Approximate Entropy as an Irregularity Measure for Financial Data

The need to assess subtle, potentially exploitable changes in serial structure is paramount in the analysis of financial and econometric data. We demonstrate the utility of approximate entropy (ApEn), a model-independent measure of sequential irregularity, towards this goal, via several distinct applications, both empirical data and model-based. We also consider cross-ApEn, a related two-variable measure of asynchrony that provides a more robust and ubiquitous measure of bivariate correspondence than does correlation, and the resultant implications to diversification strategies. We provide analytic expressions for and statistical properties of ApEn, and compare ApEn to nonlinear (complexity) measures, correlation and spectral analyses, and other entropy measures.