運用 Savitzky-Golay 濾波法改良灰色模型預測精度

Improvement of grey forecasting model precision by Savitzy-Golay filter method

黃桂芳(Guei-Fang Hunag)

指導教授 ： 陳俊益

義守大學/管理學院/工業管理學系/碩士(2015年)

https://doi.org/10.6343/ISU.2015.00055

摘要

在這個瞬息萬變的科技時代中，為了因應預測未來問題，而許多預測模型陸續被提出，但傳統的預測模型常有需要收集長期、大量的歷史資料與預測模型的反應之能力不佳等問題。因此，灰色系統理論之提出即是針對此一需求，其中，GM(1,1)在理論中是最常廣泛應用的預測模型，其特性不需要大量的歷史資料即可快速建構模型，但是其預測模型在預測長期、數據起伏波動劇烈或是資料數值包含負數時，容易產生高估或是低估的情形。
因此，本研究針對此一現象進行分析且改良灰預測GM(1,1)模型，採取結合Savitzky-Golay濾波法，Savitzky-Golay濾波法是使用最小平方多項式的迴歸方式，利用鄰近點的加權平均取代原來的資料，使原始數據更平滑、減少資料的雜訊，能提高預測模型的精確度、降低預測誤差。
在本研究利用中華民國統計資訊網的數據作為預測資料，探討SGGM(1,1)的預測過程變化，如預測過程中是否採用逆SG(ISG)、預測的數據前處理順序、SG平滑時的端點處理變化和當原始GM(1,1)預測效果極佳時，採用SGGM(1,1)預測效果是否更佳，討論以上幾種預測變化情形，研究結果發現改良後的GM(1,1)確實有明顯降低預測誤差，但是有幾種情形會使預測效果明顯降低，如預測過程採取ISG，或是將SGGM(1,1)預測的數據前處理順序做改變時，都會使預測效果變差，而且發現當原始GM(1,1)的預測誤差MAPE<5%時,相較於SGGM(1,1)繁複的數據前處理計算,本研究建議採用GM(1,1)即可達到極佳的預測能力。

關鍵字

灰色系統理論 ； Savitzky-Golay濾波法 ； 改善灰色預測

並列摘要

In an era where technologies are rapidly changing, numerous prediction models have been sequentially developed to forecast future problems. However, conventional prediction models present a number of shortcomings, such as the long-term and extensive collection of historical data and poor forecast performance. To resolve these problems, Grey System Theory (GST) was introduced. GM (1,1) in the theory is the most widely applied prediction model. The model can be established without large historical data sets. However, it is prone to produce overestimations or underestimations when forecasting long-term data, or data that fluctuates violently or contains negative values.
Therefore, the researchers of the present study focused on such problems when reviewing the GM (1,1) model and proposed a revised grey prediction GM (1,1) model by incorporating the Savitzky-Golay (SG) filter. This filter employs a least square polynomial regression approach, where the weighted averages of neighboring points are used to substitute original data, thereby smoothing the data, reducing data noise, enhancing forecast accuracy, and alleviating forecast errors.
The researchers adopted the data published on the Taiwan National Statistics website as the forecast data to examine the changes in the forecasting process using the SGGM (1,1). Observations included (1) whether an inverse SG (ISG) model was employed; (2) pre-processing order of the forecast data; (3) the influence of end points processing during SG smoothing; and (4) forecast performance of the SGGM (1,1) when that of the original GM (1,1) was excellent. Findings confirmed that the revised GM (1,1) model significantly reduced forecast errors. However, a number of situations worsened forecast effectiveness, namely, (1) when ISG was employed during forecasting and (2) when accumulated generation was employed before SG smoothing. Moreover, the researchers found out that when the mean absolute percentage error (MAPE) was less than 5 in the original GM (1,1) model, it is unnecessary to apply SGGM(1,1) because of tedious calculation comparing to accuracy improved.

並列關鍵字

Grey System Theory ； GM (1,1) ； Savitzky-Golay filter ； revised grey prediction

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