Related Experiment Video
Updated: Aug 22, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
Published on: December 9, 2015
Irregularity, volatility, risk, and financial market time series
Steve Pincus1, Rudolf E Kalman
1Swiss Federal Instutte of Technology, Zurich, Switzerland. stevepincus@alum.mit.edu
Abstract:
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.
Related Concept Videos
Variance
Standard Deviation
Random Error
First Derivative Test: Problem Solving
Variability: Analysis
The range is a simple measure of variability, indicating the difference between the highest and...
Noncompartmental Analysis: Statistical Moment Theory