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Title:

Absolute Moments of Generalized Hyperbolic Distributions and Approximate Scaling of Normal Inverse Gaussian Lévy Processes

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Expressions for (absolute) moments of generalized hyperbolic and normal inverse Gaussian (NIG) laws are given in terms of moments of the corresponding symmetric laws. For the (absolute) moments centred at the location parameter "μ" explicit expressions as series containing Bessel functions are provided. Furthermore, the derivatives of the logari...

Expressions for (absolute) moments of generalized hyperbolic and normal inverse Gaussian (NIG) laws are given in terms of moments of the corresponding symmetric laws. For the (absolute) moments centred at the location parameter "μ" explicit expressions as series containing Bessel functions are provided. Furthermore, the derivatives of the logarithms of absolute "μ"-centred moments with respect to the logarithm of time are calculated explicitly for NIG Lévy processes. Computer implementation of the formulae obtained is briefly discussed. Finally, some further insight into the apparent scaling behaviour of NIG Lévy processes is gained. Copyright 2005 Board of the Foundation of the Scandinavian Journal of Statistics. Minimize

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article

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Title:

The multivariate supOU stochastic volatility model

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2014-06-23

Source:

http://www-m4.ma.tum.de/pers/stelzer/BarndorffNielsenStelzer2009b.pdf

http://www-m4.ma.tum.de/pers/stelzer/BarndorffNielsenStelzer2009b.pdf Minimize

Document Type:

text

Language:

en

Subjects:

factor modelling ; Lévy bases ; linear transformations ; long memory ; Ornstein-Uhlenbeck type process ; second order moment structure

factor modelling ; Lévy bases ; linear transformations ; long memory ; Ornstein-Uhlenbeck type process ; second order moment structure Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Absolute moments of generalized hyperbolic distributions and approximate scaling of normal inverse Gaussian Lévy processes

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Expressions for (absolute) moments of generalized hyperbolic and normal inverse Gaussian (NIG) laws are given in terms of moments of the corresponding symmetric laws. For the (absolute) moments centred at the location parameter l explicit expressions as series containing Bessel functions are provided. Furthermore, the derivatives of the logarith...

Expressions for (absolute) moments of generalized hyperbolic and normal inverse Gaussian (NIG) laws are given in terms of moments of the corresponding symmetric laws. For the (absolute) moments centred at the location parameter l explicit expressions as series containing Bessel functions are provided. Furthermore, the derivatives of the logarithms of absolute l-centred moments with respect to the logarithm of time are calculated explicitly for NIG Lévy processes. Computer implementation of the formulae obtained is briefly discussed. Finally, some further insight into the apparent scaling behaviour of NIG Lévy processes is gained. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-01-24

Source:

http://www-m4.ma.tum.de/Papers/Stelzer/BarndorffetStelzer2005SJOS466.pdf

http://www-m4.ma.tum.de/Papers/Stelzer/BarndorffetStelzer2005SJOS466.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Some aspects of Levy copulas

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Techn. Univ.; Sonderforschungsbereich 386, Statistische Analyse Diskreter Strukturen München

Year of Publication:

2004

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

ddc:310

ddc:310 Minimize

Rights:

http://www.econstor.eu/dspace/Nutzungsbedingungen

http://www.econstor.eu/dspace/Nutzungsbedingungen Minimize

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Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 388

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Title:

Absolute moments of generalized hyperbolic distributions and approximate scaling of normal inverse Gaussian Levy-processes

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Publisher:

Techn. Univ.; Sonderforschungsbereich 386, Statistische Analyse Diskreter Strukturen München

Year of Publication:

2004

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

ddc:310

ddc:310 Minimize

Rights:

http://www.econstor.eu/dspace/Nutzungsbedingungen

http://www.econstor.eu/dspace/Nutzungsbedingungen Minimize

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Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 381

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Title:

Multivariate supOU processes

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Univariate superpositions of Ornstein--Uhlenbeck-type processes (OU), called supOU processes, provide a class of continuous time processes capable of exhibiting long memory behavior. This paper introduces multivariate supOU processes and gives conditions for their existence and finiteness of moments. Moreover, the second-order moment structure i...

