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May 2006 Continuous-time GARCH processes
Peter Brockwell, Erdenebaatar Chadraa, Alexander Lindner
Ann. Appl. Probab. 16(2): 790-826 (May 2006). DOI: 10.1214/105051606000000150


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, qp≥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.


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Peter Brockwell. Erdenebaatar Chadraa. Alexander Lindner. "Continuous-time GARCH processes." Ann. Appl. Probab. 16 (2) 790 - 826, May 2006.


Published: May 2006
First available in Project Euclid: 29 June 2006

zbMATH: 1127.62074
MathSciNet: MR2244433
Digital Object Identifier: 10.1214/105051606000000150

Primary: 60G10, 60G12, 91B70
Secondary: 60H30, 60J30, 91B28, 91B84

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.16 • No. 2 • May 2006
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