Abstract
There are two purposes in this paper. The first one is to determine the invertiability for non-Gaussian moving averages. The second one is to make comparison between the best mean square prediction and the best linear prediction after takingthe uncertainty of parameter estimation into account.For non-Gaussian moving averages, the classical Gaussian likelihood cannot determine the correct order of the invertiability because the parameter space is not identifiable. In this thesis, we develop a new method to determine the correct orderof invertiability based on the true likelihood function. The simulation results showour proposed method performs much better than the quasilikelihood method pro-posed by Huang and Pawitan (2000), especially for the non-invertible MA processes.It is well known that the best mean square error predictor is always better than the linear prediction when the parameters are known. However, this study found that the BLP is very competitive to the BP after taking the uncertainty of parameter estim-ation into account. Therefore for a non-Gaussian moving average process, the BLP is still a good choice in practice relative to the BP in terms of fast computations and good efficiency.