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abstractThis article proposes a method to quantify the structure of a bipartite graph using a network entropy per link. Collective behavior of participants¡Ç quotes and trades in the foreign exchange market is quantified by applying the proposed method to high frequency data. The network entropy per link corresponded to the macroeconomic situation. A finite mixture of Gumbel distributions is used to fit the empirical distribution for the minimum values of network entropy per link in each week. The mixture of Gumbel distributions with parameter estimates by segmentation procedure was verified by the Kolmogorov–Smirnov test. The finite mixture of Gumbel distributions that extrapolate the empirical probability of extreme events has explanatory power at a statistically significant level. These findings provide insight into how to manage collective behavior in the foreign exchange market.
abstractThis paper analyzes Grid Square Statistics on job opportunity ads collected from a Japanese Internet job matching site (¡Èfrom A navi¡É). We confirm a relationship between the number of job opportunities and socioeconomic quantities (the population, the numbers of firms and workers) in each 1-km and 10-km Grid Square. The number of workers is the best variable to explain the number of job opportunities out of the three candidates of socioeconomic quantities in the 1-km Grid Squares, however explanatory powers of three socioeconomic quantities to the number of job opportunities are just slightly different from one another in the 10-km Grid Squares depending on observation dates. We propose that the power law exponent estimated from the daily cross-sectional relationship can be used as the production ratio of job opportunities to socioeconomic quantities. It is determined that the production ratios vary in time and show seasonality associated with the Japanese calendar. Moreover, we compute 1-km Grid Square Statistics about job opportunity data based on JIS X0410 and we clarify relationships between the number of job opportunities and the number of occupation types. We extracted industrial clusters in terms of job opportunities and the types of job occupations in Japan.
abstractThis paper proposes a multi-objective optimization procedure for a global air transportation system to find a balance among risk, economy, and convenience using a ¡Èdivide and conquer¡É method while improving each corresponding metric simultaneously. To do so, we attempt to estimate several geographical parameters of airports from socioeconomic-technological-environmental databases. Considering the risk of tsunami run-up events to air transportation, we estimate physical exposures of airports utilized in global aviation networks. First, we evaluate spatial risk of tsunami run-up events, and estimate physical exposure of airports by linking OAG timetable data of international passenger flights, geographical information of airports, tsunami event catalog data, global population estimates of 2.5 minute degree grid square and global earth surface data of 1 minute degree grid square. Second, we estimate regression coefficients of a simple gravity model for a global air transportation system linking OAG timetable data of international passenger flights, geographical information of airports, and global population estimates of 2.5 minute degree grid square. Finally, imposing three types of objective functions, economy, convenience, and risks, we formalize a multi-objective optimization problem to design efficient routes for a global aviation network. These objective functions are functions in terms of physical exposures and the number of passengers from a departure airport to an arrival airport for all possible combinations. However, because the global aviation network is too large to optimize simultaneously, we use a ¡Èdivide and conquer¡É method to tackle the large-scale problem by dividing the whole global air transportation network into each airline company's network and successfully integrating them. We discuss the procedure of collecting relevant databases, analyzing the aviation networks, evaluating the performance metrics, and applying the ¡Èdivide and conquer¡É approach to the global transportation network.
abstractThis article assesses the risks posed by tsunamis to the global air transport system by estimating several associated parameters from socioeconomic-technological-environmental databases. Considering the risk of tsunami run-up events to exposed air transportation, we estimated the physical exposure of airports utilized in global aviation networks. We linked OAG timetable data on international passenger flights, geographical information on airports, NOAA tsunami-event catalog data, and NOAA global Earth-surface data per 1-minute degree-grid square. In order to extrapolate the frequency of severe tsunami run-up events, we assumed a generalized Pareto distribution and estimated its parameters from historical records on tsunamis spanning 1,000 years by using either the maximum likelihood method or the probability-weighted moments-matching method. We believe that this is the first time has assessed tsunami run-up risk to a global air transport system by exhaustively collecting relevant Big Data.
abstractThe ability to process and manage large data volumes has been proven to be not enough to tackle the current challenges presented by "Big Data". Deep insight is required for understanding interactions among connected systems, space- and time- dependent heterogeneous data structures. Emergence of global properties from locally interacting data entities and clustering phenomena demand suitable approaches and methodologies recently developed in the foundational area of Data Science by taking a Complex Systems standpoint. Here, we deal with challenges that can be summarized by the question: "What can Complex Systems Science contribute to Big Data? ". Such question can be reversed and brought to a superior level of abstraction by asking "What Knowledge can be drawn from Big Data?" These aspects constitute the main motivation behind this article to introduce a volume containing a collection of papers presenting interdisciplinary advances in the Big Data area by methodologies and approaches typical of the Complex Systems Science, Nonlinear Systems Science and Statistical Physics.
