Observation of two types of behaviors of financial bubbles and the related higher-order potential forces

Abstract

Market prices are known to be well described by the random walk model in a time-dependent potential force whose center is given by the trace of the random walker [Physica A 370 (2006), 91]. We analytically show that the higher-order potential force determines the dynamic price behaviors of the single-exponential growth and the double exponential growth. We confirm the existence of such price behaviors in real financial data and we observe the higher-order potential forces in some periods.