應用灰色理論於時間序列轉折點之分析與預測

An Analysis and Prediction of Turning Points in a Time Series Based on the Grey Theory

羅傑瀛(Chieh-Ying Lo) ； 林彥宏(Yen-Hung Lin) ； 王正賢(Jean-Shyan Wang)

《大葉學報》 11卷2期 (2002/12) Pp. 115-127

https://doi.org/10.7119/JDYU.200212.0115

摘要

灰色預測模型之特點為只需要少量的歷史資料即可達到預測的效果。然而，單純之灰色預測模型GM(1,1)雖然可以對未來變動之趨勢有大致之預測成效；但是，在趨勢曲線之轉折處往往無法達到更精確的預測效果。因此，本研究即針對此現象提出改良之方法。首先，可利用對所有造成趨勢轉折之因素進行分析，並轉換成量化的因素影響權重值，同時使用此數值將實際數據間的波動予以減緩。同時，在經過GM(1,1)進行預測後，對於預期在下一時間點產生影響之因素加以考量，而求得下一時間點之預測值。此外，由於預測之誤差是不可避免，因此本研究也利用自迴歸模型對於誤差之變化予以模式化，進而能將下一期之預測結果進行修正調整。透過實際之數據資料進行驗證，改良後之GM(1,1)預測方法與誤差修正方法之結合確能有效提升原始GM(1,1)模型之預測精準度，同時，實例中也同時說明此方法較一般傳統之方法有更好之預測績效。

關鍵字

灰色預測 ； 影響權重 ； 自迴歸模型 ； 台灣股價指數

並列摘要

The advantage of the Grey Model is that it can obtain a good forecasting effect as long as a little historical data are provided. The simple Grey Model GM(1,1) can forecast changeable trends; however, it may produce serious errors at the turning points in a curve. Hence, the aim of this research is to discover a solution to improve the condition just descrived. First, the factors which cause the turning points can be analyzed and digitalized as influential weights. In addition, the usage of these factors can also make the historical data smoother. Through a forecast from GM(1,1), these factors still need to be added to the GM(1,1) Model forecasting values at the next time point so that the forecasting values can be produced there. Meanwhile, deviation in any forecast cannot be avoided; hence; this research also uses the Auto-regression Model to forecast deviation and modify it from the forecasting values. Actual data can be used to verify the research. The accuracy of the GM(1,1) Model is indeed increased by a combination of an improved GM(1,1) Model and deviation modification. The examples in this research are verified to be, indeed, better than the traditional forecasting models.

並列關鍵字

grey model ； influential weight ； auto-regression model