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Title:

Continuous-Time GARCH Processes

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-02-18

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http://www-m4.ma.tum.de/m4/Papers/Lindner/cg.pdf

http://www-m4.ma.tum.de/m4/Papers/Lindner/cg.pdf Minimize

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text

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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:

Continuous-time GARCH processes

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A family of continuous-time generalized autoregressive conditionally heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$ process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601--622], is introduced and studied. The resulting $\operatorname {COGARCH}(p,q)$ processes, $q\ge p\ge 1$, exhibit many of the...

A family of continuous-time generalized autoregressive conditionally heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$ process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601--622], 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 continuous-time 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) Minimize

Year of Publication:

2006-07-05

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) Minimize

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510 Mathematics *(computed)*

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Title:

Continuous-time GARCH processes

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Description:

A family of continuous-time 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 continuous-time 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 continuous-time autoregressive moving average process. Minimize

Publisher:

The Institute of Mathematical Statistics

Year of Publication:

2006-05

Document Type:

Text

Language:

en

Subjects:

Autocorrelation structure ; CARMA process ; COGARCH process ; stochastic volatility ; continuous-time 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 ; continuous-time GARCH process ; Lyapunov exponent ; random recurrence equation ; stationary solution ; positivity ; 60G10 ; 60G12 ; 91B70 ; 60J30 ; 60H30 ; 91B28 ; 91B84 Minimize

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510 Mathematics *(computed)*

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Copyright 2006 Institute of Mathematical Statistics

Copyright 2006 Institute of Mathematical Statistics Minimize

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1050-5164

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Title:

A continuous time GARCH process of higher order

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

Year of Publication:

2005

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

C23 ; ddc:310

C23 ; ddc:310 Minimize

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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 428

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Title:

A Continuous Time GARCH Process of Higher Order

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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. Minimize

Year of Publication:

2005-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Language:

eng

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

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http://epub.ub.uni-muenchen.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

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