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Browsing by Author "Chadraa, Erdenebaatar, author"

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    Statistical modeling with COGARCH(p,q) processes
    (Colorado State University. Libraries, 2009) Chadraa, Erdenebaatar, author; Brockwell, Peter J., advisor
    In this paper, a family of continuous time GARCH processes, generalizing the COGARCH(1, 1) process of Klüppelberg, et al. (2004), 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 non-negative 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 squared increment processes. The volatility process is found to have the autocorrelation function of a continuous-time ARMA process while the squared increment process has the autocorrelation function of an ARMA process.