Barndorff-Nielsen, Ole E.5; Pakkanen, Mikko S.6; Schmiegel, Jürgen7
1 Department of Mathematics, Science and Technology, Aarhus University2 Department of Economics and Business Economics, Aarhus BSS, Aarhus University3 Department of Economics and Business Economics - Center for Research in Econometric Analysis of Time Series (CREATES), Department of Economics and Business Economics, Aarhus BSS, Aarhus University4 Department of Engineering - Sustainable Energy Systems, Department of Engineering, Science and Technology, Aarhus University5 Department of Mathematics, Science and Technology, Aarhus University6 Department of Economics and Business Economics, Aarhus BSS, Aarhus University7 Department of Engineering - Sustainable Energy Systems, Department of Engineering, Science and Technology, Aarhus University
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.
Electronic Journal of Statistics, 2014, Vol 8, Issue 2, p. 1996-2021
Brownian semistationary process; Energy dissipation; Intermittency; Power variation; Turbulence; Volatility