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...

Using tick-by-tick data for the dollar--yen and euro--dollar exchange rates recorded on the actual transaction platform, a ‘run’—continuous increases or decreases in deal prices for the past several ticks—does have some predictable information on the direction of the next price movement....

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)-1 times, where b is the coefficient of quadratic term of the potential. In short time scales the...

We observe temporal fluctuations of information traffic going through a link of the Internet. The fluctuations are characterized by finite correlation times implying that they can be regarded as statistically quasi-stationary. Usual methods in statistical physics become powerful and we confirm a...

We introduce an autoregressive-type model of prices in the financial market taking into account the self-modulation effect. We find that traders are mainly using strategies with weighted feedbacks of past prices. These feedbacks are responsible for the slow diffusion in short times, apparent...

We analyze high precision data of transaction intervals in a foreign exchange market, and show that it is nicely approximated by a non-stationary Poisson process whose expectation value is given by a moving average of its own trace. Generalizing this result we introduce novel stochastic...

We check the validity of the mathematical method of detecting financial bubbles or crashes, which is based on a data fitting with an exponential function. We show that the period of a bubble can be determined nearly uniquely independent of the precision of data. The method is widely applicable...

We analyze tick-by-tick data, the most high frequency data available, of yen–dollar currency exchange rates. We show that a dynamical structure can be observed in binarized data indicating the direction of up and down movement of prices, which is not apparently seen from the price change...

We introduce a mean-field-type approximation for description of company's income statistics. Utilizing huge company data we show that a discrete version of Langevin equation with additive and multiplicative noises can appropriately describe the time evolution of a company's income fluctuation in...