層級式時間序列的組合預測

Forecasting Hierarchical Time Series by Using Combined Forecasts

林豐政(Feng-Jeng Lin) ； 康銘仁(Ming-Ren Kang)

《調查研究-方法與應用》 37期 (2017/04) Pp. 53-96

https://doi.org/10.7014/TCYCFFYYY.201704_(37).0002

摘要

本文主要針對具層級的時間序列資料，提出一套結合獨立成分分析（Independent Components Analysis, ICA）中白化過程產生的特徵值比例為權重之組合方式，應用於多個預測方法的兩階段組合預測流程：第一階段為不同預測方法間預測值的組合預測，第二階段為top-down 與bottom-up 流程預測值的組合預測。為能評估與比較兩階段組合預測流程於具層級的時間序列中之可靠性與實用性，研究中以行政院主計總處總體統計資料庫之來台旅客人數的時間序列為實證資料；同時，採行算術平均、變異加權、ICA 加權等三種組合方式進行實際績效的評比。結果發現：（1）單一方法的預測績效非常不一致，但都可能具有所需要的正確訊號，故而應用組合預測予以整合之，實屬可行的方法；（2）在一階段之方法間組合預測評比中，加入ICA 權重的組合方式，相對更具有效整合單一方法的預測序列，並可降低預測誤差的雜訊；（3）在兩階段之程序間組合預測評比中，同樣是以ICA加權的組合預測結果績效最佳。由此可知，研究中所提之兩階段的組合預測流程，並採行ICA 加權的組合方式，確實可以有效提升預測績效。而在實務上，尚有許多領域的資料序列是具層級性的，故而本研究的組合預測概念亦可應用於相似的領域上。

關鍵字

層級式預測 ； 組合預測 ； 獨立成分分析 ； 白化

並列摘要

This paper examines a process that integrates the concept of combined forecast with the eigenvalue proportions resulted from the matrix formed by whitening of independent component analysis (ICA) as applied to forecast time series data with a hierarchical mode. In this process, the stage of combined forecast will be executed twice. The first stage will combine the several forecasts that derive from different forecasting methods, whereas the second stage will combine the forecasts that operate in a top-down and bottom-up manner. To evaluate and compare the reliability and applicability of the proposed process as practiced on time series data with a hierarchical mode, the official monthly number of inbound tourists to Taiwan, as obtained from the Directorate-General of Budget, Accounting and Statistics (DGBAS), will be used in this paper. Meanwhile, three combining methods (arithmetic average, variance-weighted, ICA-weighted) will also be adopted to assess their forecasting performance. As a result, we will note three important findings in this empirical study: (1) Although the forecasting performance is very inconsistent in each forecasting method, some correct signals are all required, therefore, using a combined forecast to integrate these correct signals is an optimal alternative. (2) The ICA-weighted method can decrease the error signals and be more efficient in integrating correct signals in the first combining stage. (3) The ICA-weighted method still outperformed the other two combining methods in the second combining stage. In summary, the findings demonstrate that the proposed forecasting process is feasible and reliable. The results suggest the possibility of applying forecast of hierarchical time series data to other areas as well.

並列關鍵字

Hierarchical Forecasting ； Combined Forecasting ； Independent Component Analysis ； Whitening

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