Univariate superpositions of Ornstein--Uhlenbeck-type processes (OU), called supOU processes, provide a class of continuous time processes capable of exhibiting long memory behavior. This paper introduces multivariate supOU processes and gives conditions for their existence and finiteness of moments. Moreover, the second-order moment structure is explicitly calculated, and examples exhibit the possibility of long-range dependence. Our supOU processes are defined via homogeneous and factorizable L\'{e}vy bases. We show that the behavior of supOU processes is particularly nice when the mean reversion parameter is restricted to normal matrices and especially to strictly negative definite ones. For finite variation L\'{e}vy bases we are able to give conditions for supOU processes to have locally bounded c\`{a}dl\`{a}g paths of finite variation and to show an analogue of the stochastic differential equation of OU-type processes, which has been suggested in \cite barndorffnielsen01 in the univariate case. Finally, as an important special case, we introduce positive semi-definite supOU processes, and we discuss the relevance of multivariate supOU processes in applications. ; Comment: Published in at http://dx.doi.org/10.1214/10-AAP690 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) Minimize

Year of Publication:

2010-12-30

Document Type:

text

Subjects:

Mathematics - Probability

Mathematics - Probability Minimize

DDC:

510 Mathematics *(computed)*

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Title:

Absolute Moments of Generalized Hyperbolic Distributions and Approximate Scaling of Normal Inverse Gaussian Lévy-Processes

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Expressions for (absolute) moments of generalized hyperbolic (GH) and normal inverse Gaussian (NIG) laws are given in terms of moments of the corresponding symmetric laws. For the (absolute) moments centered at the location parameter mu explicit expressions as series containing Bessel functions are provided. Furthermore the derivatives of the lo...

Expressions for (absolute) moments of generalized hyperbolic (GH) and normal inverse Gaussian (NIG) laws are given in terms of moments of the corresponding symmetric laws. For the (absolute) moments centered at the location parameter mu explicit expressions as series containing Bessel functions are provided. Furthermore the derivatives of the logarithms of (absolute) mu-centered moments with respect to the logarithm of time are calculated explicitly for NIG Levy processes. Computer implementation of the formulae obtained is briefly discussed. Finally some further insight into the apparent scaling behaviour of NIG Levy processes (previously discussed in Barndorff-Nielsen and Prause (2001)) is gained. Minimize

Year of Publication:

2004-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

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http://epub.ub.uni-muenchen.de/1751/1/paper_381.pdf ; Barndorff-Nielsen, Ole Eiler und Stelzer, Robert (2004): Absolute Moments of Generalized Hyperbolic Distributions and Approximate Scaling of Normal Inverse Gaussian Lévy-Processes. Sonderforschungsbereich 386, Discussion Paper 381

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Title:

Some aspects of Lévy copulas

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Levy processes and infinitely divisible distributions are increasingly defined in terms of their Levy measure. In order to describe the dependence structure of a multivariate Levy measure, Tankov (2003) introduced positive Levy copulas. Together with the marginal Levy measures they completely describe multivariate Levy measures on the first quad...

Levy processes and infinitely divisible distributions are increasingly defined in terms of their Levy measure. In order to describe the dependence structure of a multivariate Levy measure, Tankov (2003) introduced positive Levy copulas. Together with the marginal Levy measures they completely describe multivariate Levy measures on the first quadrant. In this paper, we show that any such Levy copula defines itself a Levy measure with 1-stable margins, in a canonical way. A limit theorem is obtained, characterising convergence of Levy measures with the aid of Levy copulas. Homogeneous Levy copulas are considered in detail. They correspond to Levy processes which have a time-constant Levy copula. Furthermore, we show how the Levy copula concept can be used to construct multivariat distributions in the Bondesson class with prescribed margins in the Bondesson class. The construction depends on a mapping Upsilon, recently introduced by Barndorff-Nielsen and Thorbjornsen (2004a,b) and Barndorff-Nielsen, Maejima and Sato (2004). Similar results are obtained for self-decomposable distributions and for distributions in the Thorin class. Minimize