abstractThe Accommodation Survey in Japanese Tourism Statistics is a quarterly survey conducted by the Japan Tourism Agency of the Ministry of Land, Infrastructure, Transport and Tourism. The aim of the survery is to capture a whole picture of monthly travel and tourism trends in Japan and obtain data to inform for Japanese tourism policies. Data collected include the total number of travelers, the number of foreign travelers with their nationality and the number of Japanese travelers with their residential prefecture. These data are collected from hotels, inns, and other private and public accommodations listed in the establishment frame database defined in Article 27 of the Statistics Act. In this study, the 1-km grid square statistics data were generated by using micro-data from 50,802 accommodations that took place from January 2013 to June 2014 (18 months); use of this data is in accordance with Article 33 of the Statistics Act. These data were analyzed for spatio-temporal patterns of Japanese travel trends. The 1-km grid square statistics data were computed by converting postal addresses into geographical information expressed as latitude and longitude and encoding it into 1-km grid square code standardized in JIS X0410. The relationships between the total number of travelers and the total number of foreign travelers in each 1-km grid square were clarified. It was confirmed that the power-law relationship between the number of travelers and the number of foreign travelers exists. The power-law exponent is greater than 1 for 15 months of the observation period. This implies that foreign travelers tend to choose accommodations concentrated in several areas, including areas in which Japanese travelers frequently visit and stay. Furthermore, Japanese travelers tend to stay in some areas close to their residence prefecture.
abstractThis study investigates the number of job opportunities collected from Japanese job searching site (¡ÈFromA¡É) and international job searching site (¡ÈIndeed¡É). We confirm that a relationship between the number of job opportunities and socioeconomic quantities (the number of populations, firms and workers) in each 1-km grid in Japan. The number of workers is the best explanatory variable to explain the number of job opportunities in Japan. The regression coefficients can be used as an indicator to Japanese grasp macroeconomic conditions. From the global point of view, we analyse the number of job opportunities in about 16,000 cities all over the world. We confirm the daily number of job opportunities in each city varies in time and show some associations with macroeconomic indicators. We compute a relationship between means of the daily number of job opportunities and their standard deviations and confirm that it follows a scaling relationship with power law exponent alpha = 1. A possible model based on Poisson processes with intensity of which varies in time on the basis of a common noise is proposed to explain the phenomenon empirically observed.
abstractThis article analyses socioeconomic flows and social stocks by using governmental statistics data on both air transportation and demographic and economic censuses from a holistic point of view. The network analysis of the Japanese air transportation network consists of 86 domestic airports with 476 connections. Betweenness centrality and PageRank? are computed for the network structure. Furthermore, a relationship between socioeconomic flows (passengers and freight) and social stocks (population, the number of workers and the number of firms) is investigated based on governmental statistics data. To determine the relationship, a gravity model, which proposes that a socioeconomic flow between two places is proportional to a power law relationship among social stocks around the places and their geodesic distance, is assumed. Parameters with the relationship for passengers and freight are estimated, and an adequate radius distance to compute social stocks around Japanese airports is determined. This result can be used to infer socioeconomic flows from social stocks.
abstractSystemic risk in banking systems is a crucial issue that remains to be completely addressed. In our toy model, banks are exposed to two sources of risks, namely, market risk from their investments in assets external to the system and credit risk from their lending in the interbank market. By and large, both risks increase during severe financial turmoil. Under this scenario, the paper shows how both the individual and the systemic default tend to coincide.
abstractOur society has been computerised and globalised due to emergence and spread of information and communications technology (ICT). This enables us to investigate our own socio-economic systems based on large amounts of data on human activities. In this article, methods of treating complexity arising from a vast amount of data, and linking data from diﬀerent sources, are discussed. Furthermore, several examples are given of studies into the applications of econoinformatics to the Japanese stock exchange, foreign exchange markets, domestic hotel booking data and international ﬂight booking data are shown. It is the main message that spatio-temporal information is a key element to synthesise data from diﬀerent data sources.
