Irregularity, volatility, risk, and financial market time series.

The need to assess subtle, potentially exploitable changes in serial structure is paramount in the analysis of financial data. Herein, we demonstrate the utility of approximate entropy (ApEn), a model-independent measure of sequential irregularity, toward this goal, by several distinct applications. We consider both empirical data and models, including composite indices (Standard and Poor's 500 and Hang Seng), individual stock prices, the random-walk hypothesis, and the Black-Scholes and fractional Brownian motion models. Notably, ApEn appears to be a potentially useful marker of system stability, with rapid increases possibly foreshadowing significant changes in a financial variable.