Using the uniform most powerful unbiased test, we observed the sales distribution of consumer electronics in Japan on a daily basis and report that it follows both a lognormal distribution and a power-law distribution and depends on the state of the market. We show that these switches occur...

We introduce a weighted-moving-average analysis for the tick-by-tick data of yen–dollar exchange rates. The weights are determined automatically for given data by applying the Yule–Walker formula for autoregressive model. Although the data are non-stationary, the resulting moving average...

We discuss a mechanism through which inversion symmetry (i.e., invariance of a joint probability density function under the exchange of variables) and Gibrat’s law generate power-law distributions with different tail exponents. Using a dataset of firm size variables, that is, tangible fixed...

We show that random walks in a moving potential function, with its center at the moving average of market prices, are represented in the form of the self-modulation model. From this point of view we confirm the existence of non-trivial autocorrelation in real market price changes. By...

In this study, the authors examine exhaustive business data on Japanese firms, which cover nearly all companies in the mid- and large-scale ranges in terms of firm size, to reach several key findings on profits/sales distribution and business growth trends. Here, profits denote net profits....

We analyze high-resolution foreign exchange data consisting of 20 million data points of USD-JPY for 13 years to report firm statistical laws in distributions and correlations of exchange rate fluctuations. A conditional probability density analysis clearly shows the existence of trend-following...

By using the historical data from the Japanese banks’ database at “The Bankers Library” of Japanese Banker Association, we analyze the historical network of banks from 1868 to 2006. Firstly, we define a bank every year by a particle and draw a space–time evolution process of merger,...

We study the statistical laws of the expenditure of a person in convenience stores by analyzing around 100 million receipts. The density function of expenditure exhibits a fat tail that follows a power law. Using the Lorenz curve, the Gini coefficient is estimated to be 0.70; this implies that...

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 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...