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...

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...

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...