  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.
