摘要
本研究提出一個結合ARIMA與倒傳遞網路(Back-Propagation Network, BPN)優點的ARIMA-BPN神經網路，它是以BPN爲模型，將ARIMA模式的輸入，包括前時p個時刻的數列值與前q個時刻的數列殘差值做爲輸入值，組成y(下標 t)=f(y(下標 t-1), y(下標 t-2), …, y(下標 t-p), ε(下標 t-1), ε(下標 t-2), …, ε(下標 t-q))的非線性函數，以建立更準確的時間數列預測模型。因爲數列殘差值在BPN的訓練過程中會因網路連結權值的調整而改變，因此必須修改BPN的演算法來適應此需求，即藉由不斷更新每次預測所得之殘差值做爲網路的輸入值。本研究以六個人爲設計的例題，及四個現實世界的例題來比較ARIMA、BPN和ARIMA-BPN三者的效能。研究結果顯示，ARIMA-BPN神經網路演算法在部份例題比ARIMA與BPN方法更準確。
並列摘要
In this paper we propose an ARIMA-BPN algorithm combining the advantages of ARIMA and Back-propagation networks (BPN). The algorithm is based on BPN and its inputs are the same as ARIMA. It can generate a non-linear function y(subscript t)=f (y(subscript t-1), y(subscript t-2), …, y(subscript t-p), ε(subscript t-1), ε(subscript t-2), …, ε(subscript t-q)) to create an accurate model to predict time series. The BPN algorithm must be modified because residuals will be changed when the weights are changed during continuous BPN training. Therefore, the continuously updated residuals are used as the inputs of ARIMA-BPN. This study examined 6 artificially designed cases and 4 real world cases to evaluate the abilities of the ARIMA, BPN, and ARIMA-BPN. The results showed that ARIMA-BPN is the most accurate method of the three.