Electronic Journal of Statistics

Assessing relative volatility/ intermittency/energy dissipation

Ole E. Barndorff-Nielsen, Mikko S. Pakkanen, and Jürgen Schmiegel

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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.

Article information

Electron. J. Statist., Volume 8, Number 2 (2014), 1996-2021.

First available in Project Euclid: 29 October 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M09: Non-Markovian processes: estimation
Secondary: 76F55: Statistical turbulence modeling [See also 76M35]

Brownian semistationary process energy dissipation intermittency power variation turbulence volatility


Barndorff-Nielsen, Ole E.; Pakkanen, Mikko S.; Schmiegel, Jürgen. Assessing relative volatility/ intermittency/energy dissipation. Electron. J. Statist. 8 (2014), no. 2, 1996--2021. doi:10.1214/14-EJS942. https://projecteuclid.org/euclid.ejs/1414588185

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