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2014 Assessing relative volatility/ intermittency/energy dissipation
Ole E. Barndorff-Nielsen, Mikko S. Pakkanen, Jürgen Schmiegel
Electron. J. Statist. 8(2): 1996-2021 (2014). DOI: 10.1214/14-EJS942

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.

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Ole E. Barndorff-Nielsen. Mikko S. Pakkanen. Jürgen Schmiegel. "Assessing relative volatility/ intermittency/energy dissipation." Electron. J. Statist. 8 (2) 1996 - 2021, 2014. https://doi.org/10.1214/14-EJS942

Information

Published: 2014
First available in Project Euclid: 29 October 2014

zbMATH: 1302.60115
MathSciNet: MR3273617
Digital Object Identifier: 10.1214/14-EJS942

Subjects:
Primary: 62M09
Secondary: 76F55

Keywords: Brownian semistationary process , energy dissipation , Intermittency , power variation , turbulence , Volatility

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.8 • No. 2 • 2014
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