science is starting to make important contributions to performance assessment and system design: selected, applied air traffic management case studies are explored. The important contexts of…

Taxonomy of stock market indices

We investigate sets of financial non-redundant and nonsynchronously recorded time series. The sets are composed by a number of stock market indices located all over the world in five continents. By properly selecting the time horizon of returns and by using a reference currency we find a meaningful taxonomy. The detection of such a taxonomy proves that interpretable information can be stored in a set of nonsynchronously recorded time series.

Multi-scale analysis of the European airspace using network community detection

We show that the European airspace can be represented as a multi-scale traffic network whose nodes are airports, sectors, or navigation points and links are defined and weighted according to the traffic of flights between the nodes. By using a unique database of the air traffic in the European airspace, we investigate the architecture of these networks with a special emphasis on their community structure. We propose that unsupervised network community detection algorithms can be used to monitor the current use of the airspaces and improve it by guiding the design of new ones. Specifically, we compare the performance of three community detection algorithms, also by using a null model which t…

Backbone of credit relationships in the Japanese credit market

We detect the backbone of the weighted bipartite network of the Japanese credit market relationships. The backbone is detected by adapting a general method used in the investigation of weighted networks. With this approach we detect a backbone that is statistically validated against a null hypothesis of uniform diversification of loans for banks and firms. Our investigation is done year by year and it covers more than thirty years during the period from 1980 to 2011. We relate some of our findings with economic events that have characterized the Japanese credit market during the last years. The study of the time evolution of the backbone allows us to detect changes occurred in network size,…

Anomalous Spreading of Power-Law Quantum Wave Packets

We introduce power-law tail quantum wave packets. We show that they can be seen as eigenfunctions of a Hamiltonian with a physical potential. We prove that the free evolution of these packets presents an asymptotic decay of the maximum of the wave packets which is anomalous for an interval of the characterizing power-law exponent. We also prove that the number of finite moments of the wave packets is a conserved quantity during the evolution of the wave packet in the free space.

Identification of clusters of investors from their real trading activity in a financial market

We use statistically validated networks, a recently introduced method to validate links in a bipartite system, to identify clusters of investors trading in a financial market. Specifically, we investigate a special database allowing to track the trading activity of individual investors of the stock Nokia. We find that many statistically detected clusters of investors show a very high degree of synchronization in the time when they decide to trade and in the trading action taken. We investigate the composition of these clusters and we find that several of them show an over-expression of specific categories of investors.

Variety and volatility in financial markets

We study the price dynamics of stocks traded in a financial market by considering the statistical properties both of a single time series and of an ensemble of stocks traded simultaneously. We use the $n$ stocks traded in the New York Stock Exchange to form a statistical ensemble of daily stock returns. For each trading day of our database, we study the ensemble return distribution. We find that a typical ensemble return distribution exists in most of the trading days with the exception of crash and rally days and of the days subsequent to these extreme events. We analyze each ensemble return distribution by extracting its first two central moments. We observe that these moments are fluctua…

Bank-firm credit network in Japan. An analysis of a bipartite network

We present an analysis of the credit market of Japan. The analysis is performed by investigating the bipartite network of banks and firms which is obtained by setting a link between a bank and a firm when a credit relationship is present in a given time window. In our investigation we focus on a community detection algorithm which is identifying communities composed by both banks and firms. We show that the clusters obtained by directly working on the bipartite network carry information about the networked nature of the Japanese credit market. Our analysis is performed for each calendar year during the time period from 1980 to 2011. Specifically, we obtain communities of banks and networks …

An empirically grounded agent based model for modeling directs, conflict detection and resolution operations in air traffic management

We present an agent based model of the Air Traffic Management socio-technical complex system that aims at modeling the interactions between aircrafts and air traffic controllers at a tactical level. The core of the model is given by the conflict detection and resolution module and by the directs module. Directs are flight shortcuts that are given by air controllers to speed up the passage of an aircraft within a certain airspace and therefore to facilitate airline operations. Conflicts resolution between flight trajectories can arise during the en-route phase of each flight due to both not detailed flight trajectory planning or unforeseen events that perturb the planned flight plan. Our mod…

Do firms share the same functional form of their growth rate distribution? A statistical test

We introduce a new statistical test of the hypothesis that a balanced panel of firms have the same growth rate distribution or, more generally, that they share the same functional form of growth rate distribution. We applied the test to European Union and US publicly quoted manufacturing firms data, considering functional forms belonging to the Subbotin family of distributions. While our hypotheses are rejected for the vast majority of sets at the sector level, we cannot rejected them at the subsector level, indicating that homogenous panels of firms could be described by a common functional form of growth rate distribution.

Quantum Stochastic Resonance in a Micromaser

We demonstrate that quantum stochastic resonance allows for the noise-controlled synchronization of quantum jumps between the metastable states of the quantized radiation field in a micromaser. Under readily accessible experimental conditions optimal synchronization is achieved at a finite temperature $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}500\mathrm{mK}$ of the environment.

Network structure and optimal technological innovation

The role of networks in the emergence, diffusion and evolution of technological innovations has attracted much theoretical and empirical attention. Yet, much of the work has explored the role of undirected and homogeneous networks. In real cases, many networks are directed. The flow of information, benefits or observations is directed from one node towards another node. Real networks are also heterogeneous, for example, few nodes have a high degree while many others have a low degree. In this article, we report on the results of an evolutionary agent-based model in which a group of agents, in our case firms, collectively search a complex (rugged) technological landscape and observe each oth…

Hierarchical Structure in Financial Markets

I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between all pairs of stocks of the portfolio by considering the synchronous time evolution of the difference of the logarithm of daily stock price. The hierarchical tree of the subdominant ultrametric space associated with the graph provides information useful to investigate the number and nature of the common economic factors affecting the time evolution of logarithm of price of well defined groups of sto…

The Rise and Fall of Business Firms: A Stochastic Framework on Innovation, Creative

High Frequency Data Analysis in an Emerging and a Developed Market

We compare distributional properties of high frequency (tick by tick) returns of stocks traded at the NASDAQ, NYSE, and BSE (Budapest Stock Exchange). In particular, we model returns with a mixture of a degenerate (zero) and a symmetric stable distribution. We measure time with the number of successive price changes on the market and study the convergence of the index of stability on increasing time horizons. We apply results to calculate expected waiting times to reach given levels of value at risk.

Numerical Analysis of Word Frequencies in Artificial and Natural Language Texts

We perform a numerical study of the statistical properties of natural texts written in English and of two types of artificial texts. As statistical tools we use the conventional Zipf analysis of the distribution of words and the inverse Zipf analysis of the distribution of frequencies of words, the analysis of vocabulary growth, the Shannon entropy and a quantity which is a nonlinear function of frequencies of words, the frequency "entropy". Our numerical results, obtained by investigation of eight complete books and sixteen related artificial texts, suggest that, among these analyses, the analysis of vocabulary growth shows the most striking difference between natural and artificial texts…

Bootstrap validation of links of a minimum spanning tree

We describe two different bootstrap methods applied to the detection of a minimum spanning tree obtained from a set of multivariate variables. We show that two different bootstrap procedures provide partly distinct information that can be highly informative about the investigated complex system. Our case study, based on the investigation of daily returns of a portfolio of stocks traded in the US equity markets, shows the degree of robustness and completeness of the information extracted with popular information filtering methods such as the minimum spanning tree and the planar maximally filtered graph. The first method performs a "row bootstrap" whereas the second method performs a "pair bo…

Quantifying the relationship between specialisation and reputation in an online platform

AbstractOnline platforms implement digital reputation systems in order to steer individual user behaviour towards outcomes that are deemed desirable on a collective level. At the same time, most online platforms are highly decentralised environments, leaving their users plenty of room to pursue different strategies and diversify behaviour. We provide a statistical characterisation of the user behaviour emerging from the interplay of such competing forces in Stack Overflow, a long-standing knowledge sharing platform. Over the 11 years covered by our analysis, we represent the interactions between users and topics as bipartite networks. We find such networks to display nested structures akin …

Linear and nonlinear experimental regimes of stochastic resonance

We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude. We observe both a regime described by the linear response theory and the nonlinear deviation from it. In the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density. When these effects are observed we detect a phase and frequency synchronization between the st…

Scale-free relaxation of a wave packet in a quantum well with power-law tails

We propose a setup for which a power-law decay is predicted to be observable for generic and realistic conditions. The system we study is very simple: A quantum wave packet initially prepared in a potential well with (i) tails asymptotically decaying like ~ x^{-2} and (ii) an eigenvalues spectrum that shows a continuous part attached to the ground or equilibrium state. We analytically derive the asymptotic decay law from the spectral properties for generic, confined initial states. Our findings are supported by realistic numerical simulations for state-of-the-art expansion experiments with cold atoms.

