We advocate the use of an Indirect Inference method to estimate the parameter of a COGARCH(1,1) process for equally spaced observations. This requires that the true model can be simulated and a reasonable estimation method for an approximate auxiliary model. We follow previous approaches and use...

In this paper we introduce a fractionally integrated exponential continuous time GARCH(p,d,q) process. It is defined in such a way it is a continuous time extension of the discrete time FIEGARCH(p,d,q) process. We investigate stationarity and moment properties of the new model. It is also shown...

In this paper we introduce an exponential continuous time GARCH(p, q) process. It is defined in such a way that it is a continuous time extension of the discrete time EGARCH(p, q) process. We investigate stationarity and moment properties of the new model. An instantaneous leverage effect can be...

We suggest moment estimators for the parameters of a continuous time GARCH(1,1) process based on equally spaced observations. Using the fact that the increments of the COGARCH(1,1) process are ergodic, the resulting estimators are consistent. We investigate the quality of our estimators in a...

Considering absolute log returns as a proxy for stochastic volatility, the influence of explanatory variables on absolute log returns of ultra high frequency data is analysed. The irregular time structure and time dependency of the data is captured by utilizing a continuous time ARMA(p,q)...

A multivariate extension of the exponential continuous time GARCH (<italic>p</italic>, <italic>q</italic>) model (ECOGARCH) is introduced and studied. Stationarity and mixing properties of the new stochastic volatility model are investigated, and ways to model a component-wise leverage effect are presented.