Random walker in a temporally deforming higher-order potential forces observed in financial crisis

TL;DR

This paper analyzes high-frequency financial data to confirm the presence of nonlinear, temporally deforming potential forces influencing market fluctuations, using a novel random walk model validated by statistical criteria.

Contribution

It introduces a new method for detecting non-stationary forces in financial markets through time series analysis of extreme events.

Findings

Confirmation of nonlinear potential forces during market crashes and bubbles

Statistical validation of the deforming potential model

Potential for broader application in non-stationary phenomena detection

Abstract

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.