abstractThis study proposes a method to measure geographical risk from tsunami run-up events based on socioeconomic-environmental data. The physical exposure of Japan to tsunami run-up events} is computed based upon 1-km grid square statistics from the population census of the Japanese Statistics Bureau of the Ministry of Internal Affairs and Communication, 1-km grid square national land numerical information downloaded from the National and Regional Policy Bureau of the Japanese Ministry of Land, Infrastructure, Transport and Tourism, and tsunami run-up catalog data downloaded from NOAA Tsunami Data and Information. Using estimates of physical exposure in each 1-km square grid, we define the physical exposure of potential passengers and freight as the sum of physical exposures over the area close to an airport. Information on Japanese domestic air transportation is further extracted as a network consisting of airports and flights. Using an exposed value as the sum of passengers of flights landing at and taking off from each airport and the sum of freight weight at each airport, we compute values of the physical exposure of both confluence and logistics for 86 Japanese airports in terms of tsunami run-up events.
abstractThis study analyzes the availability of room opportunity types collected from a Japanese hotel booking site. The status of opportunity type is empirically analyzed from a comprehensive point of view. We characterize demand-supply situations of room prices at each region with both room availability and average room rate. The average room rate decreases in terms of the room availability in many districts. However, it is found that the average room rate increases with respect to the room availability in some districts. This is an evidence that the theory of demand and supply is not always satisfied in Japanese hotel industry.
abstractThis study comprises a comprehensive analysis of time series segmentation on the Japanese stock prices listed on the first section of the Tokyo Stock Exchange during the period from 4 January 2000 to 30 January 2012. A recursive segmentation procedure is used under the assumption of a Gaussian mixture. The number of each quintile of variance for all the segments is used as an indicator of macroeconomic situations and is investigated empirically. The results show that from June 2004 to June 2007, a large majority of stocks were stable and that from 2008 several stocks were unstable. In March 2011, the number of unstable stocks increased dramatically due to societal turmoil after the Great East Japan Earthquake. It is concluded that the number of stocks included in each quintile of volatility provides useful information about the Japanese macroeconomic situation.
abstractThis study proposes a recursive segmentation procedure for multivariate time series based on Akaike information criterion. The Akaike information criterion, between independently identically distributed multivariate Gaussian samples and two successive segments drawn from different multivariate Gaussian distributions, is used as a discriminator to segment multivariate time series. The bootstrap method is employed in order to evaluate the statistical significance level. The proposed method is performed for an artificial multi-dimensional time series consisting of two segments with different statistics. The log-return time series of currency exchange rates for 30 currency pairs for the period from January 4, 2001 to December 30, 2011 are also divided into 11 segments with the proposed method. This method confirms that some segments correspond to historical events recorded as critical situations.
abstractWe investigate relationship between annual electric power consumption per capita and gross domestic production (GDP) per capita for 131 countries. We found that the relationship can be fitted with a power-law function. We examine the relationship for 47 prefectures in Japan. Furthermore, we investigate values of annual electric power production reported by four international organizations. We collected the data from U.S. Energy Information Administration (EIA), Statistics by International Energy Agency (IEA), OECD Factbook (Economic, Environmental and Social Statistics), and United Nations (UN) Energy Statistics Yearbook. We found that the data structure, values, and unit depend on the organizations. This implies that it is further necessary to establish data standards and an organization to collect, store, and distribute the data on socio-economic systems.
abstractThis article investigates correlational properties of two-dimensional chaotic maps on the unit circle. We give analytical forms of higher-order covariances. We derive the characteristic function of their simultaneous and lagged ergodic densities. We found that these characteristic functions are described by three types of two-dimensional Bessel functions. Higher-order covariances between x and y and those between y and y show non-positive values. Asymmetric features between cosine and sine functions are elucidated.
abstractThis article proposes a method to quantify the structure of a bipartite graph using a network entropy per link. The network entropy of a bipartite graph with random links is calculated both numerically and theoretically. As an application of the proposed method to analyze collective behavior, the affairs in which participants quote and trade in the foreign exchange market are quantified. The network entropy per link is found to correspond to the macroeconomic situation. A finite mixture of Gumbel distributions is used to fit the empirical distribution for the minimum values of network entropy per link in each week. The mixture of Gumbel distributions with parameter estimates by segmentation procedure is verified by the Kolmogorov--Smirnov test. The finite mixture of Gumbel distributions that extrapolate the empirical probability of extreme events has explanatory power at a statistically significant level.