Long-term ecology of investors in a financial market

AbstractThe cornerstone of modern finance is the efficient market hypothesis. Under this hypothesis all information available about a financial asset is immediately incorporated into its price dynamics by fully rational investors. In contrast to this hypothesis many studies have pointed out behavioral biases in investors. Recently it has become possible to access databases that track the trading decisions of investors. Studies of such databases have shown that investors acting in a financial market are highly heterogeneous among them, and that heterogeneity is a common characteristic of many financial markets. The article describes an empirical study of the daily trading decisions of all Fi…

Univariate and multivariate statistical aspects of equity volatility

We discuss univariate and multivariate statistical properties of volatility time series of equities traded in a financial market. Specifically, (i) we introduce a two-region stochastic volatility model able to well describe the unconditional pdf of volatility in a wide range of values and (ii) we quantify the stability of the results of a correlation-based clustering procedure applied to synchronous time evolution of a set of volatility time series.

Statistically validated networks in bipartite complex systems.

Many complex systems present an intrinsic bipartite nature and are often described and modeled in terms of networks [1-5]. Examples include movies and actors [1, 2, 4], authors and scientific papers [6-9], email accounts and emails [10], plants and animals that pollinate them [11, 12]. Bipartite networks are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set. When one constructs a projected network with nodes from only one set, the system heterogeneity makes it very difficult to identify preferential links between the elements. Here we introduce an unsupervised method to statistically validate each link of the pr…

Information and hierarchical structure in financial markets

I investigate the information content present in the time series of stock prices of a portfolio of stocks traded in a financial market. By investigating the correlation coefficient between pairs of stocks I provide a working definition of a generalized distance between the stocks of the portfolio. This generalized distance is used to obtain an ultrametric distance matrix between the stocks. The ultrametric structure of the portfolio investigated has associated a taxonomy which is meaningful from an economic point of view.

Quantifying Preferential Trading in the e-MID Interbank Market

Interbank markets allow credit institutions to exchange capital for purposes of liquidity management. These markets are among the most liquid markets in the financial system. However, liquidity of interbank markets dropped during the 2007-2008 financial crisis, and such a lack of liquidity influenced the entire economic system. In this paper, we analyze transaction data from the e-MID market which is the only electronic interbank market in the Euro Area and US, over a period of eleven years (1999-2009). We adapt a method developed to detect statistically validated links in a network, in order to reveal preferential trading in a directed network. Preferential trading between banks is detecte…

Statistical properties of thermodynamically predicted RNA secondary structures in viral genomes

By performing a comprehensive study on 1832 segments of 1212 complete genomes of viruses, we show that in viral genomes the hairpin structures of thermodynamically predicted RNA secondary structures are more abundant than expected under a simple random null hypothesis. The detected hairpin structures of RNA secondary structures are present both in coding and in noncoding regions for the four groups of viruses categorized as dsDNA, dsRNA, ssDNA and ssRNA. For all groups hairpin structures of RNA secondary structures are detected more frequently than expected for a random null hypothesis in noncoding rather than in coding regions. However, potential RNA secondary structures are also present i…

Kullback-Leibler distance as a measure of the information filtered from multivariate data

We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation matrix from a reference model and we show that the expected values are known also when the specific model is unknown. We propose to make use of the Kullback-Leibler distance to estimate the information extracted from a correlation matrix by correlation filtering procedures. We also show how to use this distance to measure the stability of filtering procedures with respect to s…

Turbulence and financial markets

Modeling the Dynamics of a Financial Index after a Crash

Supply and demand are perhaps the most fundamental concepts in economics. In a financial market they reflects the orders of the agents to buy or sell a given asset. In turn the fluctuations of supply and demand influence the dynamics of the price of an asset, as, for example, a stock or a financial index. Therefore the dynamics of the price of an asset is affected by the actions and of the beliefs of the agents. It is known that the dynamics of the price of an asset is far from simple, Several stylized facts has been empirically discovered such as, for example, the fat tails in the return distribution and the clustered volatility. These stylized facts has been detected by considering long t…

A comparative analysis of the statistical properties of large mobile phone calling networks.

Mobile phone calling is one of the most widely used communication methods in modern society. The records of calls among mobile phone users provide us a valuable proxy for the understanding of human communication patterns embedded in social networks. Mobile phone users call each other forming a directed calling network. If only reciprocal calls are considered, we obtain an undirected mutual calling network. The preferential communication behavior between two connected users can be statistically tested and it results in two Bonferroni networks with statistically validated edges. We perform a comparative analysis of the statistical properties of these four networks, which are constructed from …

Focus on statistical physics modeling in economics and finance

This focus issue presents a collection of papers on recent results in statistical physics modeling in economics and finance, commonly known as econophysics. We touch briefly on the history of this relatively new multi-disciplinary field, summarize the motivations behind its emergence and try to characterize its specific features. We point out some research aspects that must be improved and briefly discuss the topics the research field is moving toward. Finally, we give a short account of the papers collected in this issue.

Evolution of Worldwide Stock Markets, Correlation Structure and Correlation Based Graphs

We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period Jan 1996 - Jul 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globalization. The fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system. We provide evidence that the short term timescale of correlation among market indices is less than 3 trading months (about 60 trading days). The average values of the non diagonal elements of the correlation matrix, corre…

Statistical identification with hidden Markov models of large order splitting strategies in an equity market

Large trades in a financial market are usually split into smaller parts and traded incrementally over extended periods of time. We address these large trades as hidden orders. In order to identify and characterize hidden orders we fit hidden Markov models to the time series of the sign of the tick by tick inventory variation of market members of the Spanish Stock Exchange. Our methodology probabilistically detects trading sequences, which are characterized by a net majority of buy or sell transactions. We interpret these patches of sequential buying or selling transactions as proxies of the traded hidden orders. We find that the time, volume and number of transactions size distributions of …

Statistically validated mobile communication networks: the evolution of motifs in European and Chinese data

Big data open up unprecedented opportunities to investigate complex systems including the society. In particular, communication data serve as major sources for computational social sciences but they have to be cleaned and filtered as they may contain spurious information due to recording errors as well as interactions, like commercial and marketing activities, not directly related to the social network. The network constructed from communication data can only be considered as a proxy for the network of social relationships. Here we apply a systematic method, based on multiple hypothesis testing, to statistically validate the links and then construct the corresponding Bonferroni network, gen…

Patterns of trading profiles at the Nordic Stock Exchange. A correlation-based approach.

