Aki-Hiro Sato | Kyoto University (original) (raw)
Papers by Aki-Hiro Sato
This article proposes methods to detect states of financial markets both comprehensively and with... more This 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.
We investigate quotation and transaction activities in the foreign exchange market for every week... more We 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 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 Deltat\Delta tDeltat.
The financial markets started to be computerized due to development and spread of the Information... more The financial markets started to be computerized due to development and spread of the Information and Communication Technology (ICT) in early 1990s. As the result rapid development and spread of electrical trading systems occurred all over the world. Moreover advance of processing speed of computers and capacity of storages leads to accumulation of activity records of market participants, high frequency financial data. By utilizing the high frequency financial data one can observe behavior of the market participants with high resolutions and analyze a large amount of data enough to quantify them in the statistically significant.
This study considers the multivariate segmentation procedure under the assumption of the multivar... more This 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.
Physica A-statistical Mechanics and Its Applications, 2010
This study investigates scaling behavior of quotation activities in the foreign exchange market. ... more This 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 α on the time window ∆t is calculated. It is found that the scaling exponent fluctuates temporally in a range from 0.8 to 0.9 at ∆t = 1 [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.
Progress of Theoretical Physics Supplement, 2009
This article proposes mathematical methods to quantify states of marketparticipants in the foreig... more This article proposes mathematical methods to quantify states of marketparticipants 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. 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.
We constructed an analog electrical circuit which generates fluctuations in which probability den... more We 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 exchang rates can be generated as fast as an expensive digital computer.
Physical Review Letters, 1997
Physical Review E, 2000
The random multiplicative process is studied for the case of a colored multiplicative noise with ... more The 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.
A model of fluctuations in the market price including many deterministic dealers, who predict the... more A 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.
We constructed an analog circuit generating fluctuations of which a probability density function ... more We 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 integral 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.
Physica A-statistical Mechanics and Its Applications, 1998
A variant of threshold dynamics is introduced to model the behaviors of a large assembly of deale... more A 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 uctuations. The statistical properties of market price change can be well approximated by a simple discrete Langevin-type equation with random ampliÿcation. 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.
We propose an artificial market model based on deterministic agents. The agents modify their ask/... more We propose an artificial market model based on deterministic agents. The agents modify their ask/bid price depending on past price changes. The temporal development of market price fluctuations is calculated numerically. A probability density function of market price changes has power law tails. Autocorrelation coefficient of the changes has an anti-correlation, and autocorrelation coefficient of squared changes (volatility correlation function) has a long time correlation. A probability density function of intervals between successive trading follows a geometric distribution. GARCH type stochastic process is theoretically derived from this market model in a limit case. We discuss factors of the market price fluctuations and a relation between the volatility of the market prices and a demand-supply curve. We conclude that the power law tails and the long time volatility result from mechanism of the GARCH type stochastic process.
This paper investigates the impact of the Great Japan Earthquake (and subsequent tsunami turmoil)... more This 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. typeset using PTPT E X.cls Ver.0.9
This study considers the availability of room opportunities collected from a Japanese hotel booki... more This 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 demandsupply situations by means of relationship between the averaged room prices and the probability of opportunity existing.
A model of fluctuations in the market price including many deterministic dealers, who predict the... more A 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.
This article proposes methods to detect states of financial markets both comprehensively and with... more This 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.
We investigate quotation and transaction activities in the foreign exchange market for every week... more We 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 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 Deltat\Delta tDeltat.
The financial markets started to be computerized due to development and spread of the Information... more The financial markets started to be computerized due to development and spread of the Information and Communication Technology (ICT) in early 1990s. As the result rapid development and spread of electrical trading systems occurred all over the world. Moreover advance of processing speed of computers and capacity of storages leads to accumulation of activity records of market participants, high frequency financial data. By utilizing the high frequency financial data one can observe behavior of the market participants with high resolutions and analyze a large amount of data enough to quantify them in the statistically significant.
This study considers the multivariate segmentation procedure under the assumption of the multivar... more This 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.
Physica A-statistical Mechanics and Its Applications, 2010
This study investigates scaling behavior of quotation activities in the foreign exchange market. ... more This 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 α on the time window ∆t is calculated. It is found that the scaling exponent fluctuates temporally in a range from 0.8 to 0.9 at ∆t = 1 [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.
Progress of Theoretical Physics Supplement, 2009
This article proposes mathematical methods to quantify states of marketparticipants in the foreig... more This article proposes mathematical methods to quantify states of marketparticipants 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. 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.
We constructed an analog electrical circuit which generates fluctuations in which probability den... more We 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 exchang rates can be generated as fast as an expensive digital computer.
Physical Review Letters, 1997
Physical Review E, 2000
The random multiplicative process is studied for the case of a colored multiplicative noise with ... more The 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.
A model of fluctuations in the market price including many deterministic dealers, who predict the... more A 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.
We constructed an analog circuit generating fluctuations of which a probability density function ... more We 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 integral 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.
Physica A-statistical Mechanics and Its Applications, 1998
A variant of threshold dynamics is introduced to model the behaviors of a large assembly of deale... more A 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 uctuations. The statistical properties of market price change can be well approximated by a simple discrete Langevin-type equation with random ampliÿcation. 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.
We propose an artificial market model based on deterministic agents. The agents modify their ask/... more We propose an artificial market model based on deterministic agents. The agents modify their ask/bid price depending on past price changes. The temporal development of market price fluctuations is calculated numerically. A probability density function of market price changes has power law tails. Autocorrelation coefficient of the changes has an anti-correlation, and autocorrelation coefficient of squared changes (volatility correlation function) has a long time correlation. A probability density function of intervals between successive trading follows a geometric distribution. GARCH type stochastic process is theoretically derived from this market model in a limit case. We discuss factors of the market price fluctuations and a relation between the volatility of the market prices and a demand-supply curve. We conclude that the power law tails and the long time volatility result from mechanism of the GARCH type stochastic process.
This paper investigates the impact of the Great Japan Earthquake (and subsequent tsunami turmoil)... more This 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. typeset using PTPT E X.cls Ver.0.9
This study considers the availability of room opportunities collected from a Japanese hotel booki... more This 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 demandsupply situations by means of relationship between the averaged room prices and the probability of opportunity existing.
A model of fluctuations in the market price including many deterministic dealers, who predict the... more A 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.