Multipower Variation for Brownian Semistationary Processes
Abstract
In this paper we study the asymptotic behaviour of power and multipower variations of stochatstic processes. Processes of the type considered serve in particular, to analyse data of velocity increments of a uid in a turbulence regime with spot intermittency sigma. The purpose of the present paper is to determine the probabilistic limit behaviour of the (multi)power variations of Y , as a basis for studying properties of the intermittency process. Notably the processes Y are in general not of the semimartingale kind and the established theory of multipower variation for semimartingales does not suffice for deriving the limit properties. As a key tool for the results a general central limit theorem for triangular Gaussian schemes is formulated and proved. Examples and an application to realised variance ratio are given.Download Info
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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-21.Length: 45
Date of creation: 26 May 2009
Date of revision:
Handle: RePEc:aah:create:2009-21
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Web page: http://www.econ.au.dk/afn/
Related research
Keywords: Central Limit Theorem; Gaussian Processes; Intermittency; Nonsemimartingales; Turbulence; Volatility; Wiener Chaos;Find related papers by JEL classification:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-06-03 (All new papers)
- NEP-ECM-2009-06-03 (Econometrics)
- NEP-ETS-2009-06-03 (Econometric Time Series)
References
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"Bipower variation for Gaussian processes with stationary increments,"
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- José Manuel Corcuera & Emil Hedevang & Mikko S. Pakkanen & Mark Podolskij, 2012. "Asymptotic theory for Brownian semi-stationary processes with application to turbulence," CREATES Research Papers 2012-52, School of Economics and Management, University of Aarhus.
- Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Limit theorems for functionals of higher order differences of Brownian semi-stationary processes," CREATES Research Papers 2009-60, School of Economics and Management, University of Aarhus.
- Nourdin, Ivan & Peccati, Giovanni & Podolskij, Mark, 2011.
"Quantitative Breuer-Major theorems,"
Stochastic Processes and their Applications,
Elsevier, vol. 121(4), pages 793-812, April.
- Ivan Nourdin & Giovanni Peccati & Mark Podolskij, 2010. "Quantitative Breuer-Major Theorems," CREATES Research Papers 2010-22, School of Economics and Management, University of Aarhus.
- Mark Podolskij & Katrin Wasmuth, 2012. "Goodness-of-fit testing for fractional diffusions," CREATES Research Papers 2012-12, School of Economics and Management, University of Aarhus.
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