We investigate the trading behavior of Finnish individual investors trading the stocks selected to compute the OMXH25 index in 2003 by tracking the individual daily investment decisions. We verify that the set of investors is a highly heterogeneous system under many aspects. We introduce a correlation based method that is able to detect a hierarchical structure of the trading profiles of heterogeneous individual investors. We verify that the detected hierarchical structure is highly overlapping with the cluster structure obtained with the approach of statistically validated networks when an appropriate threshold of the hierarchical trees is used. We also show that the combination of the cor…

Detecting informative higher-order interactions in statistically validated hypergraphs

Recent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. These data are better described by hypergraphs, where hyperlinks encode higher-order interactions among a group of nodes. In spite of the large number of works on networks, highlighting informative hyperlinks in hypergraphs obtained from real world data is still an open problem. Here we propose an analytic approach to filter hypergraphs by identifying those hyperlinks that are over-expressed with respect to a random null hypothesis, and represent the most relevant higher-order connections. We apply…

Stochastic resonance in magnetic systems described by Preisach hysteresis model

We present a numerical study of stochastic resonance in magnetic systems described by Preisach hysteresis model. It is shown that stochastic resonance occurs in these systems. Specifically, the signal-to-noise ratio sSNRd and the signal amplification sSAd present a maximum as a function of noise intensity. We also found that the hysteresis loops, dynamically described by the system, are strongly modified near the maxima of SNR and of SA.

Statistical characterization of deviations from planned flight trajectories in air traffic management

Understanding the relation between planned and realized flight trajectories and the determinants of flight deviations is of great importance in air traffic management. In this paper we perform an in depth investigation of the statistical properties of planned and realized air traffic on the German airspace during a 28 day periods, corresponding to an AIRAC cycle. We find that realized trajectories are on average shorter than planned ones and this effect is stronger during night-time than daytime. Flights are more frequently deviated close to the departure airport and at a relatively large angle to destination. Moreover, the probability of a deviation is higher in low traffic phases. All the…

The value of statistical laws in physics and social sciences

The deterministic conception of nature implies in itself a real cause of weakness in the irremediable contradiction that it faces with the most certain data of our consciousness. G. SOREL attempted to compose this disagreement with the distinction between artificial nature and natural nature (this last acausal), but in this way he denied the unity of science. On the other hand, the formal analogy between the statistical laws of physics and the ones of social sciences credited the opinion that human facts also undergo a rigid determinism. It is therefore important that quantum mechanics principles have brought to recognize the statistical character of basic laws of elementary processes, in a…

Specialization and herding behavior of trading firms in a financial market

Agent-based models of financial markets usually make assumptions about agent’s preferred stylized strategies. Empirical validations of these assumptions have not been performed so far on a full-market scale. Here we present a comprehensive study of the resulting strategies followed by the firms which are members of the Spanish Stock Exchange. We are able to show that they can be characterized by a resulting strategy and classified in three well- defined groups of firms. Firms of the first group have a change of inventory of the traded stock which is positively correlated with the synchronous stock return whereas firms of the second group show a negative correlation. Firms of the third group…

Degree stability of a minimum spanning tree of price return and volatility

We investigate the time series of the degree of minimum spanning trees obtained by using a correlation based clustering procedure which is starting from (i) asset return and (ii) volatility time series. The minimum spanning tree is obtained at different times by computing correlation among time series over a time window of fixed length $T$. We find that the minimum spanning tree of asset return is characterized by stock degree values, which are more stable in time than the ones obtained by analyzing a minimum spanning tree computed starting from volatility time series. Our analysis also shows that the degree of stocks has a very slow dynamics with a time-scale of several years in both cases.

Empirical investigation of stock price dynamics in an emerging market

Abstract We study the development of an emerging market – the Budapest Stock Exchange – by investigating the time evolution of some statistical properties of heavily traded stocks. Moving quarter by quarter over a period of two and a half years we analyze the scaling properties of the standard deviation of intra-day log-price changes. We observe scaling using both seconds and ticks as units of time. For the investigated stocks a Levy shape is a good approximation to the probability density function of tick-by-tick log-price changes in each quarter: the index of the distribution follows an increasing trend, suggesting it could be used as a measure of market efficiency.

THE ROLE OF UNBOUNDED TIME-SCALES IN GENERATING LONG-RANGE MEMORY IN ADDITIVE MARKOVIAN PROCESSES

Any additive stationary and continuous Markovian process described by a Fokker–Planck equation can also be described in terms of a Schrödinger equation with an appropriate quantum potential. By using such analogy, it has been proved that a power-law correlated stationary Markovian process can stem from a quantum potential that (i) shows an x-2 decay for large x values and (ii) whose eigenvalue spectrum admits a null eigenvalue and a continuum part of positive eigenvalues attached to it. In this paper we show that such two features are both necessary. Specifically, we show that a potential with tails decaying like x-μ with μ < 2 gives rise to a stationary Markovian process which is not p…

Econophysics: Scaling and its breakdown in finance

We discuss recent empirical results obtained by analyzing high-frequency data of a stock market index, the Standard and Poor’s 500. We focus on the scaling properties and on its breakdown of the index dynamics. A simple stochastic model, the truncated Levy flight, is illustrated. Successes and limitations of this model are presented. A discussion about similarities and differences between the scaling properties observed in financial markets and in fully developed turbulence is also provided.

Emergence of Statistically Validated Financial Intraday Lead-Lag Relationships

According to the leading models in modern finance, the presence of intraday lead-lag relationships between financial assets is negligible in efficient markets. With the advance of technology, however, markets have become more sophisticated. To determine whether this has resulted in an improved market efficiency, we investigate whether statistically significant lagged correlation relationships exist in financial markets. We introduce a numerical method to statistically validate links in correlation-based networks, and employ our method to study lagged correlation networks of equity returns in financial markets. Crucially, our statistical validation of lead-lag relationships accounts for mult…

Price Impact Function of a Single Transaction

Although supply and demand are perhaps the most fundamental concepts in economics, finding any general form for their behavior has proved to be elusive. Here we discuss our recent findings [1] on the price impact function empirically detected in the New York Stock Exchange (NYSE). Our study builds on earlier studies of how trading affects prices [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. In particular, we look at the short term response to a single trade. This is done by using huge amounts of data and by measuring the market activity in units of transactions rather than seconds, so that we can more naturally aggregate data for many different stocks. This allows us to find regularities in the respons…

Hierarchically nested factor model from multivariate data

We show how to achieve a statistical description of the hierarchical structure of a multivariate data set. Specifically we show that the similarity matrix resulting from a hierarchical clustering procedure is the correlation matrix of a factor model, the hierarchically nested factor model. In this model, factors are mutually independent and hierarchically organized. Finally, we use a bootstrap based procedure to reduce the number of factors in the model with the aim of retaining only those factors significantly robust with respect to the statistical uncertainty due to the finite length of data records.

Inverted Repeats in Viral Genomes

We investigate 738 complete genomes of viruses to detect the presence of short inverted repeats. The number of inverted repeats found is compared with the prediction obtained for a Bernoullian and for a Markovian control model. We find as a statistical regularity that the number of observed inverted repeats is often greater than the one expected in terms of a Bernoullian or Markovian model in several of the viruses and in almost all those with a genome longer than 30,000 bp.

Statistical Properties of Statistical Ensembles of Stock Returns

We select n stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the k trading days of our database from the stock price time series. We analyze each ensemble of stock returns by extracting its first four central moments. We observe that these moments are fluctuating in time and are stochastic processes themselves. We characterize the statistical properties of central moments by investigating their probability density function and temporal correlation properties.

Identification of clusters of companies in stock indices via Potts super-paramagnetic transitions

The clustering of companies within a specific stock market index is studied by means of super-paramagnetic transitions of an appropriate q-state Potts model where the spins correspond to companies and the interactions are functions of the correlation coefficients determined from the time dependence of the companies' individual stock prices. The method is a generalization of the clustering algorithm by Domany et. al. to the case of anti-ferromagnetic interactions corresponding to anti-correlations. For the Dow Jones Industrial Average where no anti-correlations were observed in the investigated time period, the previous results obtained by different tools were well reproduced. For the Standa…

Noise Enhanced Stability in an Unstable System

We experimentally detect noise enhanced stability in an unstable physical system. The average escape time from a metastable, periodically driven, system is measured in the stable and unstable regimes in a noisy environment. In the unstable regime, we measure that the average escape time has a maximum for a finite value of the noise intensity. The scaling properties of the average escape time and of the variance of escape times are compared with the predictions obtained for a system in a marginal state.