abstractThis study proposes a pseudo random number generator of q-Gaussian random variables for a range of q values, -infinity < q < 3, based on deterministic chaotic map dynamics. Our method consists of chaotic maps on the unit circle and map dynamics based on the piecewise linear map. We perform the q-Gaussian random number generator for several values of q and conduct both Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) tests. The q-Gaussian samples generated by our proposed method pass the KS test at more than 5% significance level for values of q ranging from -1.0 to 2.7, while they pass the AD test at more than 5% significance level for $q$ ranging from -1 to 2.4.
abstractThis study comprises a comprehensive analysis of time series segmentation on the Japanese stock prices listed on the first section of the Tokyo Stock Exchange during the period from 4 January 2000 to 30 January 2012. A recursive segmentation procedure is used under the assumption of a Gaussian mixture. The number of each quintile of variance for all the segments is used as an indicator of macroeconomic situations and is investigated empirically. The results show that from June 2004 to June 2007, a large majority of stocks were stable and that from 2008 several stocks were unstable. In March 2011, the number of unstable securities increased dramatically due to societal turmoil after the Great East Japan Earthquake. It is concluded that the number of stocks included in each quintile of volatility provides useful information about the Japanese macroeconomic situation.
abstractThis article considers the relationship between the price of flight tickets and their geodesic distance from the departure airport to the destination. Using the data collected from a Japanese flight booking site, I empirically investigated demand-supply situations from parameter estimates of an nth order polynomial function of the price in terms of the distance on each observation date. An adequate order of the polynomial function is determined by using two kinds of information criterions (AIC and BIC). It is confirmed that the ticket availability strongly depends on the Japanese calendar date and that the parameter estimates also depend on the calendar date. The parameter estimates may correspond to demand-supply situations of the Japanese air travel market.
abstractThis study considers the multivariate segmentation procedure under the assumption of the multivariate Gaussian mixture. Jensen-Shannon divergence between two multivariate Gaussian distributions is employed as a discriminator and a recursive segmentation procedure is proposed. The daily log-return time series for 30 currency pairs consisting of 12 currencies for the last decade (January 3, 2001 to December 30, 2011) are analyzed using the proposed method. The proposed method can detect several important periods related to the significant affairs of the international economy.
abstractThis paper investigates the impact of the Great Japan Earthquake (and subsequent tsunami turmoil) on socio-economic activities by using data on hotel opportunities collected from an electronic hotel booking service. A method to estimate both primary and secondary regional effects of a natural disaster on human behavior is proposed. It is confirmed that temporal variation in the regional share of available hotels before and after a natural disaster may be an indicator to measure the socio-economic impact at each district.
abstractThis paper investigates regionality and seasonality of room plan availability in Japan. We employ the singular spectrum analysis to the daily plan availability and extract the trends. We examine the coefficient of a linear relation between a normalized trend at each prefecture and a normalized trend of the whole of Japan. It is concluded that the coefficients, with respect to the four seasons, characterize properties of the prefectures.
abstractWe investigate quotation and transaction activities in the foreign exchange market for every week during the period of June 2007 to December 2010. A scaling relationship between the mean values of red number of quotations (or number of transactions) for various currency pairs and the corresponding standard deviations holds for a majority of the weeks. However, the scaling breaks in some time intervals, which is related to the emergence of market shocks. There is a monotonous relationship between values of scaling indices and global averages of currency pair cross-correlations when both quantities are observed for various window lengths Delta t.
abstractThis study investigates unconditional distributions of daily log-returns of Japanese security prices from a comprehensive point of view. The purpose of this article is to estimate a risk distribution of stocks in terms of Value-at-Risk (VaR) in order to select low risk securities from many securities. Daily log-return time series of 1,340 Japanese companies listed on the first section of Tokyo Stock Exchange are examined during the last one decade. I develop a method to estimate VaR by both the maximum likelihood estimation procedure under a q-Gaussian assumption and analytical form of its cumulative distribution function. It is confirmed that they are fitted to q-Gaussian distributions (Student t-distributions) with Kolmogorov-Smirnov test. It is found that the complementary cumulative distribution function of VaR has a power-law tail with its characteristic exponent depending on values of the VaR percentile.
