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1.
ContinuousTime GARCH Processes
Open Access
Title:
ContinuousTime GARCH Processes
Author:
Peter Brockwell
;
Erdenebaatar Chadraa
;
Alexander Lindner
Peter Brockwell
;
Erdenebaatar Chadraa
;
Alexander Lindner
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20110218
Source:
http://wwwm4.ma.tum.de/m4/Papers/Lindner/cg.pdf
http://wwwm4.ma.tum.de/m4/Papers/Lindner/cg.pdf
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Document Type:
text
Language:
en
Rights:
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.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.3605
http://wwwm4.ma.tum.de/m4/Papers/Lindner/cg.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.3605
http://wwwm4.ma.tum.de/m4/Papers/Lindner/cg.pdf
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2.
Continuoustime GARCH processes
Open Access
Title:
Continuoustime GARCH processes
Author:
Brockwell, Peter
;
Chadraa, Erdenebaatar
;
Lindner, Alexander
Brockwell, Peter
;
Chadraa, Erdenebaatar
;
Lindner, Alexander
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Description:
A family of continuoustime generalized autoregressive conditionally heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$ process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601622], is introduced and studied. The resulting $\operatorname {COGARCH}(p,q)$ processes, $q\ge p\ge 1$, exhibit many of the...
A family of continuoustime generalized autoregressive conditionally heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$ process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601622], is introduced and studied. The resulting $\operatorname {COGARCH}(p,q)$ processes, $q\ge p\ge 1$, exhibit many of the characteristic features of observed financial time series, while their corresponding volatility and squared increment processes display a broader range of autocorrelation structures than those of the $\operatorname {COGARCH}(1,1)$ process. We establish sufficient conditions for the existence of a strictly stationary nonnegative solution of the equations for the volatility process and, under conditions which ensure the finiteness of the required moments, determine the autocorrelation functions of both the volatility and the squared increment processes. The volatility process is found to have the autocorrelation function of a continuoustime autoregressive moving average process. ; Comment: Published at http://dx.doi.org/10.1214/105051606000000150 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
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Year of Publication:
20060705
Document Type:
text
Subjects:
Mathematics  Probability ; 60G10 ; 60G12 ; 91B70 (Primary) 60J30 ; 60H30 ; 91B28 ; 91B84 (Secondary)
Mathematics  Probability ; 60G10 ; 60G12 ; 91B70 (Primary) 60J30 ; 60H30 ; 91B28 ; 91B84 (Secondary)
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DDC:
510 Mathematics
(computed)
URL:
http://arxiv.org/abs/math/0607109
http://arxiv.org/abs/math/0607109
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Content Provider:
ArXiv.org (Cornell University Library)
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3.
Continuoustime GARCH processes
Title:
Continuoustime GARCH processes
Author:
Brockwell, Peter
;
Chadraa, Erdenebaatar
;
Lindner, Alexander
Brockwell, Peter
;
Chadraa, Erdenebaatar
;
Lindner, Alexander
Minimize authors
Description:
A family of continuoustime generalized autoregressive conditionally heteroscedastic processes, generalizing the COGARCH(1,1) process of Klüppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601–622], is introduced and studied. The resulting COGARCH(p,q) processes, q≥p≥1, exhibit many of the characteristic features of observed financial ti...
A family of continuoustime generalized autoregressive conditionally heteroscedastic processes, generalizing the COGARCH(1,1) process of Klüppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601–622], is introduced and studied. The resulting COGARCH(p,q) processes, q≥p≥1, exhibit many of the characteristic features of observed financial time series, while their corresponding volatility and squared increment processes display a broader range of autocorrelation structures than those of the COGARCH(1,1) process. We establish sufficient conditions for the existence of a strictly stationary nonnegative solution of the equations for the volatility process and, under conditions which ensure the finiteness of the required moments, determine the autocorrelation functions of both the volatility and the squared increment processes. The volatility process is found to have the autocorrelation function of a continuoustime autoregressive moving average process.
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Publisher:
The Institute of Mathematical Statistics
Year of Publication:
200605
Document Type:
Text
Language:
en
Subjects:
Autocorrelation structure ; CARMA process ; COGARCH process ; stochastic volatility ; continuoustime GARCH process ; Lyapunov exponent ; random recurrence equation ; stationary solution ; positivity ; 60G10 ; 60G12 ; 91B70 ; 60J30 ; 60H30 ; 91B28 ; 91B84
Autocorrelation structure ; CARMA process ; COGARCH process ; stochastic volatility ; continuoustime GARCH process ; Lyapunov exponent ; random recurrence equation ; stationary solution ; positivity ; 60G10 ; 60G12 ; 91B70 ; 60J30 ; 60H30 ; 91B28 ; 91B84
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DDC:
510 Mathematics
(computed)
Rights:
Copyright 2006 Institute of Mathematical Statistics
Copyright 2006 Institute of Mathematical Statistics
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Relations:
10505164
URL:
http://projecteuclid.org/euclid.aoap/1151592251
http://projecteuclid.org/euclid.aoap/1151592251
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Content Provider:
Project Euclid (Cornell University Library)
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4.