Hybrid recommendation methods in complex networks

We propose here two new recommendation methods, based on the appropriate normalization of already existing similarity measures, and on the convex combination of the recommendation scores derived from similarity between users and between objects. We validate the proposed measures on three relevant data sets, and we compare their performance with several recommendation systems recently proposed in the literature. We show that the proposed similarity measures allow to attain an improvement of performances of up to 20\% with respect to existing non-parametric methods, and that the accuracy of a recommendation can vary widely from one specific bipartite network to another, which suggests that a …

Special issue of Quantitative Finance on ‘Interlinkages and Systemic Risk’

This special issue of Quantitative Finance collects eight papers on the relation between interlinkages and systemic risk. The papers cover several types of interlinkages and follow different approaches, from agent-based modelling to empirical investigation of large and sometimes confidential data. The special issue collects some of the contributions presented at the international workshop‘Interlinkages and systemic risk ’ , which took place in Ancona (Italy) on 4 – 5 July 2013. The workshop, organized within the research project‘. New tools in the credit network modeling with agents ’ heterogeneity ’ funded by the Institute for New Economic Thinking, was attended by a balanced mix of schola…

A dynamic analysis of SP 500, FTSE 100 and EURO STOXX 50 indices under different exchange rates.

In this study, we assess the dynamic evolution of short-term correlation, long-term cointe-gration and Error Correction Model (hereafter referred to as ECM)-based long-term Granger causality between each pair of US, UK, and Eurozone stock markets from 1980 to 2015 using the rolling-window technique. A comparative analysis of pairwise dynamic integration and causality of stock markets, measured in common and domestic currency terms, is conducted to evaluate comprehensively how exchange rate fluctuations affect the time-varying integration among the S&P 500, FTSE 100 and EURO STOXX 50 indices. The results obtained show that the dynamic correlation, cointegration and ECM-based long-run Gra…

Experimental Studies of Noise—Induced Phenomena in a Tunnel Diode

Noise induced phenomena are investigated in a physical system based on a tunnel diode. The stochastic differential equation describing this physical system is analog to the Langevin equation of an overdamped Brownian particle diffusing in a nonlinear potential. This simple and versatile physical system allows a series of experiments testing and clarifying the role of the noise and of its correlation in the stochastic dynamics of bistable or metastable systems. Experimental investigations of stochastic resonance, resonant activation and noise enhanced stability are discussed.

When financial economics influences physics: The role of Econophysics

This paper aims at analyzing the unexpected influence of Financial economics on Physics. The rise of Econophysics, a fundamentally new approach in finance, suggests that the influence between the two disciplines becomes less unilateral than in the past. Methodological debates emerging in Econophysics led physicists to acknowledge that dealing with financial complex systems contributed to a wider modelling of their field. The approach of econophysicists suggests that physicists might try to conceptualize physical phenomena by integrating elements they faced with in Financial economics, and more generally in Economics. Surprisingly, many of econophysicists’ argumentations have some methodolog…

The Phenomenology of Specialization of Criminal Suspects

A criminal career can be either general, with the criminal committing different types of crimes, or specialized, with the criminal committing a specific type of crime. A central problem in the study of crime specialization is to determine, from the perspective of the criminal, which crimes should be considered similar and which crimes should be considered distinct. We study a large set of Swedish suspects to empirically investigate generalist and specialist behavior in crime. We show that there is a large group of suspects who can be described as generalists. At the same time, we observe a non-trivial pattern of specialization across age and gender of suspects. Women are less prone to commi…

On the dependence of magnetic stochastic resonance features on the features of magnetic hysteresis

Numerical study of magnetic stochastic resonance (SR) in several magnetic systems having different hysteresis loops was performed. The various hysteresis loops were modeled by using Preisach model in which several identification functions were used. The results showed the dependence of SR on the parameters of Preisach function. The results also showed how the field H/sub 0/ shifted the onset of SR and how a large dispersion of the distribution of hysterons degraded the SR.

Dominating Clasp of the Financial Sector Revealed by Partial Correlation Analysis of the Stock Market

What are the dominant stocks which drive the correlations present among stocks traded in a stock market? Can a correlation analysis provide an answer to this question? In the past, correlation based networks have been proposed as a tool to uncover the underlying backbone of the market. Correlation based networks represent the stocks and their relationships, which are then investigated using different network theory methodologies. Here we introduce a new concept to tackle the above question--the partial correlation network. Partial correlation is a measure of how the correlation between two variables, e.g., stock returns, is affected by a third variable. By using it we define a proxy of stoc…

Market Impact and Trading Profile of Hidden Orders in Stock Markets

We empirically study the market impact of trading orders. We are specifically interested in large trading orders that are executed incrementally, which we call hidden orders. These are statistically reconstructed based on information about market member codes using data from the Spanish Stock Market and the London Stock Exchange. We find that market impact is strongly concave, approximately increasing as the square root of order size. Furthermore, as a given order is executed, the impact grows in time according to a power law; after the order is finished, it reverts to a level of about 0.5-0.7 of its value at its peak. We observe that hidden orders are executed at a rate that more or less m…

Probability Distribution of the Residence Times in Periodically Fluctuating Metastable Systems

We investigate experimentally and numerically the probability distribution of the residence times in periodically fluctuating metastable systems. The experiments are performed in a physical metastable system which is the series of a biasing resistor with a tunnel diode in parallel to a capacitor. The numerical simulations are performed in an overdamped model system with a time-dependent potential. We investigate both the cases where the system is deterministically overall-stable and overall-unstable. In the overall-unstable regime, the experimental and the numerically investigated systems show noise enhanced stability in the presence of a finite amount of noise. The determined P(T) is mult…

A tool for filtering information in complex systems

We introduce a technique to filter out complex data-sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation based graphs giving filtered graphs which preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0) triangular loops and 4 element cliques are formed. The application of this filtering procedure to 100 stocks in the USA equity markets shows that such loops and cliqu…

Master curve for price-impact function

The price reaction to a single transaction depends on transaction volume, the identity of the stock, and possibly many other factors. Here we show that, by taking into account the differences in liquidity for stocks of different size classes of market capitalization, we can rescale both the average price shift and the transaction volume to obtain a uniform price-impact curve for all size classes of firm for four different years (1995–98). This single-curve collapse of the price-impact function suggests that fluctuations from the supply-and-demand equilibrium for many financial assets, differing in economic sectors of activity and market capitalization, are governed by the same statistical r…

Multiple Time Scales in the Microwave Ionization of Rydberg Atoms

We investigate the time dependence of the ionization probability of Rydberg atoms driven by microwave fields, both numerically and experimentally. Our exact quantum results provide evidence for an algebraic decay law on suitably chosen time scales, a phenomenon that is considered to be the signature of nonhyperbolic scattering in unbounded classically chaotic motion.

