Chadraa, Erdenebaatar, authorBrockwell, Peter J., advisor2024-03-132024-03-132009https://hdl.handle.net/10217/237634In 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.To estimate the parameters of the COGARCH(2, 2) processes, the least-squares method is used. We give conditions under which the volatility and the squared increment processes are strongly mixing, from which it follows that the least-squares estimators are strongly consistent and asymptotically normal. Finally, the model is fitted to a high frequency dataset.born digitaldoctoral dissertationsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.GARCH processesleast-squares estimatorsvolatility processstatisticsfinanceapplied mathematicsTextPer the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users.