arXiv subjects

Hideki Takayasu

Publications and source records attributed to Hideki Takayasu.

At least 37 records · Page 2Linked to original sources

arXiv2014

Generalised central limit theorems for growth rate distribution of complex systems

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety of fields can be derived from this basic physical model. Statistical data of growth rates for about 1 million business firms are analysed as a real-world example of randomly growing systems. Not only are the scaling relations consistent with the theoretical solution, but the entire functional form of the growth rate distribution is fitted with a theoretical distribution that has a power-law tail.

physics.soc-ph↗

arXiv2013

Segmentation procedure based on Fisher's exact test and its application to foreign exchange rates

This study proposes the segmentation procedure of univariate time series based on Fisher's exact test. We show that an adequate change point can be detected as the minimum value of p-value. It is shown that the proposed procedure can detect change points for an artificial time series. We apply the proposed method to find segments of the foreign exchange rates recursively. It is also applied to randomly shuffled time series. It concludes that the randomly shuffled data can be used as a level to determine the null hypothesis.

stat.ME↗

arXiv2013

Ecosystems perspective on financial networks: diagnostic tools

The economical world consists of a highly interconnected and interdependent network of firms. Here we develop temporal and structural network tools to analyze the state of the economy. Our analysis indicates that a strong clustering can be a warning sign. Reduction in diversity, which was an essential aspect of the dynamics surrounding the crash in 2008, is seen as a key emergent feature arising naturally from the evolutionary and adaptive dynamics inherent to the financial markets. Similarly, collusion amongst construction firms in a number of regions in Japan in the 2000s can be identified with the formation of clusters of anomalous highly connected companies.

q-fin.RM↗

arXiv2012

Empirical analysis of collective human behavior for extraordinary events in blogosphere

To uncover underlying mechanism of collective human dynamics, we survey more than 1.8 billion blog entries and observe the statistical properties of word appearances. We focus on words that show dynamic growth and decay with a tendency to diverge on a certain day. After careful pretreatment and fitting method, we found power laws generally approximate the functional forms of growth and decay with various exponents values between -0.1 and -2.5. We also observe news words whose frequency increase suddenly and decay following power laws. In order to explain these dynamics, we propose a simple model of posting blogs involving a keyword, and its validity is checked directly from the data. The model suggests that bloggers are not only responding to the latest number of blogs but also suffering deadline pressure from the divergence day. Our empirical results can be used for predicting the number of blogs in advance and for estimating the period to return to the normal fluctuation level.

physics.soc-ph↗

arXiv2012

Relations between allometric scalings and fluctuations in complex systems: The case of Japanese firms

To elucidate allometric scaling in complex systems, we investigated the underlying scaling relationships between typical three-scale indicators for approximately 500,000 Japanese firms; namely, annual sales, number of employees, and number of business partners. First, new scaling relations including the distributions of fluctuations were discovered by systematically analyzing conditional statistics. Second, we introduced simple probabilistic models that reproduce all these scaling relations, and we derived relations between scaling exponents and the magnitude of fluctuations.

physics.soc-ph↗

arXiv2011

Biased diffusion on Japanese inter-firm trading network: Estimation of sales from network structure

To investigate the actual phenomena of transport on a complex network, we analysed empirical data for an inter-firm trading network, which consists of about one million Japanese firms and the sales of these firms (a sale corresponds to the total in-flow into a node). First, we analysed the relationships between sales and sales of nearest neighbourhoods from which we obtain a simple linear relationship between sales and the weighted sum of sales of nearest neighbourhoods (i.e., customers). In addition, we introduce a simple money transport model that is coherent with this empirical observation. In this model, a firm (i.e., customer) distributes money to its out-edges (suppliers) proportionally to the in-degree of destinations. From intensive numerical simulations, we find that the steady flows derived from these models can approximately reproduce the distribution of sales of actual firms. The sales of individual firms deduced from the money-transport model are shown to be proportional, on an average, to the real sales.

q-fin.GN↗

arXiv2008

Random walker in a temporally deforming higher-order potential forces observed in financial crisis

Basic peculiarities of market price fluctuations are known to be well described by a recently developed random walk model in a temporally deforming quadric potential force whose center is given by a moving average of past price traces [Physica A 370, pp91-97, 2006]. By analyzing high-frequency financial time series of exceptional events such as bubbles and crashes, we confirm the appearance of nonlinear potential force in the markets. We show statistical significance of its existence by applying the information criterion. This new time series analysis is expected to be applied widely for detecting a non-stationary symptom in random phenomena.