Community characterization of heterogeneous complex systems

We introduce an analytical statistical method to characterize the communities detected in heterogeneous complex systems. By posing a suitable null hypothesis, our method makes use of the hypergeometric distribution to assess the probability that a given property is over-expressed in the elements of a community with respect to all the elements of the investigated set. We apply our method to two specific complex networks, namely a network of world movies and a network of physics preprints. The characterization of the elements and of the communities is done in terms of languages and countries for the movie network and of journals and subject categories for papers. We find that our method is ab…

Diffusive behavior and the modeling of characteristic times in limit order executions

We present an empirical study of the first passage time (FPT) of order book prices needed to observe a prescribed price change Delta, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled ones in a double auction market. We find that the distribution of all three quantities decays asymptotically as a power law, but that of FPT has significantly fatter tails than that of TTF. Thus a simple first passage time model cannot account for the observed TTF of limit orders. We propose that the origin of this difference is the presence of cancellations. We outline a simple model, which assumes that prices are characterized by the empirically observed distribution …

Emergence of statistically validated financial intraday lead-lag relationships

According to the leading models in modern finance, the presence of intraday lead-lag relationships between financial assets is negligible in efficient markets. With the advance of technology, however, markets have become more sophisticated. To determine whether this has resulted in an improved market efficiency, we investigate whether statistically significant lagged correlation relationships exist in financial markets. We introduce a numerical method to statistically validate links in correlation-based networks, and employ our method to study lagged correlation networks of equity returns in financial markets. Crucially, our statistical validation of lead-lag relationships accounts for mult…

Experimental investigation of resonant activation

We experimentally investigate the escape from a metastable state over a fluctuating barrier of a physical system. The system is switching between two states under electronic control of a dichotomous noise. We measure the escape time and its probability density function as a function of the correlation rate of the dichotomous noise in a frequency interval spanning more than 4 frequency decades. We observe resonant activation, namely a minimum of the average escape time as a function of the correlation rate. We detect two regimes in the study of the shape of the escape time probability distribution: (i) a regime of exponential and (ii) a regime of non-exponential probability distribution.

Correlation based hierarchical clustering in financial time series

We review a correlation based clustering procedure applied to a portfolio of assets synchronously traded in a financial market. The portfolio considered consists of the set of 500 highly capitalized stocks traded at the New York Stock Exchange during the time period 1987-1998. We show that meaningful economic information can be extracted from correlation matrices.

Clusters of Traders in Financial Markets

In this chapter we discuss Aoki’s work on the description of clusters of economic agents acting in a market. Specifically, we briefly discuss his work on the Ewens distribution and its application in a model of stock market with heterogeneous agents. We then review recent empirical analyses on the heterogeneity of financial market participants and make a working hypothesis for an empirical study on the distribution of the number of clusters of market participants in a real stock market monitored with a resolution down to the shadowed identity of market participants.

Stochastic resonance in a tunnel diode in the presence of white or coloured noise

We study the signal-to-noise ratio, signal and noise output levels in a fast bistable electronic system: a tunnel diode. We observe stochastic resonance when the system is driven by a sum of a small periodic signal and noise. The phenomenon is investigated for values of the driving frequency as high as 10 kHz. This is the highest frequency value used in SR experiments until now. In the presence of «white noise», we observe a nonmonotonic behavior characterized by a sharp dip in the output noise level measured at 100Hz and 1 kHz. A similar behavior is predicated by recent theories. We also present preliminary experimental results of SR in the presence of an Ornstein-Uhlenbeck noise. For the …

Correlation based networks of equity returns sampled at different time horizons

We investigate the planar maximally filtered graphs of the portfolio of the 300 most capitalized stocks traded at the New York Stock Exchange during the time period 2001-2003. Topological properties such as the average length of shortest paths, the betweenness and the degree are computed on different planar maximally filtered graphs generated by sampling the returns at different time horizons ranging from 5 min up to one trading day. This analysis confirms that the selected stocks compose a hierarchical system progressively structuring as the sampling time horizon increases. Finally, a cluster formation, associated to economic sectors, is quantitatively investigated.

How Lead-Lag Correlations Affect the Intraday Pattern of Collective Stock Dynamics

The degree of correlation among stock returns aects the possibility to diversify the risk of investment,

Stock market dynamics and turbulence: parallel analysis of fluctuation phenomena

Abstract We report analogies and differences between the fluctuations in an economic index and the fluctuations in velocity of a fluid in a fully turbulent state. Specifically, we systematically compare (i) the statistical properties of the S&P 500 cash index recorded during the period January 84–December 89 with (ii) the statistical properties of the velocity of turbulent air measured in the atmospheric surface layer about 6 m above a wheat canopy in the Connecticut Agricultural Research Station. We find non-Gaussian statistics, and intermittency, for both processes (i) and (ii) but the deviation from a Gaussian probability density function are different for stock market dynamics and turbu…

A Dynamic Analysis of S&P 500, FTSE 100 and EURO STOXX 50 Indices Under Different Exchange Rates

The persistence analysis of short- and long-term interaction and causality in the international financial markets is a key issue for policy makers and portfolio investors. This paper assesses the dynamic evolution of short-term correlation, long-term cointegration and Error Correction Model (hereafter referred to as ECM)-based long-term Granger causality between each pair of US, UK, and Eurozone stock markets over the period of 1980--2015 using the rolling-window technique. A comparative analysis of pairwise dynamic integration and causality of stock markets, measured in common and domestic currency terms, is conducted to evaluate comprehensively how exchange rate fluctuations affect the ti…

Identification of Clusters of Investors from Their Real Trading Activity in a Financial Market

We use statistically validated networks, a recently introduced method to validate links in a bipartite system, to identify clusters of investors trading in a financial market. Specifically, we investigate a special database allowing to track the trading activity of individual investors of the stock Nokia. We find that many statistically detected clusters of investors show a very high degree of synchronization in the time when they decide to trade and in the trading action taken. We investigate the composition of these clusters and we find that several of them show an over-expression of specific categories of investors.

Complex Networks in Air Transport

The application of CNT to air traffic management has seen significant growth in recent years. This is partly because air traffic can be seen as the superposition of different networks, including the networks of airports, sectors and navigation points. Moreover each of these networks can be seen as a multiplex – for example, by associating each layer with a different airline. The study of the topology of these networks is important for several reasons related to understanding, monitoring, controlling, and optimising the air traffic system. The topological properties of air traffic networks are useful: (i) for studying how the air traffic has changed in recent years; (ii) for identifying the …

Dynamics of the Number of Trades of Financial Securities

We perform a parallel analysis of the spectral density of (i) the logarithm of price and (ii) the daily number of trades of a set of stocks traded in the New York Stock Exchange. The stocks are selected to be representative of a wide range of stock capitalization. The observed spectral densities show a different power-law behavior. We confirm the $1/f^2$ behavior for the spectral density of the logarithm of stock price whereas we detect a $1/f$-like behavior for the spectral density of the daily number of trades.

Variety of Stock Returns in Normal and Extreme Market Days: The August 1998 Crisis

We investigate the recently introduced variety of a set of stock returns traded in a financial market. This investigation is done by considering daily and intraday time horizons in a 15-day time period centered at the August 31st, 1998 crash of the S&P500 index. All the stocks traded at the NYSE during that period are considered in the present analysis. We show that the statistical properties of the variety observed in analyses of daily returns also hold for intraday returns. In particular the largest changes of the variety of the return distribution turns out to be most localized at the opening or (to a less degree) at the closing of the market.

An interest rates cluster analysis

An empirical analysis of interest rates in money and capital markets is performed. We investigate a set of 34 different weekly interest rate time series during a time period of 16 years between 1982 and 1997. Our study is focused on the collective behavior of the stochastic fluctuations of these time-series which is investigated by using a clustering linkage procedure. Without any a priori assumption, we individuate a meaningful separation in 6 main clusters organized in a hierarchical structure.

Cluster analysis for portfolio optimization

We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio between predicted and realized risk. Bootstrap analysis indicates that this improvement is obtained in a wide range of the parameters N (number of assets) and T (investment horizon). The predicted and realized risk level and the relative portfolio composition of the selected portfolio for a given value of the portfolio return are also investigated for each considered filtering method.

Networks of equities in financial markets

We review the recent approach of correlation based networks of financial equities. We investigate portfolio of stocks at different time horizons, financial indices and volatility time series and we show that meaningful economic information can be extracted from noise dressed correlation matrices. We show that the method can be used to falsify widespread market models by directly comparing the topological properties of networks of real and artificial markets.

