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研究生： 謝功進
TA - CONG TIEN
論文名稱： 組合資料的預測分析研究
A study of forecasting analysis in compositional data
指導教授： 王福琨
Fu-Kwun Wang
口試委員: 歐陽超
Chao Ou-Yang
羅士哲
Shih-Che Lo
學位類別： 碩士
Master
系所名稱： 管理學院 - 工業管理系
Department of Industrial Management
論文出版年： 2012
畢業學年度： 100
語文別： 英文
論文頁數： 65
中文關鍵詞： 組合資料 、對數比值分析轉換法 、多變量預測
外文關鍵詞： Compositional data, Log-ratio analysis transformation, Multivariate forecasting
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    • 組合時間序列資料是隨著時間變化之比例向量所組成，在許多學術研究上被使用，例如地質學等。特別是以統計方法應用於預測之領域。然而，基於每一向量元素之總和必須等於一之研究設計限制，因此組合時間序列資料已被證明很難利用統計方法解決問題。在本研究中，對數比值分析轉換法可以有效的解決多變量常態分配的組合型資料固有的問題，此新方法主要是在 simplex space 與 real space 之間轉換，以三家知名電腦公司的操作費用資料將此方法與傳統三種多變量預測模型做比較，以驗證所提出的預測模型。結果顯示本研究出所提出之預測方法有較佳的結果。

    Compositional time series data, which consists of vectors of proportions changing over time, usually occurs in many disciplines, such as geosciences, financial analysis etc. and give rise to some interesting statistical considerations, especially forecasting issue. However, it has proved to be difficult to handle statistically stem from the awkward constraint that the components of each vector must sum to unity. In this research, the log-ratio analysis transformation algorithm could be effectively used in conjunction with the notation of multi-logistic normal distribution to deal with this inherent awkwardness of compositional time series data. Furthermore, a new forecasting approach based on the core idea of transforming and retransforming all raw compositional time series between the simplex space and real space will be proposed. And then, the proposed approach will compare with three conventional multivariate forecasting models. Three compositional operation expense series from well-known computer manufacturing companies are used to demonstrate the forecasting performance in terms of the Aitchison distance value. The results showed that our approach outperforms other models.

    Abstract i Content ii Acknowledgement v List of figures vi List of tables vii Chapter 1: INTRODUCTION 1 1.1 Research background and motivation 1 1.2 Research objectives 2 1.3 Research limitations 3 1.4 Research flow 3 Chapter 2: LITERATURE REVIEW 6 2.1 Compositional data 6 2.1.1 Overview of compositional data 6 2.1.2 Simplex sample space 8 2.1.3 Operations in the simplex 9 2.1.4 Aitchison distance 11 2.1.5 Multivariate logistic normal distribution in the simplex 12 2.2 Forecasting methods for compositional data 13 2.2.1 Dimension reduction approach through a hyper-spherical transformation (DRHT) 13 2.2.2 Non-centered principal component analysis (PCA) 15 2.2.3 Compositional single exponential smoothing (CSES) and compositional double exponential smoothing (CDES) 17 Chapter 3: METHODOLOGY 19 3.1 General procedure 19 3.2 Testing the multivariate logistic normal distribution 22 3.3 Transformation procedure for compositional time series data 26 3.4 Forecasting procedure for compositional time series data 27 3.5 Conventional multivariate forecasting models 27 3.5.1 Multivariate quadratic non-linear regression (MNLR) 28 3.5.2 Multivariate double exponential smoothing (MDES) 29 3.5.3 Multivariate rolling grey model (MRGM) 30 Chapter 4: ILLUSTRATIVE EXAMPLES 33 4.1 OPEX data overview 33 4.2 OPEX compositional data of DELL 34 4.2.1 Data collection 34 4.2.2 Data visualization by ternary diagram 35 4.2.3 Testing for the multivariate logistic normal distribution and transformation 36 4.2.4 Forecasting and result analysis 37 4.3 OPEX compositional data of IBM 42 4.3.1 Data collection 42 4.3.2 Data visualization by ternary diagram 42 4.3.3 Testing for the multivariate logistic normal distribution and transformation 43 4.3.4 Forecasting and result analysis 45 4.4 OPEX compositional data of APPLE 49 4.4.1 Data collection 49 4.4.2 Data visualization by ternary diagram 50 4.4.3 Testing for the multivariate logistic normal distribution and transformation 50 4.4.4 Forecasting and result analysis 52 4.5 Summary of results 56 Chapter 5: CONCLUSIONS 58 5.1 Conclusions 58 5.2 Future studies 58 References 59 Appendix A 62 Appendix B 65

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