abstractThis study considers the availability of room opportunities collected from a Japanese hotel booking site. We empirically analyze the daily number of room opportunities for four areas. To determine the migration trends of travelers, we discuss a finite mixture of Poisson distributions and the EM-algorithm as its parameter estimation method. We further propose a method to infer the probability of opportunities existing for each observation. We characterize demand-supply situations by means of relationship between the averaged room prices and the probability of opportunity existing.
abstractWe investigate a power-law relationship between means of constituents' flows and their standard deviations / covariances on a directed bipartite network. We propose a binomial mixture model and a method to infer states of the constituents' flows on such a bipartite network from empirical observation without a priori knowledge on the network structure. By using a proposed parameter estimation method with high frequency financial data we found that the scaling exponent and simultaneous cross-correlation matrix have a positive correspondence relationship. Consequently we conclude that the scaling exponent tends to be 1/2 in the case of desynchronous (specific dynamics is dominant), and to be 1 in the case of synchronous (common dynamics is dominant).
abstractRecent development of Information and Communication Technology enables us to collect and store data on human activities both circumstantially and comprehensively. In such circumstances it is necessary to consider trade-off between personal privacy and public utility. In the present article I discuss methods to quantify comprehensive states of human activities without private information and propose a measure to characterize global states of societies from a holistic point of view based on an information-theoretic methodology. By means of the proposed method I investigate participants' states of the foreign exchange market during the period of the recent financial crisis which started around the middle of 2008. The results show that drastic changes of market states frequently occurred at the foreign exchange market during the period of global financial crisis staring from 2008.
abstractThis study investigates scaling behavior of quotation activities in the foreign exchange market. The power-law relationship between a mean of quotation activities and their standard deviation for each currency pair is found, and the dependence of the scaling exponent on the time window is calculated. It is found that the scaling exponent fluctuates temporally in a range from 0.8 to 0.9 at [min], depending on observation days. The extraction between specific fluctuations and a common fluctuation from quotation activities is conducted. It is concluded that quotation activities in the foreign exchange market are not independently Poissonian, and that temporally or mutually correlated activities of quotations happen. We propose a stochastic model for the foreign exchange market based on a bipartite graph representation. The components' centrality on a bipartite graph is estimated from multiple time series and visualized on a currency pair network. Consequently, the scaling exponents can be used to quantify market participants' states based on information flows in the foreign exchange market. We found that as increasing the window length market participants are affected by exogenous field.
abstractThis study considers -Gaussian distributions and stochastic differential equations with both multiplicative and additive noises. In the M-dimensional case a -Gaussian distribution can be theoretically derived as a stationary probability distribution of the multiplicative stochastic differential equation with both mutually independent multiplicative and additive noises. By using the proposed stochastic differential equation a method to evaluate a default probability under a given risk buffer is proposed.
AbstractThis article proposes methods to detect states of financial markets both comprehensively and with a high-resolution. In order to quantify trading patterns several mathematical methods are proposed based on frequencies of quotations/transactions estimated from high-resolution data of financial markets. The empirical results (graphical network representation and quantification of states of market participants) for the foreign exchange market are shown. It is concluded that synchronous behavior associated with a large population of market participants may be a candidate of precursory signs leading to an environmental change.
abstractThis article proposes mathematical methods to quantify states of market participants in the foreign exchange market (FX market) and conduct comprehensive analysis on behavior of market participants by means of high-frequency financial data. Based on econophysics tools and perspectives we study similarity measures for both rate movements and quotation activities among various currency pairs. We perform also clustering analysis on market states for observation days, and find scaling relationship between mean values of quotation activities and their standard deviations. By using these mathematical methods we can visualize states of the FX market comprehensively. Finally we conclude that states of market participants temporally vary due to both external and internal factors.
abstractAs the result of empirical investigations into the foreign exchange market a group structure of characteristic periodic decisions of market participants is found. In order to explain this finding at the microscopic level the agent-based model of a financial market in which N market participants trade financial commodities is considered. If different sources of periodic information exist then the relationship among these characteristic periodic behaviors may be associated with a special structure where market participants perceive such information in the foreign exchange market.
abstractEmpirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi-dimensional time series with spectral distances introduced in [A.-H. Sato, Physica A, 382 (2007) 258--270]. As a result it is found that the similarities among currency pairs fluctuate with the rotation of the earth, and that the similarities among best quotation rates are associated with those among quotation frequencies. Furthermore it is shown that the Jensen-Shannon spectral divergence is proportional to a mean of the Kullback-Leibler spectral distance both empirically and numerically. It is confirmed that these spectral distances are connected with distributions for behavioral parameters of the market participants from numerical simulation. This concludes that spectral distances of representative quantities of financial markets are related into diversification of behavioral parameters of the market participants.
