Assessing Relative Volatility/Intermittency/Energy Dissipation

TL;DR

This paper introduces a method to estimate the temporal variation of volatility and intermittency in complex stochastic processes, with applications to turbulence data, by developing a probabilistic asymptotic theory and inference techniques.

Contribution

It presents a novel approach to assess relative volatility and intermittency in non-semimartingale processes, extending existing theories and providing empirical analysis of turbulence data.

Findings

Consistent estimation of volatility variation in complex processes.

Development of asymptotic theory for relative power variations.

Application to empirical turbulence data revealing energy dissipation patterns.

Abstract

We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency when the data of interest are generated by a non-semimartingale, or a Brownian semistationary process in particular. This estimation method is motivated by the assessment of relative energy dissipation in empirical data of turbulence, but it is also applicable in other areas. We develop a probabilistic asymptotic theory for realised relative power variations of Brownian semistationary processes, and introduce inference methods based on the theory. We also discuss how to extend the asymptotic theory to other classes of processes exhibiting stochastic volatility/intermittency. As an empirical application, we study relative energy dissipation in data of atmospheric turbulence.