Assessing Relative Volatility/Intermittency/Energy Dissipation

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 even when the data of interest are generated by a non-semimartingale, or a Brownian semistationary process in particular. While this estimation method is motivated by the assessment of relative energy dissipation in empirical data of turbulence, we apply it also to energy price data. Moreover, we develop a probabilistic asymptotic theory for relative power variations of Brownian semistationary processes and Ito semimartingales and discuss how it can be used for inference on relative volatility/intermittency.

[1]  Almut E. D. Veraart,et al.  Modelling energy spot prices by volatility modulated Levy-driven Volterra processes , 2013, 1307.6332.

[2]  A. Kolmogorov.  Dissipation of energy in the locally isotropic turbulence , 1941, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[3]  J. Coeurjolly,et al.  Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths , 2001 .

[4]  T. Killeen,et al.  An Explicit Formula for the C.D.F. of the $L_1$ Norm of the Brownian Bridge , 1983 .

[5]  Stefano Grassi,et al.  It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model , 2013 .

[6]  D. E. R E K A B B O T T.  Addressing the Intermittency Challenge : Massive Energy Storage in a Sustainable Future , 2012 .

[7]  A. Kolmogorov.  A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number , 1962, Journal of Fluid Mechanics.

[8]  S. Johansen,et al.  Asymptotic Analysis of the Forward Search , 2013 .

[9]  Jean Jacod,et al.  A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales , 2004 .

[10]  M. Kosorok.  Introduction to Empirical Processes and Semiparametric Inference , 2008 .

[11]  Testing the parametric form of the volatility in continuous time diffusion models - a stochastic process approach , 2008 .

[12]  Ole E. Barndorff-Nielsen,et al.  Brownian Semistationary Processes and Volatility/Intermittency , 2009 .

[13]  Tom Engsted,et al.  Housing Market Volatility in the OECD Area: Evidence from VAR Based Return Decompositions , 2014 .

[14]  Stefano M. Iacus,et al.  Parameter estimation for the discretely observed fractional Ornstein–Uhlenbeck process and the Yuima R package , 2011, Computational Statistics.

[15]  Predicting Returns and Rent Growth in the Housing Market Using the Rent-to-Price Ratio: Evidence from the OECD Countries , 2015 .

[16]  Two highly singular intermittent structures: Rain and turbulence , 2006 .

[17]  Carbone,et al.  Intermittency and turbulence in a magnetically confined fusion plasma , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Jesús Fernández-Villaverde,et al.  The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications , 2013 .

[19]  Mark Podolskij,et al.  Limit Theorems for Functionals of Higher Order Differences of Brownian Semi-Stationary Processes , 2009 .

[20]  Almut E. D. Veraart,et al.  Risk premia in energy markets , 2013 .

[21]  Shaun Lovejoy,et al.  Multifractals, cloud radiances and rain , 2006 .

[22]  Philippe Soulier,et al.  Estimating the scaling function of multifractal measures and multifractal random walks using ratios , 2011 .

[23]  Katepalli R. Sreenivasan.  Possible Effects of Small-Scale Intermittency in Turbulent Reacting Flows , 2004 .

[24]  T. Kármán.  Progress in the Statistical Theory of Turbulence , 1948 .

[25]  David Aldous,et al.  On Mixing and Stability of Limit Theorems , 1978 .

[26]  O. Barndorff-Nielsen,et al.  Volatility determination in an ambit process setting , 2011, Journal of Applied Probability.

[27]  Michel Mandjes,et al.  ON SPECTRAL SIMULATION OF FRACTIONAL BROWNIAN MOTION , 2003, Probability in the Engineering and Informational Sciences.

[28]  G. Taylor.  The Spectrum of Turbulence , 1938 .

[29]  Laurent Duvernet,et al.  Convergence of the Structure Function of a Multifractal Random Walk in a Mixed Asymptotic Setting , 2009, 0905.3405.

[30]  D. Ventosa-Santaulària,et al.  Changes in persistence, spurious regressions and the Fisher hypothesis , 2013 .

[31]  Mark Podolskij,et al.  Asymptotic theory for Brownian semi-stationary processes with application to turbulence , 2012, 1211.4221.

[32]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[33]  R. Engle,et al.  And Now, The Rest of the News: Volatility and Firm Specific News Arrival , 2012 .

[34]  Goodness-of-fit testing for fractional diffusions , 2013 .

[35]  Arkady Tsinober,et al.  An informal conceptual introduction to turbulence , 2009 .

[36]  P. Dupas,et al.  NBER WORKING PAPER SERIES ESTIMATING THE IMPACT OF MEANS-TESTED SUBSIDIES UNDER TREATMENT EXTERNALITIES WITH APPLICATION TO ANTI-MALARIAL BEDNETS , 2013 .

[37]  Hendrik Kaufmannz,et al.  Bias-corrected estimation in potentially mildly explosive autoregressive models , 2013 .

[38]  Mark Podolskij,et al.  Multipower Variation for Brownian Semistationary Processes , 2009 .

[39]  J. Durbin,et al.  Techniques for Testing the Constancy of Regression Relationships Over Time , 1975 .

[40]  Ulrich Hounyo,et al.  Bootstrap Inference for Pre-averaged Realized Volatility based on Nonoverlapping Returns , 2014 .

[41]  Mark Podolskij,et al.  Understanding Limit Theorems for Semimartingales: A Short Survey , 2009 .

[42]  P. Mininni,et al.  Finite dissipation and intermittency in magnetohydrodynamics. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Peter Guttorp,et al.  On the Whittle-Matérn correlation family , 2005 .

[44]  Tom Engsted,et al.  Bond return predictability in expansions and recessions , 2014 .

[45]  Mikko S. Pakkanen.  Limit theorems for power variations of ambit fields driven by white noise , 2013, 1301.2107.

[46]  T. W. Anderson,et al.  Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes , 1952 .

[47]  Power variation of some integral fractional processes , 2006 .

[48]  P. Frantsuzov,et al.  Universality of the fluorescence intermittency in nanoscale systems: experiment and theory. , 2013, Nano letters.

[49]  J. Jacod,et al.  A Test for the Rank of the Volatility Process: The Random Perturbation Approach , 2012, 1212.5490.

[50]  Herman K. van Dijk,et al.  Parallel Sequential Monte Carlo for Efficient Density Combination: The Deco Matlab Toolbox , 2013 .

[51]  H. Dette,et al.  Estimation of Integrated Volatility in Continuous‐Time Financial Models with Applications to Goodness‐of‐Fit Testing , 2006 .