Some computational aspects of Gaussian CARMA modelling

Representation of continuous-time ARMA (Auto-Regressive-Moving-Average), CARMA, time-series models is reviewed. Computational aspects of simulating and calculating the likelihood-function of CARMA models are summarized. Some numerical properties are illustrated by simulations. Methods for enforcing the stationarity restriction on the parameter space are discussed. Due to such methods restricted numerical estimation enforcing stationarity is possible. The impact of scaling of time axis on the magnitude of the parameters is demonstrated. Proper scaling of the time axis can give parameter values of similar magnitude which is useful for numerical work. The practicality of the computational approach is illustrated with some real and simulated data.