arXiv subjects

Misako Takayasu

Publications and source records attributed to Misako Takayasu.

At least 37 records · Page 2Linked to original sources

arXiv2016

Statistical properties of fluctuations of time series representing the appearance of words in nationwide blog data and their applications: An example of observations and the modelling of fluctuation scalings of nonstationary time series

To elucidate the non-trivial empirical statistical properties of fluctuations of a typical non-steady time series representing the appearance of words in blogs, we investigated approximately five billion Japanese blogs over a period of six years and analyse some corresponding mathematical models. First, we introduce a solvable non-steady extension of the random diffusion model, which can be deduced by modelling the behaviour of heterogeneous random bloggers. Next, we deduce theoretical expressions for both the temporal and ensemble fluctuation scalings of this model, and demonstrate that these expressions can reproduce all empirical scalings over eight orders of magnitude. Furthermore, we show that the model can reproduce other statistical properties of time series representing the appearance of words in blogs, such as functional forms of the probability density and correlations in the total number of blogs. As an application, we quantify the abnormality of special nationwide events by measuring the fluctuation scalings of 1771 basic adjectives.

physics.soc-ph↗

arXiv2015

Financial Knudsen number: breakdown of continuous price dynamics and asymmetric buy and sell structures confirmed by high precision order book information

We generalise the description of the dynamics of the order book of financial markets in terms of a Brownian particle embedded in a fluid of incoming, exiting and annihilating particles by presenting a model of the velocity on each side (buy and sell) independently. The improved model builds on the time-averaged number of particles in the inner layer and its change per unit time, where the inner layer is revealed by the correlations between price velocity and change in the number of particles (limit orders). This allows us to introduce the Knudsen number of the financial Brownian particle motion and its asymmetric version (on the buy and sell sides). Not being considered previously, the asymmetric Knudsen numbers are crucial in finance in order to detect asymmetric price changes. The Knudsen numbers allows us to characterise the conditions for the market dynamics to be correctly described by a continuous stochastic process. Not questioned until now for large liquid markets such as the USD/JPY and EUR/USD exchange rates, we show that there are regimes when the Knudsen numbers are so high that discrete particle effects dominate, such as during market stresses and crashes. We document the presence of imbalances of particles depletion rates on the buy and sell sides that are associated with high Knudsen numbers and violent directional price changes. This indicator can detect the direction of the price motion at the early stage while the usual volatility risk measure is blind to the price direction.

q-fin.TR↗

arXiv2014

Financial Brownian particle in the layered order book fluid and Fluctuation-Dissipation relations

We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner-layer, the correlation is strong and with short memory while, in the outer-layer, it is weaker and with long memory. By interpreting and estimating the contribution from the outer-layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation (FDR) in this non-material Brownian motion process.

q-fin.TR↗

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

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↗

arXiv2010

Macroscopic and microscopic statistical properties observed in blog entries

We observe the statistical properties of blogs that are expected to reflect social human interaction. Firstly, we introduce a basic normalization preprocess that enables us to evaluate the genuine word frequency in blogs that are independent of external factors such as spam blogs, server-breakdowns, increase in the population of bloggers, and periodic weekly behaviors. After this process, we can confirm that small frequency words clearly follow an independent Poisson process as theoretically expected. Secondly, we focus on each blogger's basic behaviors. It is found that there are two kinds of behaviors of bloggers. Further, Zipf's law on word frequency is confirmed to be universally independent of individual activity types.

physics.soc-ph↗

arXiv2009

The statistical relationship between product life cycle and repeat purchase behavior in convenience stores

The density function of product life cycles in convenience stores is found to follow the Weibull distribution. To clarify the parameters that determine these life cycles, we introduce the conditional market share-defined as the probability that a product is selected by customers only if it had been previously purchased-and the market share without any conditions. The product life cycle is more strongly correlated with the conditional market share of the product than with the latter type of market share.

physics.soc-ph↗

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↗

arXiv2007

Pareto law of the expenditure of a person in convenience stores

We study the statistical laws of the expenditure of a person in convenience stores by analysing around 100 million receipts. The density function of expenditure exhibits a fat tail that follows a power law. We observe the Pareto principle where both the top 25% and 2% of the customers account for 80% and 25% of the store's sales, respectively. Using the Lorenz curve, the Gini coefficient is estimated to be 0.70; this implies a strong economic inequality.

physics.soc-ph↗

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↗