Dynamics of fintech terms in news and blogs and specialization of companies of the fintech industry

We perform a large scale analysis of a list of fintech terms in (i) news and blogs in English language and (ii) professional descriptions of companies operating in many countries. The occurrence and co-occurrence of fintech terms and locutions shows a progressive evolution of the list of fintech terms in a compact and coherent set of terms used worldwide to describe fintech business activities. By using methods of complex networks that are specifically designed to deal with heterogeneous systems, our analysis of a large set of professional descriptions of companies shows that companies having fintech terms in their description present over-expressions of specific attributes of country, muni…

Spectral properties of correlation matrices for some hierarchically nested factor models

We show that spectral methods, such as Principal Component Analysis and Random Matrix Theory, are unable to reveal the hierarchical (or nested) structure of a set of mutivariate data. We consider the method introduced in M. Tumminello et al., EPL 78, 30006 (2007) to associate a hierarchical factor model with a set of data by making use of clustering algorithms. This is done by proving the existence of a bijective correspondence between a hierarchical tree and a factor model.

Evolution of correlation structure of industrial indices of U.S. equity markets

We investigate the dynamics of correlations present between pairs of industry indices of US stocks traded in US markets by studying correlation based networks and spectral properties of the correlation matrix. The study is performed by using 49 industry index time series computed by K. French and E. Fama during the time period from July 1969 to December 2011 that is spanning more than 40 years. We show that the correlation between industry indices presents both a fast and a slow dynamics. The slow dynamics has a time scale longer than five years showing that a different degree of diversification of the investment is possible in different periods of time. On top to this slow dynamics, we als…

When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators

The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for the period 1997-2007. We find that the usefulness of covariance matrix estimators strongly depends on the ratio between estimation period T and number of stocks N, on the presence or absence of short selling, and on the performance metric considered. When short selling is allowed, several estimation methods achieve a realized risk that is significantly smaller than the one obtai…

Economic Sector Identification in a Set of Stocks Traded at the New York Stock Exchange: A Comparative Analysis

We review some methods recently used in the literature to detect the existence of a certain degree of common behavior of stock returns belonging to the same economic sector. Specifically, we discuss methods based on random matrix theory and hierarchical clustering techniques. We apply these methods to a set of stocks traded at the New York Stock Exchange. The investigated time series are recorded at a daily time horizon. All the considered methods are able to detect economic information and the presence of clusters characterized by the economic sector of stocks. However, different methodologies provide different information about the considered set. Our comparative analysis suggests that th…

Plasticity of brain wave network interactions and evolution across physiologic states

Neural plasticity transcends a range of spatio-temporal scales and serves as the basis of various brain activities and physiologic functions. At the microscopic level, it enables the emergence of brain waves with complex temporal dynamics. At the macroscopic level, presence and dominance of specific brain waves is associated with important brain functions. The role of neural plasticity at different levels in generating distinct brain rhythms and how brain rhythms communicate with each other across brain areas to generate physiologic states and functions remains not understood. Here we perform an empirical exploration of neural plasticity at the level of brain wave network interactions repre…

Trading activity and price impact in parallel markets: SETS vs. off-book market at the London Stock Exchange

We empirically study the trading activity in the electronic on-book segment and in the dealership off-book segment of the London Stock Exchange, investigating separately the trading of active market members and of other market participants which are non-members. We find that (i) the volume distribution of off-book transactions has a significantly fatter tail than the one of on-book transactions, (ii) groups of members and non-members can be classified in categories according to their trading profile (iii) there is a strong anticorrelation between the daily inventory variation of a market member due to the on-book market transactions and inventory variation due to the off-book market transac…

The Effect of Spectral Diffusion on the Saturation Transient Regime

Saturation kinetics of inhomogeneous resonance lines has been investigated in very dilute ruby samples at T=4.2°K by the saturation transient technique. Experimental evidence of the effectiveness of intraline spectral diffusion is reported. Satisfactory agreement is found between the experimental results and a theoretical model in which spectral diffusion is ascribed to the time fluctuations of the hyperfine field. Spectral diffusion times of the order of 10-5 sec are determined.

Quantitative Analysis of Gender Stereotypes and Information Aggregation in a National Election

By analyzing a database of a questionnaire answered by a large majority of candidates and elected in a parliamentary election, we quantitatively verify that (i) female candidates on average present political profiles which are more compassionate and more concerned with social welfare issues than male candidates and (ii) the voting procedure acts as a process of information aggregation. Our results show that information aggregation proceeds with at least two distinct paths. In the first case candidates characterize themselves with a political profile aiming to describe the profile of the majority of voters. This is typically the case of candidates of political parties which are competing for…

Topology of correlation-based minimal spanning trees in real and model markets

We present here a topological characterization of the minimal spanning tree that can be obtained by considering the price return correlations of stocks traded in a financial market. We compare the minimal spanning tree obtained from a large group of stocks traded at the New York Stock Exchange during a 12-year trading period with the one obtained from surrogated data simulated by using simple market models. We find that the empirical tree has features of a complex network that cannot be reproduced, even as a first approximation, by a random market model and by the one-factor model.

How news affect the trading behavior of different categories of investors in a financial market

We investigate the trading behavior of a large set of single investors trading the highly liquid Nokia stock over the period 2003-2008 with the aim of determining the relative role of endogenous and exogenous factors that may affect their behavior. As endogenous factors we consider returns and volatility, whereas the exogenous factors we use are the total daily number of news and a semantic variable based on a sentiment analysis of news. Linear regression and partial correlation analysis of data show that different categories of investors are differently correlated to these factors. Governmental and non profit organizations are weakly sensitive to news and returns or volatility, and, typica…

On the interplay between multiscaling and stocks dependence

We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate this result conditional on the stocks' capitalization and on the kurtosis of stocks' log-returns in order to search for possible confounding effects. We show that a linear dependence with the logarithm of the capitalization and the logarithm of kurtosis does not explain the observed stylized fact, which we interpret as being originated from a deeper relationship.

Spanning Trees and bootstrap reliability estimation in correlation based networks

We introduce a new technique to associate a spanning tree to the average linkage cluster analysis. We term this tree as the Average Linkage Minimum Spanning Tree. We also introduce a technique to associate a value of reliability to links of correlation based graphs by using bootstrap replicas of data. Both techniques are applied to the portfolio of the 300 most capitalized stocks traded at New York Stock Exchange during the time period 2001-2003. We show that the Average Linkage Minimum Spanning Tree recognizes economic sectors and sub-sectors as communities in the network slightly better than the Minimum Spanning Tree does. We also show that the average reliability of links in the Minimum …

The Rise and Fall of Business Firms: A Stochastic Framework on Innovation, Creative

© 2020, Cambridge University PressThe book ‘The Rise and Fall of Business Firms: A Stochastic Framework on Innovation, Creative Destruction and Growth’ by S.V. Buldyrev, F. Pammolli, M. Riccaboni a...

Value-at-Risk and Tsallis statistics: risk analysis of the aerospace sector

In this study, we analyze the aerospace stocks prices in order to characterize the sector behavior. The data analyzed cover the period from January 1987 to April 1999. We present a new index for the aerospace sector and we investigate the statistical characteristics of this index. Our results show that this index is well described by Tsallis distribution. We explore this result and modify the standard Value-at-Risk (VaR), financial risk assessment methodology in order to reflect an asset which obeys Tsallis non-extensive statistics.

