以插分整合移動平均自迴歸模型、類神經網路模型與離散小波轉換構成之時間序列混合模型效果評估

Abstract

在現今不同研究領域中，時間序列預測是其中深具挑戰的項目。通過整合不同領域的技術，數個混合模型先後被提出。然而在前人研究中，即便混合模型的功效有經過驗證，卻未進行過嚴謹的統計檢定來檢視不同模型的差異。 本研究提出基於經驗法則的逐步式ANN模型架構方法和兩個由ARIMA、ANN及DWT構成的混合模型。通過模擬資料比較ARIMA、ANN、ARIMA-ANN、DWT-ARIMA、DWT-A1-ARIMA、DWT-ARIMA-ANN與兩個新提出的模型：DWT-2-ARIMA-ANN及ARIMA-DWT-ANN之表現差異。此外，關於山貓與高麗菜菜價的兩筆真實資料被用於實證模型的功效。新提出的ARIMA-DWT-ANN在模擬資料與山貓資料中皆有最佳的表現，而ANN則是高麗菜菜價資料中表現最好的模型。在二因子變異數分析中，不同模型的差異在結果上是顯著的。 做為一個簡短的結論，ARIMA、ANN、ARIMA-ANN、DWT-ARIMA-ANN與ARIMA-DWT-ANN是較為推薦的模型。由於混合模型面對不同資料的表現可能因內含的ARIMA或ANN架構而有所差異，因此在面對新資料時，應將上述所有模型列入考慮。

Nowadays, time series forecasting is a challenging task of interest in many disciplines. A variety of techniques have been developed to deal with the problem through a combination of different disciplines. Although various researches have proved successful for hybrid models, none of them carried out the comparisons with solid statistical test. This study proposes a new stepwise model determination method for ANN based rule of thumb and two novel hybrid models combining ARIMA, ANN and DWT. Simulation studies are conducted to compare the performance of different models, including ARIMA, ANN, ARIMA-ANN, DWT-ARIMA, DWT-A1-ARIMA, DWT-ARIMA-ANN and the two proposed methods, DWT-2-ARIMA-ANN and ARIMA-DWT-ANN. Also, two real data sets, lynx data and cabbage data, are used to demonstrate the applications. Our proposed method, ARIMA-DWT-ANN, outperforms other methods in both simulated datasets and lynx data, while ANN shows a better performance in the cabbage data. We conducted a two-way ANOVA test to compare the performances of methods. The results showed a significant difference between methods. As a brief conclusion, it is suggested to try on ARIMA, ANN, ARIMA-ANN, DWT-ARIMA-ANN and the proposed model, ARIMA-DWT-ANN. Since the performance of these hybrid models may vary across data sets based on their ARIMA alike or ANN alike natures, they should all be considered when encountering a new data to reach an optimal performance.