運用 Savitzky-Golay 濾波法改良灰色模型預測精度

Abstract

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.