abstractWe apply the Beck model, developed for turbulent systems that exhibit scaling properties, to stock markets. Our study reveals that the Beck model elucidates properties of stock market returns and is applicable to practical use such as the Value-at-Risk estimation and the portfolio analysis. We perform empirical analysis with daily/intraday data of the S & P500 index return and find that the volatility fluctuation of real markets is well consistent with the assumptions of the Beck model: The volatility fluctuates at a much larger time scale than return itself and the inverse of variance, or ``inverse temperature,'' obeys -distribution. As predicted by the Beck model, the distribution of returns is well fitted by -Gaussian distribution of Tsallis statistics.
abstractIn this article an informational method to quantify behavioral similarities of the market participants is proposed regarding a financial market as a many-body system. An agent-based model of the financial market in which market participants deal with financial commodities is considered. In order to measure the agents' interaction the spectral distance defined by the Kullback-Leibler divergence between two normalized spectra of behavioral frequencies is introduced. The validity of the method is evaluated by using the behavioral frequencies obtained from the agent-based model. It is concluded that the perception and decision parameters of agents who treat two commodities tend to be similar when those behavioral frequencies are similar.
abstractThe high frequency financial data of the foreign exchange market (EUR/CHF, EUR/GBP, EUR/JPY, EUR/NOK, EUR/SEK, EUR/USD, NZD/USD, USD/CAD, USD/CHF, USD/JPY, USD/NOK, and USD/SEK) are analyzed by utilizing the Kullback-Leibler divergence between two normalized spectrograms of the tick frequency. We detect and characterize temporal structure variations of the similarity between currency pairs. A simple agent-based model that market participants exchange currency pairs is proposed. The equation for the tick frequency is approximately derived in the theoretical manner. From the analysis of this model the spectral distance of the tick frequency is associated with the similarity of behavior (perception and decision) of the market participants to exchange these currency pairs.
abstractRecent accumulation of high frequency financial data due to development of information technology allows us to analyze behaviors of market participants in high resolution. In this article, we focus on tick frequency obtained from the high frequency data and investigate the characteristics of the tick frequency by utilizing spectrograms. Moreover the method to quantify the similarity between currency pairs based on the Kullback-Leibler divergence between spectrograms of the tick frequency for two currency pairs is proposed, and the time series of the similarities between currency pairs are computed. It is found that the recent markets are more similar than the past markets from the viewpoint of the tick frequency.
abstractPower spectrum densities for the number of tick quotes per minute (market activity) on three currency markets (USD/JPY, EUR/USD, and JPY/EUR) are analyzed for periods from January 2000 to December 2000. We find some peaks on the power spectrum densities at a few minutes. We develop the double-threshold agent model and confirm that the corresponding periodicity can be observed for the activity of this model even though market participants perceive common weaker periodic information than threshold for decision-making of them. This model is numerically performed and theoretically investigated by utilizing the mean-field approximation. We propose a hypothesis that the periodicities found on the power spectrum densities can be observed due to nonlinearity and diversity of market participants.
abstractPower spectrum densities for the number of tick quotes per minute (market activity) on three currency markets (USD/JPY, EUR/USD, and JPY/EUR) for periods from January 1999 to December 2000 are analyzed. We find some peaks on the power spectrum densities at a few minutes. We develop the double-threshold agent model and confirm that stochastic resonance occurs for the market activity of this model. We propose a hypothesis that the periodicities found on the power spectrum densities can be observed due to stochastic resonance.
abstractWe consider solutions of the self-consistent equation of an array of double threshold noisy devices with a positive feedback of an aggregation of the output from each device. Stationary solutions of the aggregation (order parameter) as a function of the input signal are investigated. We classify stationary solutions as three types: (1) monotonically increasing function (for large noise strength and small feedback strength), which is approximated by a linear function around a small input signal; (2) single-hysteresis function (for a large feedback strength), which is observed in the Ising model; (3) double-hysteresis function (for a small noise strength and a small feedback strength), which is never found in the Ising model. The diagram to show the three different types is theoretically calculated. We discuss a method to improve a performance of a stochastic resonator by tuning a system near a phase transition point. We conclude that the response of the system exhibits three different types of behaviors depending on the feedback strength and the standard deviation of the noise.
