本篇論文的目的有兩個，第一個要討論的是非高斯的移動平均(moving
averages)過程之可逆性質的判斷。第二個研究目的是比較最佳預測(best prediction
，簡稱BP。或稱之為最小均方誤差預測)及最佳線性預測(best linear prediction，簡稱BLP)在考慮參數估計誤差下的預測表現。
在非高斯移動平均過程中，如果依舊使用傳統的高斯概似函數法，求其最大概似估計，將會因無法判別其模式之可逆性質而產生錯估，進而影響後續的預測結果。本文將提出另一個以真正概似函數為基礎的可逆性判斷法，此法相較於Huang與Pawitan (2000)的quasi-likelihood的方法，有更正確的判斷能力。
若考慮的是高斯移動平均過程，則最小均方誤差預測即是最佳線性預測。但如果是一個非高斯過程時，則最小均方誤差預測一般皆是非線性預測(non-linear prediction)。在參數已知的情況下，BP必優於BLP。在此研究中，我們發現，在考慮參數估計誤差的影響下，BP只是稍微優於BLP，差別非常小。因此對於非高斯的移動平均模式，在考慮參數估計下，BLP已有相當好的預測表現。

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 taking
the 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 order
of invertiability based on the true likelihood function. The simulation results show
our 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.

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