層級式時間序列的組合預測

Forecasting Hierarchical Time Series by Using Combined Forecasts

10.7014/SRMA.2017040002

林豐政(Feng-Jeng Lin)；康銘仁(Ming-Ren Kang)

層級式預測 ； 組合預測 ； 獨立成分分析 ； 白化 ； Hierarchical Forecasting ； Combined Forecasting ； Independent Component Analysis ； Whitening

調查研究-方法與應用

37期（2017 / 04 / 01）

53 - 96

繁體中文

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。

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.

1. Huang, K. K.,Cheng, C. S.(2014).Integrating Independent Component Analysis and Support Vector Machine for Identifying Process Status Changes.Journal of Quality,21(6),413-426.
   連結：
2. 張育維(2014)。組合模式於桃園機場貨物運量預測之研究。運輸學刊，26(2)，203-230。
   連結：
3. 行政院主計總處，2015，交通統計，總體統計資料庫。（http://statdb.dgbas.gov.tw/pxweb/dialog/statfile9l.asp，取用日期：2015 年3 月15 日）。
4. Athanasopoulos, G.,Ahemd, R. A.,Hyndman, R. J.(2009).Hierarchical Forecasts for Australian Domestic Tourism.International Journal of Forecasting,25(1),146-166.
5. Back, A. D.,Weigend, A. S. A.(1997).A First Application of Independent Component Analysis to Extracting Structure from Stock Returns.International Journal on Neural Systems,8(4),473-484.
6. Bates, J. M.,Granger, C. W. J.(1969).The Combination of Forecasts.Operational Research Quarterly,20(4),451-468.
7. Bell, A.,Sejnowski, T.(1995).An Information Maximization Approach to Blind Separation and Blind Deconvolution.Neural Computation,7,1129-1159.
8. Bowerman, B. L.,O'Connell, R. T.(1993).Forecasting and Time Series: An Applied Approach.Belmont, CA:Duxbury Press.
9. Bowerman, B. L.,O'Connell, R. T.,Koehler, A. B.(2004).Forecasting, Time Series, and Regression: An Applied Approach.Belmont, CA:Wadsworth/Thomson Learning.
10. Bunn, D. W.(1977).A Comparative Evaluation of the Outperformance and Minimum Variance Procedures for the Linear Synthesis of Forecasts.Journal of Operational Research Society,28(3),653-662.
11. Chambers, J. C.,Mullick, S. K.,Smith, D. D.(1971).How to Choose the Right Forecasting Technique.Harvard Business Review,49,45-71.
12. Clemen, R. T.(1989).Combining Forecasts: A Review and Annotated Bibliography.International Journal of Forecasting,5(4),559-583.
13. Comon, P.(1994).Independent Component Analysis-A New Concept?.Signal Processing,36,287-314.
14. Crane, D. B.,Crotty, J. R.(1967).A Two-Stage Forecasting Model: Exponential Smoothingand Multiple Regression.Management Science,13(8),B501-B507.
15. Dalrymple, D. J.(1987).Sales Forecasting Practices: Results from a United States Survey.International Journal of Forecasting,3(3-4),379-391.
16. Dekker, M.,van Donselaar, K.,Ouwehand, P.(2004).How to Use Aggregation and Combined Forecasting to Improve Seasonal Demand Forecasts.International Journal of Production Economics,90(2),151-167.
17. Fliedner, E. B.,Mabert, V. A.(1992).Constrained Forecasting: Some Implementation Guidelines.Decision Sciences,23(5),1143-1161.
18. Gross, C. W.,Sohl, J. E.(1990).Disaggregation Methods to Expedite Product Line Forecasting.Journal of Forecasting,9(3),233-254.
19. Hyndman, J. R.,Ahmed, R. A.,Athanasopoulos, G.,Shang, H. L.(2011).Optimal Combination Forecasts for Hierarchical Time Series.Computational Statistics and Data Analysis,55(9),2579-2589.
20. Hyvärinen, A.,Oja, E.(1997).A Fast Fixed-point Algorithm for Independent Component Analysis.Neural Computation,9(7),1483-1492.
21. Jutten, C.,Hérault, J.(1991).Blind Separation of Sources, Part 1: An Adaptive Algorithm Based on Neuromimetic Architecture.Signal Processing,24(1),1-10.