abstractSignal processing in a simple threshold system is studied with use of a static mutual information between the input and output data, with main emphasis put on stochastic resonance (SR) and a feedback mechanism to enhance information transmission through the system. First we verify that the proposed static mutual information is well correlated with the existing measures for SR, such as the signal to noise ratio and the normalized power norm. Secondly we try to use output information to improve quality of signal processing and show by a self-consistent theory that a feedback mechanism can usefully be applied to improve performance (i.e., to increase the mutual information) of the simple threshold system.
abstractWe consider the problem of optimizing signal transmission through multi-channel noisy devices. We investigate an array of bithreshold noisy devices which are connected in parallel and convergent on a summing center. Utilizing the concept of noise-induced linearization we derive an analytical approximation of the normalized power norm and clarify the relation between the optimum threshold and the standard deviation of noises. We show that the optimum threshold value is 0.63 times the standard deviation of the noises. This relation is applicable to both subthreshold and suprathreshold inputs.
abstractRecently it has been shown that inter-transaction interval (ITI) distribution of ofreign currency rates has a fat tail. In order to understand the statistical property of the ITI the dealer mode with N interactive agents is proposed. From numerical simulations it is confirmed that ITI distribution of the dealer model has a power law tail. The random multiplicative process (RMP) can be approximately derived from the ITI of the dealer model. Consequently we conclude that the power law tail of the ITI distribution of the dealer model is a result of the RMP.
abstractAutoregressive conditional duration (ACD) processes, which have potential to be applied to power law distributions of complex systems found in natural science, life science and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown.
abstractA model of fluctuations in the market price including many deterministic dealers, who predict their buying and selling prices from the latest price change, is developed. We show that price changes of the model is approximated by ARCH(1) process. We conclude that predictions of dealers affected by the past price changes cause the fat tails of probability density function. We believe that this study bridges stochastic processes in econometrics with multi-agent simulation approaches.
abstractWe constructed an analog electrical circuit which generates fluctuations in which probability density function has power law tails. In the circuit fluctuations with an arbitrary exponent of the power law can be obtained by adjusting the resistance. With this low cost circuit the random fluctuations which have the similar statistics to foreign exchange rates can be generated as fast as an expensive digital computer.
abstractI present a contact point between agent based approach and stochastic processes. From three viewpoints market price fluctuations are approached; statistical properties of foreign exchange rates (macroscopic), a artificial market (microscopic) and stochastic processes (mesoscopic). A simple artificial market model is introduced and investigated both numerically and analytically. A stochastic process for price dynamics is derived from the artificial market model and its statistical property is exhibited. I believe that this study establishes a bridge between artificial market model and stochastic processes.
abstractWe constructed an analog circuit generating fluctuations of which a probability density function has power law tails. In the circuit fluctuations with an arbitrary exponent of the power law can be obtained by tuning the resistance. A theory of a differential equation with both multiplicative and additive noises which describes the circuit is introduced. The circuit is composed of a noise generator, an analog multiplier and an integration circuit. Sequential outputs of the circuit are observed and their probability density function and autocorrelation coefficients are shown. It is found that correlation time of the autocorrelation coefficient is dependent on the power law exponent.
abstractThe random multiplicative process is studied for the case of a colored multiplicative noise with exponentially decreasing autocorrelation function. We observe the power law exponent of probability distribution in a statistically steady state numerically to clarify the effect of finite correlation time. The renormalization procedure is applied to derive the power law exponent theoretically. The power law exponent is inversely proportional to the autocorrelation time of the multiplicative noise.
abstractA variant of threshold dynamics is introduced to model the behaviors of a large assembly of dealers in a stock market. Although the microscopic evolution dynamics is deterministic the collective behaviors such as market prices show seemingly stochastic fluctuations. The statistical properties of market price change can be well approximated by a simple discrete Langevin-type equation with random amplification. The macroscopic stochastic equation is solved both numerically and analytically showing that the market price change generally follow power law distributions in the steady state. The reason for the appearance of rapid decay in the distribution tails are discussed.
abstractA general discrete stochastic process involving random amplification with additive external noise is analyzed theoretically and numerically. Necessary and sufficient conditions to realize steady power law fluctuations with divergent variance are clarified. The power law exponent is determined by a statistical property of amplification independent of the external noise. By introducing a nonlinear effect a stretched exponential decay appears in the power law. |