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...

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...

By analyzing a huge amount of point-of-sale data collected from Japanese supermarkets, we find power law relationships between price and sales numbers. The estimated values of the exponents of these power laws depend on the category of products; however, they are independent of the stores,...

We perform a simplified Ethernet traffic simulation in order to clarify the physical mechanism of the phase transition behavior which has been experimentally observed in the flow density fluctuation of Internet traffic. In one phase, traffics from nodes connected with an Ethernet cable are...

It is shown theoretically that an apparent intellectual function of direction selectivity is naturally caused by neuronal threshold dynamics in the retinal neural network with non-uniform signal delays originating in the neuron's random dendrite geometry. By addition of information pathways via...

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...

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...

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...