22. Karhunen, J.,Hyvärinen, A.,Vigario, R.,Hurri, J.,Oja, E.(1997).Applications of Neural Blind Separation to Signal and Image Processing.Paper presented at the 1997 IEEE International Conference on Acoustics, Speech, and Signal,Munich, Germany:
23. Lee, T. W.(1998).Independent Component Analysis: Theory and Applications.Boston, MA:Kluwer Academic Publishers.
24. Lin, F. J.(2005).Forecasting Telecommunication New Service Demand by Analogy Method and Combined Forecast.Yugoslav Journal of Operations Research,15(1),97-107.
25. Lin, S. L.,Tung, P. C.,Huang, N. E.(2012).Application of ICA-EEMD to Secure Communications in Chaotic Systems.International Journal of Modern Physics C,23(4),1250028-1-1250028-11.
26. Lindsen, J. P.,Bhattacharya, J.(2010).Correction of Blink Artifacts Using Independent Component Analysis and Empirical Mode Decomposition.Psychophysiology,47(5),955-960.
27. Luna, I.,Ballini, R.(2011).Top-down Strategies Based on Adaptive Fuzzy Rule-based Systems for Daily Time Series Forecasting.International Journal of Forecasting,27(3),708-724.
28. Makridakis, S.,Wheelwright, S. C.(1989).Forecasting: Methods for Managers.New York:John Wiley & Sons.
29. Makridakis, S.,Wheelwright, S. C.,Hyndman, R. J.(1998).Forecasting: Methods and Application.New York:John Wiley & Sons.
30. Mansour, A.,Kawamoto, M.(2003).ICA Papers Classified According to Their Applications and Performances.IEICE Transactionson Fundamentals of Electronics, Communications and Computer Sciences E,86A(3),620-633.
31. Mathews, B. P.,Diamantopotdos, A.(1986).Managerial Intervention in Forecasting: An Empirical Investigation of Forecast Manipulation.International Journal of Research in Marketing,3(1),3-10.
32. Melo, L. F.,Loaiza, R. A.(2012).Bayesian Forecast Combination for Inflation Using Rolling Windows: An Emerging Country Case.Borrador de Economia,705,1-17.
33. Pindyck, R. S.,Rubinfeld, D. L.(1998).Econometric Model and Economic Forecasts.Boston, MA:McGraw-Hill.
34. Saigal, S.,Mehrotra, D.(2012).Performance Comparison of Time Series Data Using Predictive Data Mining Techniques.Advances in Information Mining,4(1),57-66.
35. Theil, H.(1954).Linear Aggregation of Economic Relations.Amsterdam:North-Holland.
36. Wei, W. W. S.,Abraham, B.(1981).Forecasting Contemporal Time Series Aggregates.Communications in Statistics,10(13),1335-1344.
37. Zhao, K.,Gan, L.,Wang, H.,Ye, A. H.(2012).Application of Combination Forecast Model in the Medium and Long Term Power Load Forecast.International Journal of Computer Science Issues,9(3),24-28.
38. 王建雄、張立民、鍾兆根(2011)。基於Fast ICA 算法的盲源分離。計算機技術與發展，21(12)，93-96。
39. 平平、劉大有、楊博、金弟、方芳、馬思佳、田野、王永(2010)。組合預測模型在豬肉價格預測中的應用研究。計算機工程與科學，32(5)，109-112。
40. 何川、舒勤、賀含峰(2014)。ICA 特徵提取與BP 神經網路在負荷預測中的應用。電力系統及其自動化學報，26(8)，40-46。
41. 余桂霖(2013)。時間序列分析。台北:五南。
42. 周程、張培林(2012)。基於關連面積法的物流貨運量組合預測模型。計算機應用，32(9)，2628-2630+2642。
43. 孫斌、姚海濤、李田、劉袖、劉博(2014)。基於Fast ICA 和改進LSSVM 的短期風速預測。電力系統及其自動化學報，26(1)，22-27。
44. 高文海(2014)。基於組合預測模型的物流需求預測實證研究。物流技術，33(3)，226-228。
45. 高寧、潘傳姣、李建剛(2014)。深埋隧道圍岩變形預測的非線性組合模型。金屬礦山，8，45-48。
46. 陳麗、張朝元(2015)。基於SOR-LS-SVM 的公路旅遊客流量組合預測模型。科技通報，31(1)，195-198+209。
47. 楊臻明、岳繼光、王曉保、蕭蘊詩(2013)。基於獨立成分分析的含噪聲時間序列預測。控制與決策，28(4)，501-505。
48. 劉斌、戴吾蛟、黃大偉、羅飛雪(2012)。獨立分量迴歸及其在變形分析中的應用研究。大地測量與地球動力學，32(6)，90-93。
49. 盧舜年、鄒坤霖(2002)。供應鏈管理的第一本書。台北:商周。
50. 羅心蓮(2005)。碩士論文(碩士論文)。新竹，國立清華大學工業工程與工程管理學系。
51. 羅偵源(2011)。碩士論文(碩士論文)。新竹，國立交通大學電子工程學系電子研究所。
52. 譚璐、劉婷、呂志勇(2013)。基於獨立成分分析的山東省就業人數預測。經濟與管理評論，3，149-153。