The comprehensive aerospace index (CASI): Tracking the economic performance of the aerospace industry

In this paper, we described the Comprehensive Aerospace Index (CASI), a financial index aimed at representing the economic performance of the aerospace industry. CASI is build upon a data set of approximately 20 years of daily close prices set, from January 1987 to June 2007, from a comprehensive sample of leading aerospace-related companies with stocks negotiated on the New York Exchange (NYSE) and on the over-the-counter (OTC) markets. We also introduced the sub-indices CASI-AERO, for aeronautical segment, and CASI-SAT for satellite segment. and considered the relation between them. These three indices are compared to others aerospace indices and to more traditional general financial indi…

Numerical simulation of resonant activation in a fluctuating metastable model system

We study the escape time from a metastable overdamped model system in the presence of two noise sources: a white noise and a random telegraph noise. The random telegraph noise controls the height of the potential barrier of the metastable system while the white noise mimics the presence of a given temperature. We report on numerical simulations about: (i) the average residence time of the system in the metastable state; (ii) the probability density function (PDF) of the residence time at various values of the correlation time T c of the random telegraph noise. Resonant activation is observed in the dynamics of the investigated system. The PDF shows different shapes for different values of τ…

Applications of statistical mechanics to finance

Abstract We discuss some apparently “universal” aspects observed in the empirical analysis of stock price dynamics in financial markets. Specifically we consider (i) the empirical behavior of the return probability density function and (ii) the content of economic information in financial time series.

Noise in physic$

Limit theorems and price changes in financial markets

Abstract We discuss the relation between limit theorems in probability theory and price change statistics in financial markets. An analysis of the published empirical results and theoretical models show that the problem of the statistical properties of price (or index) changes is still open. By using the limit theorems of probability theory and the current assumption that stock prices are well described by martingales, we point out that the probability density function (PDF) of price changes is expected to belong to theclass of infinitely divisible PDFs.

Drift-controlled anomalous diffusion: a solvable Gaussian model

We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In particular diffusive, subdiffusive, superdiffusive and stretched exponentially diffusive processes are described by this model for specific values of the two control parameters. The model is also investigated in the presence of an external harmonic potential. We prove that the relaxation to the stationary solution is power-law in time with an exponent controlled by one of model parameters.

Market reaction to temporary liquidity crises and the permanent market impact

We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden, large variation of the spread, corresponding to a temporary crisis of liquidity in a double auction financial market. We find that the spread decays very slowly to its normal value as a consequence of the strategic limit order placement of liquidity providers. We consider several quantities, such as order placement rates and distribution, that affect the decay of the spread. We measure the permanent impact both of a generic event altering the spread and of a single transaction and we find an approximately linear relation between immediate and permanent impact in both cases.

Levels of complexity in financial markets

We consider different levels of complexity which are observed in the empirical investigation of financial time series. We discuss recent empirical and theoretical work showing that statistical properties of financial time series are rather complex under several ways. Specifically, they are complex with respect to their (i) temporal and (ii) ensemble properties. Moreover, the ensemble return properties show a behavior which is specific to the nature of the trading day reflecting if it is a normal or an extreme trading day.

Correlation, hierarchies, and networks in financial markets

We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in financial markets. Specifically, we discuss how to define and obtain hierarchical trees, correlation based trees and networks from a correlation matrix. The hierarchical clustering and other procedures performed on the correlation matrix to detect statistically reliable aspects of the correlation matrix are seen as filtering procedures of the correlation matrix. We also discuss a method to associate a hierarchically nested factor model to a hierarchical tre…

Spectral density of the correlation matrix of factor models: a random matrix theory approach.

We studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series. By making use of the random matrix theory, we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample. We considered a broad range of models, ranging from one-factor models to hierarchical multifactor models.

Evolution of worldwide stock markets, correlation structure and correlation based graphs

We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period Jan 1996 - Jul 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globalization. The fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system. We provide evidence that the short term timescale of correlation among market indices is less than 3 trading months (about 60 trading days). The average values of the non diagonal elements of the correlation matrix, corre…

Analysis of the Structure and Dynamics of European Flight Networks

We analyze structure and dynamics of flight networks of 50 airlines active in the European airspace in 2017. Our analysis shows that the concentration of the degree of nodes of different flight networks of airlines is markedly heterogeneous among airlines reflecting heterogeneity of the airline business models. We obtain an unsupervised classification of airlines by performing a hierarchical clustering that uses a correlation coefficient computed between the average occurrence profiles of 4-motifs of airline networks as similarity measure. The hierarchical tree is highly informative with respect to properties of the different airlines (for example, the number of main hubs, airline participa…

When do Improved Covariance Matrix Estimators Enhance Portfolio Optimization? An Empirical Comparative Study of Nine Estimators

The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for the period 1997-2007. We find that the usefulness of covariance matrix estimators strongly depends on the ratio between estimation period T and number of stocks N, on the presence or absence of short selling, and on the performance metric considered. When short selling is allowed, several estimation methods achieve a realized risk that is significantly smaller than the one obtai…

Empirical Analyses of Networks in Finance

Abstract The recent global financial crisis has triggered a huge interest in the use of network concepts and network tools to better understand how instabilities can propagate through the financial system. The literature is today quite vast, covering both theoretical and empirical aspects. This review concentrates on empirical work, and associated methodologies, concerned with the evaluation of the fragility and resilience of financial and credit markets. The first part of the review examines the literature on systemic risk that arise from banks mutual exposures. These exposures stem primarily from interbank lending and derivative positions, but also, indirectly, from common holdings of oth…

Ensemble properties of securities traded in the NASDAQ market

We study the price dynamics of stocks traded in the NASDAQ market by considering the statistical properties of an ensemble of stocks traded simultaneously. For each trading day of our database, we study the ensemble return distribution by extracting its first two central moments. According to previous results obtained for the NYSE market, we find that the second moment is a long-range correlated variable. We compare time-averaged and ensemble-averaged price returns and we show that the two averaging procedures lead to different statistical results.

Volatility in Financial Markets: Stochastic Models and Empirical Results

We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pdf in the region of low values of volatility whereas the Hull and White model better approximates the empirical pdf for large values of volatility. Both models fails in describing the empirical pdf over a moderately large volatility range.

Happy Aged People Are All Alike, While Every Unhappy Aged Person Is Unhappy in Its Own Way

Aging of the world’s population represents one of the most remarkable success stories of medicine and of humankind, but it is also a source of various challenges. The aim of the collaborative cross-cultural European study of adult well being (ESAW) is to frame the concept of aging successfully within a causal model that embraces physical health and functional status, cognitive efficacy, material security, social support resources, and life activity. Within the framework of this project, we show here that the degree of heterogeneity among people who view aging in a positive light is significantly lower than the degree of heterogeneity of those who hold a negative perception of aging. We base…

How News Affect the Trading Behavior of Different Categories of Investors in a Financial Market

We investigate the trading behavior of a large set of single investors trading the highly liquid Nokia stock over the period 2003-2008 with the aim of determining the relative role of endogenous and exogenous factors that may affect their behavior. As endogenous factors we consider returns and volatility, whereas the exogenous factors we use are the total daily number of news and a semantic variable based on a sentiment analysis of news. Linear regression and partial correlation analysis of data show that different categories of investors are differently correlated to these factors. Governmental and non profit organizations are weakly sensitive to news and returns or volatility, and, typica…

Core of communities in bipartite networks

We use the information present in a bipartite network to detect cores of communities of each set of the bipartite system. Cores of communities are found by investigating statistically validated projected networks obtained using information present in the bipartite network. Cores of communities are highly informative and robust with respect to the presence of errors or missing entries in the bipartite network. We assess the statistical robustness of cores by investigating an artificial benchmark network, the co-authorship network, and the actor-movie network. The accuracy and precision of the partition obtained with respect to the reference partition are measured in terms of the adjusted Ran…

Comparing Correlation Matrix Estimators Via Kullback-Leibler Divergence

We use a self-averaging measure called Kullback-Leibler divergence to evaluate the performance of four different correlation estimators: Fourier, Pearson, Maximum Likelihood and Hayashi-Yoshida estimator. The study uses simulated transaction prices for a large number of stocks and different data generating mechanisms, including synchronous and non-synchronous transactions, homogeneous and heterogeneous inter-transaction time. Different distributions of stock returns, i.e. multivariate Normal and multivariate Student's t-distribution, are also considered. We show that Fourier and Pearson estimators are equivalent proxies of the `true' correlation matrix within all the settings under analysis…

When Financial Economics Influences Physics: The Role of Econophysics

This paper aims at analyzing the unexpected influence of Financial economics on Physics. The rise of Econophysics, a fundamentally new approach in finance, suggests that the influence between the two disciplines becomes less unilateral than in the past. Methodological debates emerging in Econophysics led physicists to acknowledge that dealing with financial complex systems contributed to a wider modelling of their field. The approach of econophysicists suggests that physicists might try to conceptualize physical phenomena by integrating elements they faced with in Financial economics, and more generally in Economics. Surprisingly, many of econophysicists’ argumentations have some methodolog…

Synergistic Information Transfer in the Global System of Financial Markets.

