離散時間分數維度高斯雜訊(discrete-time fractional Gaussian noise, DFGN)被證明是一種正規的程序(regular process)，此程序依據伍德(Wold)和Kolmogorov的理論能夠使用無限階數的自回歸模式來描述。考慮理論和實際的情況，我們提出一個快速且精確的演算法，此演算法在計算複雜度(computational complexity)上明顯超越其他估測器，此外在精確度上非常接近最大相似估測器(maximumlikelihood estimator, MLE)，因此它是一個很有競爭性的估測器。由於此特性，我們進一步關心離散時間分數維度高斯雜訊在遭受奇異的程序(singular process)影響後，最大相似估測器、近似最大相似估測器的移動平均法(moving averagemethod, MA)和近似最大相似估測器的自回歸模式法(autoregressive method, AR)的估測變化。
The discrete-time fractional Gaussian noise (DFGN) is shown that it is a regular process. According to Wold and Kolmogorov's theorems, this process can be decomposed into one regular process and one singular process. Take both theory and practicality into consideration, we proposed a fast and accurate algorithm. This algorithm surpasses the other estimators in computational complexity. In addition, it is very approximate to maximum likelihood estimator (MLE) in accuracy. Therefore, it is a much competitive estimator. Due to this property, we further concern the variation among the MLE, moving average method (MA), and autoregressive method (AR) when they are interfered with singular processes.