q-fin.ST↗

arXiv2008

Solvable Stochastic Dealer Models for Financial Markets

We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects, the self-modulation of transaction intervals and a forecasting tendency, which uses a moving average of the latest market price changes. Based on the present microscopic model of markets, we find a quantitative relation with market potential forces, which has recently been discovered in the study of market price modeling based on random walks.

q-fin.TR↗

arXiv2007

The Grounds For Time Dependent Market Potentials From Dealers' Dynamics

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated by dealers with positive feedback the resulting potential force is repulsive, while the effect of negative feedback enhances the attractive potential force.

q-fin.GN↗

arXiv2006

Artificial market model based on deterministic agents and derivation of limit of GARCH type process

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.

cond-mat.stat-mech↗

arXiv2006

Analysis of price diffusion in financial markets using PUCK model

Based on the new type of random walk process called the Potentials of Unbalanced Complex Kinetics (PUCK) model, we theoretically show that the price diffusion in large scales is amplified 2/(2 + b) times, where b is the coefficient of quadratic term of the potential. In short time scales the price diffusion depends on the size M of the super moving average. Both numerical simulations and real data analysis of Yen-Dollar rates are consistent with theoretical analysis.

physics.soc-ph↗

arXiv2006

Characterization of foreign exchange market using the threshold-dealer-model

We introduce a deterministic dealer model which implements most of the empirical laws, such as fat tails in the price change distributions, long term memory of volatility and non-Poissonian intervals. We also clarify the causality between microscopic dealers' dynamics and macroscopic market's empirical laws.

physics.soc-ph↗

arXiv2006

Extracting the exponential behaviors in the market data

We introduce a mathematical criterion defining the bubbles or the crashes in financial market price fluctuations by considering exponential fitting of the given data. By applying this criterion we can automatically extract the periods in which bubbles and crashes are identified. From stock market data of so-called the Internet bubbles it is found that the characteristic length of bubble period is about 100 days.

physics.soc-ph↗

arXiv2005

Potentials of Unbalanced Complex Kinetics Observed in Market Time Series

As a model of market price, we introduce a new type of random walk in a moving potential which is approximated by a quadratic function with its center given by the moving average of its own trace. The properties of resulting random walks are similar to those of ordinary random walks for large time scales; however, their short time properties are approximated by abnormal diffusion with non-trivial exponents. A new data analysis method based on this model enables us to observe temporal changes of potential forces from high precision market data directly.

physics.soc-ph↗

arXiv2005

Correlation Networks Among Currencies

By analyzing the foreign exchange market data of various currencies, we derive a hierarchical taxonomy of currencies constructing minimal-spanning trees. Clustered structure of the currencies and the key currency in each cluster are found. The clusters match nicely with the geographical regions of corresponding countries in the world such as Asia or East Europe, the key currencies are generally given by major economic countries as expected.

physics.soc-ph↗

arXiv2005

Modeling a foreign exchange rate using moving average of Yen-Dollar market data

We introduce an autoregressive-type model with self-modulation effects for a foreign exchange rate by separating the foreign exchange rate into a moving average rate and an uncorrelated noise. From this model we indicate that traders are mainly using strategies with weighted feedbacks of the past rates in the exchange market. These feedbacks are responsible for a power law distribution and characteristic autocorrelations of rate changes.

physics.soc-ph↗

arXiv2005

Characteristic market behaviors caused by intervention in a foreign exchange market

In foreign exchange markets monotonic rate changes can be observed in time scale of order of an hour on the days that governmental interventions took place. We estimate the starting time of an intervention using this characteristic behavior of the exchange rates. We find that big amount of interventions can shift the averaged rate about 1 yen per 1 dollar in an hour, and the rate change distribution becomes asymmetric for a few hours.

physics.data-an↗

arXiv2004

Herd Behaviors in Financial Markets

We investigate the herd behavior of returns for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution $P(R)$ of returns $R$ satisfies the power-law behavior $P(R) \simeq R^{-β}$ with the exponents $ β=3.11$(the time interval $τ=$ one minute) and 3.36($τ=$ one day). The informational cascade regime appears in the herding parameter $H\ge 2.33$ at $τ=$ one minute, while it occurs no herding at $τ=$ one day. Especially, we find that the distribution of normalized returns shows a crossover to a Gaussian distribution at one time step $Δt=1$ day.

cond-mat.stat-mech↗