Uncovering dynamic information flow between stock market indices has been the topic of several studies which exploited the notion of transfer entropy or Granger causality, its linear version. The output of the transfer entropy approach is a directed weighted graph measuring the information about the future state of each target provided by the knowledge of the state of each driving stock market index. In order to go beyond the pairwise description of the information flow, thus looking at higher order informational circuits, here we apply the partial information decomposition to triplets consisting of a pair of driving markets (belonging to America or Europe) and a target market in Asia. Our …

Networked relationships in the e-MID Interbank market: A trading model with memory

Interbank markets are fundamental for bank liquidity management. In this paper, we introduce a model of interbank trading with memory. Our model reproduces features of preferential trading patterns in the e-MID market recently empirically observed through the method of statistically validated networks. The memory mechanism is used to introduce a proxy of trust in the model. The key idea is that a lender, having lent many times to a borrower in the past, is more likely to lend to that borrower again in the future than to other borrowers, with which the lender has never (or has in- frequently) interacted. The core of the model depends on only one parameter representing the initial attractiven…

Scaling laws of strategic behavior and size heterogeneity in agent dynamics

The dynamics of many socioeconomic systems is determined by the decision making process of agents. The decision process depends on agent's characteristics, such as preferences, risk aversion, behavioral biases, etc.. In addition, in some systems the size of agents can be highly heterogeneous leading to very different impacts of agents on the system dynamics. The large size of some agents poses challenging problems to agents who want to control their impact, either by forcing the system in a given direction or by hiding their intentionality. Here we consider the financial market as a model system, and we study empirically how agents strategically adjust the properties of large orders in orde…

Statistically validated hierarchical clustering: Nested partitions in hierarchical trees

We develop an algorithm that is fast and scalable in the detection of a nested partition extracted from a dendrogram that is obtained from hierarchical clustering of a multivariate series. Our algorithm provides a -value for each clade observed in the hierarchical tree. The -value is obtained by computing many bootstrap replicas of the dissimilarity matrix and by performing a statistical test on each difference between the dissimilarity associated with a given clade and the dissimilarity of the clade of its parent node. We prove the efficacy of our algorithm with a set of benchmarks generated by a hierarchically nested factor model. We compare results obtained by our algorithm with those of…

Some past and present challenges of econophysics

We discuss the cultural background that was shared by some of the first econophysicists when they started to work on economic and financial problems with methods and tools of statistical physics. In particular we discuss about the role of stylized facts and statistical physical laws in economics and statistical physics respectively. As an example of the problems and potentials associated with the interaction of different communities of scholars dealing with problems observed in economic and financial systems we briefly discuss the development and the perspectives of the use of tools and concepts of networks in econophysics, economics and finance.

Scaling and data collapse for the mean exit time of asset prices

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model …

Power-law relaxation in a complex system: Omori law after a financial market crash

We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected threshold (a behavior known as the Omori law in geophysics) is consistent with the simultaneous occurrence of (i) a return probability density function characterized by a power law asymptotic behavior and (ii) a power law relaxation decay of its typical scale. Our empirical observation cannot be explained within the framework of simple and widespread stochastic volatility models.

Stochastic resonance in a tunnel diode.

We study stochastic resonance in a fast bistable electronic system: a tunnel diode. We investigate the phenomenon in a higher frequency regime than that studied in previous experiments. Detailed measurements of the output signal are reported for two values of the frequency of the periodic signal: ${\mathit{f}}_{\mathit{s}}$=1 kHz and ${\mathit{f}}_{\mathit{s}}$=10 kHz. We observe, in one case (${\mathit{f}}_{\mathit{s}}$=1 kHz), a nonmonotonic behavior characterized by a sharp dip in the output noise level measured at the frequency of the driving signal.

Market reaction to a bid-ask spread change: a power-law relaxation dynamics.

We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of price…

Dynamics of a financial market index after a crash

We discuss the statistical properties of index returns in a financial market just after a major market crash. The observed non-stationary behavior of index returns is characterized in terms of the exceedances over a given threshold. This characterization is analogous to the Omori law originally observed in geophysics. By performing numerical simulations and theoretical modelling, we show that the nonlinear behavior observed in real market crashes cannot be described by a GARCH(1,1) model. We also show that the time evolution of the Value at Risk observed just after a major crash is described by a power-law function lacking a typical scale.

Diffusive Behavior and the Modeling of Characteristic Times in Limit Order Executions

We present a study of the order book data of the London Stock Exchange for five highly liquid stocks traded during the calendar year 2002. Specifically, we study the first passage time of order book prices needed to observe a prescribed price change Delta, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled ones. We find that the distribution of the first passage time decays asymptotically in time as a power law with an exponent L_FPT ~ 1.5. The median of the same quantity scales as Delta^1.6, which is different from the Delta^2 behavior expected for Brownian motion. The quantities TTF, and TTC are also asymptotically power law distributed with exponen…

Do Firms Share the Same Functional Form of Their Growth Rate Distribution? A New Statistical Test

We propose a hypothesis testing procedure to investigate whether the same growth rate distribution is shared by all the firms in a balanced panel or, more generally, whether they share the same functional form for this distribution, without necessarily sharing the same parameters. We apply the test to panels of US and European Union publicly quoted manufacturing firms, both at the sectoral and at the subsectoral NAICS levels. We consider the following null hypotheses about the growth rate distribution of the individual firms: i) an unknown shape common to all firms, with all the firms sharing also the same parameters, or with the firm variance related to its firm size through a scaling rela…

Posidonia oceanica as a Historical Monitor Device of Lead Concentration in Marine Environment

We show that Posidonia oceanica is able to reliably monitor the variability of environmental lead (Pb). We analyze lead concentration measured in the scales and rhizomes of Posidonia oceanica collected in seven sites along the coasts of the Sicily island and subsequently fractioned them according to a lepidochronological analysis. We measure lead concentration in Posidonia oceanica tissues by using the flame atomic absorption spectrophotometry technique. We compare the measured lead concentration with the estimated lead emission in air due to the gasoline sold and used for combustion in car engines in Sicily. By computation of the Pearson cross-correlation coefficient, we show that lead con…

Quantifying preferential trading in the e-MID interbank market

Interbank markets allow credit institutions to exchange capital for purposes of liquidity management. These markets are among the most liquid markets in the financial system. However, liquidity of interbank markets dropped during the 2007-2008 financial crisis, and such a lack of liquidity influenced the entire economic system. In this paper, we analyze transaction data from the e-MID market which is the only electronic interbank market in the Euro Area and US, over a period of eleven years (1999-2009). We adapt a method developed to detect statistically validated links in a network, in order to reveal preferential trading in a directed network. Preferential trading between banks is detecte…

High-frequency trading and networked markets

Financial markets have undergone a deep reorganization during the last 20 y. A mixture of technological innovation and regulatory constraints has promoted the diffusion of market fragmentation and high-frequency trading. The new stock market has changed the traditional ecology of market participants and market professionals, and financial markets have evolved into complex sociotechnical institutions characterized by a great heterogeneity in the time scales of market members’ interactions that cover more than eight orders of magnitude. We analyze three different datasets for two highly studied market venues recorded in 2004 to 2006, 2010 to 2011, and 2018. Using methods of complex network th…