Contemporaneous Carma Modelling With Applications

This thesis presents a comprehensive study of the statistical properties of the contemporaneous Autoregressive Moving-Average (CARMA) model. The research results constitute a more general framework than previously available for the analysis of many actual sets of time series data. It is shown in the thesis that the joint estimation is asymptotically efficient. For the case of the CAR(1) model, asymptotic theory and small sample simulation show that the gain in efficiency over univariate estimation can be in excess of 50%. A computationally efficient procedure to obtain the joint estimation of the parameters together with a useful estimation procedure for the case of unequal sample sizes is also given in the thesis. Applications in hydrology are presented, where the physical restrictions of the system often suggest that a CARMA model would be appropriate. Test statistics for two important hypotheses are also considered: (a) whether a joint set of univariate models will suffice and (b) whether (beta)(,h) = (beta), or otherwise, where (beta)(,h) is the vector of parameters for the series h