Financial Time Series and Statistical Mechanics

TL;DR

This paper compares characteristic exponents in financial and mathematical time series to understand their power law behaviors, using techniques to measure and distinguish these exponents with practical examples.

Contribution

It reviews and compares methods for analyzing power law exponents in financial and mathematical time series, highlighting differences in measurement techniques.

Findings

Different exponents describe various aspects like roughness and persistence.

Techniques for measuring these exponents are clarified.

Financial data exemplifies the application of these methods.

Abstract

A few characteristic exponents describing power law behaviors of roughness, coherence and persistence in stochastic time series are compared to each other. Relevant techniques for analyzing such time series are recalled in order to distinguish how the various exponents are measured, and what basic differences exist between each one. Financial time series, like the JPY/DEM and USD/DEM exchange rates are used for illustration, but mathematical ones, like (fractional or not) Brownian walks can be used also as indicated.