Multipower variation for Brownian semistationary processes

被引:36
作者
Barndorff-Nielsen, Ole E. [1 ]
Corcuera, Jose Manuel [2 ]
Podolskij, Mark [3 ]
机构
[1] Univ Aarhus, Dept Math Sci, DK-8000 Aarhus C, Denmark
[2] Univ Barcelona, E-08007 Barcelona, Spain
[3] ETH, Dept Math, CH-8092 Zurich, Switzerland
基金
新加坡国家研究基金会;
关键词
central limit theorem; Gaussian processes; intermittency; non-semimartingales; turbulence; volatility; Wiener chaos; CENTRAL-LIMIT-THEOREM; ECONOMETRIC-ANALYSIS; QUADRATIC VARIATIONS; GAUSSIAN-PROCESSES; BIPOWER VARIATION;
D O I
10.3150/10-BEJ316
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In this paper we study the asymptotic behaviour of power and multipower variations of processes Y: Y-t =integral(t)(-infinity) g(t - s)sigma W-s(ds)+ Z(t), where g: (0, infinity) -> R is deterministic, sigma > 0 is a random process, W is the stochastic Wiener measure and Z is a stochastic process in the nature of a drift term. Processes of this type serve, in particular, to model data of velocity increments of a fluid in a turbulence regime with spot intermittency sigma. The purpose of this 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 sigma. 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 the realised variance ratio are given.
引用
收藏
页码:1159 / 1194
页数:36
相关论文
共 34 条
[1]   MIXING AND STABILITY OF LIMIT-THEOREMS [J].
ALDOUS, DJ ;
EAGLESON, GK .
ANNALS OF PROBABILITY, 1978, 6 (02) :325-331
[2]  
[Anonymous], USPEKHI MAT NAUK
[3]  
Bamdorff-Nielsen O.E., 2009, 200921 CREATES AARH
[4]   A STOCHASTIC DIFFERENTIAL EQUATION FRAMEWORK FOR THE TIMEWISE DYNAMICS OF TURBULENT VELOCITIES [J].
Barndorff-Nielsen, O. E. ;
Schmiegel, J. .
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2008, 52 (03) :372-388
[5]  
Barndorff-Nielsen O.E., 2008, 20078 THIEL CTR APPL
[6]  
Barndorff-Nielsen O.E., 2010, BERNOULLI IN PRESS
[7]  
Barndorff-Nielsen O.E., 2007, ADV EC ECONOMETRICS, VIII., P328
[8]   Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes [J].
Barndorff-Nielsen, OE ;
Shephard, N .
JOURNAL OF ECONOMETRICS, 2006, 131 (1-2) :217-252
[9]   Limit theorems for multipower variation in the presence of jumps [J].
Barndorff-Nielsen, OE ;
Shephard, N ;
Winkel, M .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2006, 116 (05) :796-806
[10]   A central limit theorem for realised power and bipower variations of continuous semimartingales [J].
Barndorff-Nielsen, OE ;
Graversen, SE ;
Jacod, J ;
Podolskij, M ;
Shephard, N .
FROM STOCHASTIC CALCULUS TO MATHEMATICAL FINANCE: THE SHIRYAEV FESTSCHRIFT, 2006, :33-+