A continuous time GARCH process of higher order
Open Access
Title:
A continuous time GARCH process of higher order
Author:
Brockwell, Peter J.
;
Chadraa, Erdenebaatar
;
Lindner, Alexander M.
Brockwell, Peter J.
;
Chadraa, Erdenebaatar
;
Lindner, Alexander M.
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Publisher:
Techn. Univ.; Sonderforschungsbereich 386, Statistische Analyse Diskreter Strukturen München
Year of Publication:
2005
Document Type:
doctype:workingPaper
Language:
eng
Subjects:
C23 ; ddc:310
C23 ; ddc:310
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DDC:
310 Collections of general statistics
Rights:
http://www.econstor.eu/dspace/Nutzungsbedingungen
http://www.econstor.eu/dspace/Nutzungsbedingungen
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Relations:
Discussion paper // Sonderforschungsbereich 386 der LudwigMaximiliansUniversität München 428
URL:
http://hdl.handle.net/10419/31103
http://hdl.handle.net/10419/31103
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Content Provider:
EconStor (German National Library of Economics, ZBW)
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5.
A Continuous Time GARCH Process of Higher Order
Title:
A Continuous Time GARCH Process of Higher Order
Author:
Brockwell, Peter J.
;
Chadraa, Erdenebaatar
;
Lindner, Alexander M.
Brockwell, Peter J.
;
Chadraa, Erdenebaatar
;
Lindner, Alexander M.
Minimize authors
Description:
A continuous time GARCH model of order (p,q) is introduced, which is driven by a single Lévy process. It extends many of the features of discrete time GARCH(p,q) processes to a continuous time setting. When p=q=1, the process thus defined reduces to the COGARCH(1,1) process of Klüppelberg, Lindner and Maller (2004). We give sufficient conditions...
A continuous time GARCH model of order (p,q) is introduced, which is driven by a single Lévy process. It extends many of the features of discrete time GARCH(p,q) processes to a continuous time setting. When p=q=1, the process thus defined reduces to the COGARCH(1,1) process of Klüppelberg, Lindner and Maller (2004). We give sufficient conditions for the existence of stationary solutions and show that the volatility process has the same autocorrelation structure as a continuous time ARMA process. The autocorrelation of the squared increments of the process is also investigated, and conditions ensuring a positive volatility are discussed.
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Year of Publication:
20050101
Document Type:
doctype:workingPaper ; Paper ; NonPeerReviewed
Language:
eng
Subjects:
Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510
Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510
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Relations:
http://epub.ub.unimuenchen.de/1797/1/paper_428.pdf ; Brockwell, Peter J. und Chadraa, Erdenebaatar und Lindner, Alexander M. (2005): A Continuous Time GARCH Process of Higher Order. Sonderforschungsbereich 386, Discussion Paper 428
URL:
http://epub.ub.unimuenchen.de/1797/
http://nbnresolving.de/urn/resolver.pl?urn=nbn:de:bvb:19epub17976
http://epub.ub.unimuenchen.de/1797/
http://nbnresolving.de/urn/resolver.pl?urn=nbn:de:bvb:19epub17976
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Content Provider:
LudwigMaximiliansUniversity Munich: Open Access LMU
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Author
(4) Chadraa, Erdenebaatar
(2) Brockwell, Peter
(2) Brockwell, Peter J.
(2) Lindner, Alexander
(2) Lindner, Alexander M.
(1) Alexander Lindner
(1) Erdenebaatar Chadraa
(1) Peter Brockwell
(1) The Pennsylvania State University CiteSeerX...
Author:
Subject
(2) 60g10
(2) 60g12
(2) 60h30
(2) 91b28
(1) 60j30
(1) 91b70
(1) 91b70 primary 60j30
(1) 91b84
(1) 91b84 secondary
(1) autocorrelation structure
(1) c23
(1) carma process
(1) cogarch process
(1) continuous time garch process
(1) ddc 310
(1) ddc 510
(1) lyapunov exponent
(1) mathematics probability
(1) positivity
(1) random recurrence equation
(1) sonderforschungsbereich 386
(1) stationary solution
(1) stochastic volatility
Subject:
Dewey Decimal Classification (DDC)
(2) Mathematics [51*]
(1) Statistics [31*]
Dewey Decimal Classification (DDC):
Year of Publication
(2) 2005
(2) 2006
(1) 2011
Year of Publication:
Content Provider
(1) ArXiv.org
(1) CiteSeerX
(1) Project Euclid
(1) Munich LMU: Open Access
(1) EconStor
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(4) English
(1) Unknown
Language:
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(3) Text
(2) Reports, Papers, Lectures
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