Year of Publication:

2004-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

DDC:

519 Probabilities & applied mathematics *(computed)*

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http://epub.ub.uni-muenchen.de/1758/1/paper_388.pdf ; Barndorff-Nielsen, Ole Eiler und Lindner, Alexander M. (2004): Some aspects of Lévy copulas. Sonderforschungsbereich 386, Discussion Paper 388

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Title:

Multivariate supOU processes

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Univariate superpositions of Ornstein–Uhlenbeck-type processes (OU), called supOU processes, provide a class of continuous time processes capable of exhibiting long memory behavior. This paper introduces multivariate supOU processes and gives conditions for their existence and finiteness of moments. Moreover, the second-order moment structure is...

Univariate superpositions of Ornstein–Uhlenbeck-type processes (OU), called supOU processes, provide a class of continuous time processes capable of exhibiting long memory behavior. This paper introduces multivariate supOU processes and gives conditions for their existence and finiteness of moments. Moreover, the second-order moment structure is explicitly calculated, and examples exhibit the possibility of long-range dependence. ¶ Our supOU processes are defined via homogeneous and factorizable Lévy bases. We show that the behavior of supOU processes is particularly nice when the mean reversion parameter is restricted to normal matrices and especially to strictly negative definite ones. ¶ For finite variation Lévy bases we are able to give conditions for supOU processes to have locally bounded càdlàg paths of finite variation and to show an analogue of the stochastic differential equation of OU-type processes, which has been suggested in [2] in the univariate case. Finally, as an important special case, we introduce positive semi-definite supOU processes, and we discuss the relevance of multivariate supOU processes in applications. Minimize

Publisher:

The Institute of Mathematical Statistics

Year of Publication:

2011-02

Document Type:

Text

Language:

en

Subjects:

Lévy bases ; long memory ; normal matrices ; Ornstein–Uhlenbeck-type processes ; positive semi-definite stochastic processes ; second-order moment structure ; stochastic differential equation ; 60G10 ; 60H20 ; 60E07 ; 60G51 ; 60G57

Lévy bases ; long memory ; normal matrices ; Ornstein–Uhlenbeck-type processes ; positive semi-definite stochastic processes ; second-order moment structure ; stochastic differential equation ; 60G10 ; 60H20 ; 60E07 ; 60G51 ; 60G57 Minimize

DDC:

510 Mathematics *(computed)*

Rights:

Copyright 2011 Institute of Mathematical Statistics

Copyright 2011 Institute of Mathematical Statistics Minimize

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1050-5164

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Title:

Time Change, Volatility, and Turbulence

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A concept of Volatility Modulated Volterra Processes is introduced. Apart from some brief discussion of generalities, the paper focusses on the special case of backward moving average processes driven by Brownian motion. In this framework, a review is given of some recent modelling of turbulent velocities and associated questions of time change ...

A concept of Volatility Modulated Volterra Processes is introduced. Apart from some brief discussion of generalities, the paper focusses on the special case of backward moving average processes driven by Brownian motion. In this framework, a review is given of some recent modelling of turbulent velocities and associated questions of time change and universality. A discussion of similarities and differences to the dynamics of financial price processes is included. ; Published in: Sarychev A, Shiryaev A, Guerra M, Grossinho MDR red., Mathematical Control Theory and Finance. Springer. 2008. s. 29-53. Minimize

Publisher:

Department of Mathematical Sciences , University of Aarhus

Year of Publication:

2007

Source:

(31).

(31). Minimize

Document Type:

info:eu-repo/semantics/paper ; publishedVersion

Language:

en

Rights:

info:eu-repo/semantics/openAccess

info:eu-repo/semantics/openAccess Minimize

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