本篇論文的主要目的是探討在時間序列中MA(q)模式下，計算最佳預測的演算法。除了在高斯過程之外，MA(q)模式下的最佳預測都是非線性，一般情況下無解析解，只能透過數值方法得出數值解。但最佳線性預測可藉由高斯過程的特性精確的求出解析解。Breidt and Hsu (2005)採用Monte Carlo 法有效地求最佳預測的數值解，因此本論文擬加入control variate來改進Breidt and Hsu的方法，希望能在同樣的計算量下得到更準的數值解。

The main purpose in the paper is to discuss algorithm of computing the best prediction in MA(q) time series model. Except in Gaussian process, the best prediction in MA(q) model is nonlinear, generally there is no exact solution, it could compute numeric solution by numeric method. But the exact solution of best linear prediction could be evaluate via characteristic of Gaussian process. Breidt and Hsu(2005) evaluate numeric solution effectively by Monte Carlo method. This paper will use control variate to improve the Breidt and Hsu's method, we hope that we could get better numeric solution in same computation quantity.

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