Asymptotic theory for Brownian semi-stationary processes with application to turbulence

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Standard

Asymptotic theory for Brownian semi-stationary processes with application to turbulence. / Corcuera, José Manuel; Hedevang, Emil; Pakkanen, Mikko S. et al.

In: Stochastic Processes and Their Applications, Vol. 123, No. 7, 2013, p. 2552-2574.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Vancouver

Corcuera JM, Hedevang E, Pakkanen MS , Podolskij M. Asymptotic theory for Brownian semi-stationary processes with application to turbulence. Stochastic Processes and Their Applications. 2013;123(7):2552-2574. doi: 10.1016/j.spa.2013.03.011

Author

Corcuera, José Manuel ; Hedevang, Emil ; Pakkanen, Mikko S. et al. / Asymptotic theory for Brownian semi-stationary processes with application to turbulence. In: Stochastic Processes and Their Applications. 2013 ; Vol. 123, No. 7. pp. 2552-2574.

Bibtex

@article{34af9ebe52404f118962830431c517b2,

title = "Asymptotic theory for Brownian semi-stationary processes with application to turbulence",

abstract = "This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed in [Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2011): Multipower variation for Brownian semistationary processes. Bernoulli 17(4), 1159-1194; Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2012): Limit theorems for functionals of higher order differences of Brownian semi-stationary processes. In {"}Prokhorov and Contemporary Probability Theory{"}, Springer.] and present some new connections to fractional diffusion models. We apply our probabilistic results to construct a family of estimators for the smoothness parameter of the BSS process. In this context we develop estimates with gaps, which allow to obtain a valid central limit theorem for the critical region. Finally, we apply our statistical theory to turbulence data.",

keywords = "Brownian semi-stationary processes, High frequency data, Limit theorems, Stable convergence, Turbulence",

author = "Corcuera, {Jos{\'e} Manuel} and Emil Hedevang and Pakkanen, {Mikko S.} and Mark Podolskij",

year = "2013",

doi = "10.1016/j.spa.2013.03.011",

language = "English",

volume = "123",

pages = "2552--2574",

journal = "Stochastic Processes and Their Applications",

issn = "0304-4149",

publisher = "Elsevier BV * North-Holland",

number = "7",

}

RIS

TY - JOUR

T1 - Asymptotic theory for Brownian semi-stationary processes with application to turbulence

AU - Corcuera, José Manuel

AU - Hedevang, Emil

AU - Pakkanen, Mikko S.

AU - Podolskij, Mark

PY - 2013

Y1 - 2013

N2 - This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed in [Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2011): Multipower variation for Brownian semistationary processes. Bernoulli 17(4), 1159-1194; Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2012): Limit theorems for functionals of higher order differences of Brownian semi-stationary processes. In "Prokhorov and Contemporary Probability Theory", Springer.] and present some new connections to fractional diffusion models. We apply our probabilistic results to construct a family of estimators for the smoothness parameter of the BSS process. In this context we develop estimates with gaps, which allow to obtain a valid central limit theorem for the critical region. Finally, we apply our statistical theory to turbulence data.

AB - This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed in [Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2011): Multipower variation for Brownian semistationary processes. Bernoulli 17(4), 1159-1194; Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2012): Limit theorems for functionals of higher order differences of Brownian semi-stationary processes. In "Prokhorov and Contemporary Probability Theory", Springer.] and present some new connections to fractional diffusion models. We apply our probabilistic results to construct a family of estimators for the smoothness parameter of the BSS process. In this context we develop estimates with gaps, which allow to obtain a valid central limit theorem for the critical region. Finally, we apply our statistical theory to turbulence data.

KW - Brownian semi-stationary processes

KW - High frequency data

KW - Limit theorems

KW - Stable convergence

KW - Turbulence

U2 - 10.1016/j.spa.2013.03.011

DO - 10.1016/j.spa.2013.03.011

M3 - Journal article

VL - 123

SP - 2552

EP - 2574

JO - Stochastic Processes and Their Applications

JF - Stochastic Processes and Their Applications

SN - 0304-4149

IS - 7

ER -

Department of Economics and Business Economics