Electronic Journal of Statistics

Assessing relative volatility/ intermittency/energy dissipation

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

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 29 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1414588185

Digital Object Identifier
doi:10.1214/14-EJS942

Mathematical Reviews number (MathSciNet)
MR3273617

Zentralblatt MATH identifier
1302.60115

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

Keywords
Brownian semistationary process energy dissipation intermittency power variation turbulence volatility

Citation

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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