一個混合時間序列法與指數平滑法的預測流程：列車旅運需求預測之應用

A Hybrid Predicting Procedure Based on ARIMA and Exponential Smoothing Models: Applications for Railway Demand Forecasting

本研究提出一個以時間序列法與指數平滑法為基礎的混合模式，旨在提升時間序列模式的預測績效。所提出的預測流程首先使用Holt-Winters模式將原始資料分解成基礎量（level）、趨勢（trend）、週期性（periodicity），以及誤差項（irregular term）。預測流程的第二階段則使用Seasonal Autoregressive Integrated Moving Average（SARIMA）模式針對各分解元素進行資料的配適並產生分解元素預測值。最終各分解元素的預測值被整合在一起以產生輸出值。本研究也進一步探討模式更新與資料轉換兩種建模策略對於混合模式在預測績效上的影響。臺鐵每日的實際銷售量時間序列資料被用來做為模式驗證的對象；實證結果發現，本研究所提的混合模式比個別的Holt-Winters模式與SARIMA模式在預測績效表現上有顯著的改善。採逐月更新與Box-Cox資料轉換後的混合模式比不更新及不轉換的混合模式，可以更進一步提升預測績效。

A hybrid predicting model based on Holt-Winters exponential smoothing (HW) and Seasonal Autoregressive Integrated Moving Average model (SARIMA) for time series forecasting tasks is proposed in this study. The proposed procedure first decomposes raw data into four components, namely level, trend, periodicity, and irregular term, by HW. Then each decomposed component is modeled by a respective SARIMA model. In the second stage, the proposed procedure integrates the prediction of four individual components to generate final forecasts. The necessity of updating and data transformation in the proposed procedure is also discussed. Real railway daily sales data are utilized to verify the performance of the proposal. Empirical study shows that the designed hybrid model can outperform individual HW and SARIMA models. In addition, update and Box-Cox transformation are two good modeling strategies for further upgrading the predictive performance.