PARAMETERIZATION OF CONTINUOUS-TIME AUTOREGRESSIVE MODELS FOR IRREGULARLY SAMPLED TIME-SERIES DATA

An increasingly valuable tool for modelling irregularly sampled time s eries data is the continuous time autoregressive model. The natural pa rameters in this model are the coefficients of the linear stochastic d ifferential equation describing the process which gives rise to the da ta. A transformation of these parameters is introduced, based on the C ayley-Hamilton transformation. The new parameter space is identical wi th that of discrete time autoregressive models. The model is also modi fied by the introduction of prescribed moving average terms. The resul ting modelling improvements include rapid and reliable convergence of parameter estimates and the ability to select the model order by testi ng whether the highest order coefficient is 0. A geophysical and a med ical application illustrate the detection of periodicities in data by using the spectrum of the fitted model.