Assessing Relative Volatility/Intermittency/Energy Dissipation

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.

25 pages, 4 figures, v3: major revision, this version contains an application to electricity prices that was omitted from the published version

References in corpus (6)

• Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes
• Multipower variation for Brownian semistationary processes
• Asymptotic theory for Brownian semi-stationary processes with application to turbulence
• Assessing Relative Volatility/Intermittency/Energy Dissipation
• Limit theorems for power variations of ambit fields driven by white noise
• Discretization of Lévy semistationary processes with application to estimation

Cited by in corpus (9)

• Hybrid scheme for Brownian semistationary processes
• High-frequency analysis of parabolic stochastic PDEs
• Assessing Relative Volatility/Intermittency/Energy Dissipation
• Limit theorems for power variations of ambit fields driven by white noise
• Large and moderate deviations for stochastic Volterra systems
• Discretization of Lévy semistationary processes with application to estimation
• Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data
• The Local Fractional Bootstrap
• Feasible Inference for Stochastic Volatility in Brownian Semistationary Processes