臺灣博碩士論文加值系統

灰色預測模式為一適用於短期預測之有效工具，其中，GM(1,1)為灰色預測中廣為使用模型之一。然而， GM(1,1) 對於波動性明顯之數據資料卻未能有效的掌握其變動趨勢，因此，本研究之目的即在短期預測之要求下，建構一有效之GM(1,1) 預測方法，而此方法也能對具有明顯波動性之資料達到理想的預測結果。
本研究嘗試從三個不同的觀點對波動性資料進行解析，期望能降低資料之波動性。首先從序列關係與因素分析的角度探討，分析一時間序列的變動趨勢中，是否有其他序列或非預期因素的發生而導致序列之波動性增加，而後並將此些訊息移除。其次為從時間序列之特徵角度探討，尤其是對季節性或週期性的效果進行分解，透過時間序列的分解過程，將季節性或週期性之特徵排除，如此將可大幅改善序列波動的情況。最後為以平滑曲線之數學方法配適原始資料序列，並以此配適曲線取代原始序列成為預測過程中之輸入值，期望透過曲線的平滑而提昇預測績效。綜觀上述所示，本研究之目的為以不同方法改變時間序列之波動性，藉以創造理想的序列型態以提昇灰色預測之運用成效。
最後本研究以台灣股價加權指數為列，說明如何使用上述所示之方法，並應用灰色理論之GM(1,1) 以有效達成短期預測之目標。

The grey prediction theory is a suitable tool for dealing with a short-term forecasting. One of general used prediction model is GM(1,1). However, GM(1,1) has not yielded good results for data with obvious fluctuation. Thus, the purpose in this study is constructing an effective prediction system that approaches desirable prediction results under the requirement of short-term prediction in real situations.
In this study, investigations of the fluctuating data discriminate aspects from three directions for aforementioned purpose. The series and factors analysis is first applied for analyzing whether a time series is affected by other series or unexpected factors. Then, these influences lead to the increasing of fluctuation in data are removed from original data in order to decrease the fluctuation. In addition, the decomposition of the time series, especially the seasonal effect, is studied for realizing influences of seasonal or periodic effects. Furthermore, estimates obtained from smoothing mathematical techniques are using for fitting the original data and becoming input values of GM(1,1). Summarizing above methods, all of them are using for smoothing an original time series in order to reduce fluctuation in data and creating an ideal form of series for improving the precision of GM(1,1).
Finally, the Taiwan stock index are using for verifying aforementioned methods are useful for improving the precision of GM(1,1) and suitable for purpose of short-term prediction.

國家圖書館博碩士論文電子檔案上網授權書 iii
國科會博碩士論文授權書 iv
中文摘要 v
ABSTRACT vi
ACKNOWLEDGEMENTS vii
TABLE OF CONTENTS viii
LIST OF FIGURES xiii
LIST OF TABLES xvi
CHAPTER 1. INTRODUCTION 1
1.1 Research Motive 1
1.2 Direction of Research 2
1.2.1 Series and Factor Analysis 4
1.2.2 Decomposition of characters in a time series 4
1.2.3 Fitting by smoothing estimates 5
1.3 The Objective of Research 5
1.4 Outline of This Thesis 7
CHAPTER 2. REVIEW OF REFERENCE 8
2.1 Review of Grey Prediction Theory 8
2.2 Review of Series and Factors Analysis 8
2.3 Review the decomposition of a Time Series 11
2.4 Review of Smoothing Fitting 11
CHAPTER 3. PHILOSOPHIES AND EVALUATIONS OF PREDICTIVE MODELS 13
3.1 Concept of Grey Theory 13
3.1.1 Foundations of Grey System 13
3.1.2 Framework of Grey System 15
3.2 Grey Generating and Grey Modeling 16
3.2.1 Generating Operations and Grey Generating Space 16
3.2.2 Grey Models 19
3.2.3 Features of GM(1,1) 22
3.2.4 Reliability of Grey Model 25
3.3 Grey Prediction 26
3.3.1 Series Grey Prediction 26
3.3.2 Calamities Grey Prediction 27
3.3.3 Seasonal Calamities Grey Prediction 28
3.3.4 Topological Grey Prediction 31
3.3.5 Systematic Grey Prediction 31
3.4 Other Traditional Models for Prediction 32
3.4.1 Simple Linear Regression Model 33
3.4.2 Multiple Linear Regression Model 33
3.4.3 Nonlinear Regression Model 34
3.4.4 Fuzzy Regression Model 39
3.5 Measures of Accuracy for Predictive Models 40
CHAPTER 4. SERIES RELATION AND FACTOR ANALYSIS 42
4.1 Grey Relational Analysis 42
4.1.1 Basis of Grey Relational Analysis 42
4.1.2 General Grey Relational Grade 44
4.1.3 Entropy Grey Relational Grade 46
4.1.4 Subsistence of Quantitative Grey Relational Grade 50
4.1.5 Coexistence of Nearness and Similarity 53
4.2 Fuzzy AHP Method 55
4.2.1 Fuzzy Number and Fuzzy Operations 58
4.2.2 Procedures of Fuzzy AHP 59
4.3 Adjustment of Data Series 62
4.3.1 Consistency of measures 62
4.3.2 Factors Removing and Adding 63
CHAPTER 5. DECOMPOSITION AND SMOOTHING FITTING OF A TIME SERIES 65
5.1 Transformation based on Decomposition of Series 65
5.1.1 The Nature of Seasonality 66
5.1.2 Modeling Seasonality 68
5.1.3 Basic Grey Periodic Prediction Model 74
5.1.4 Grey Periodic Prediction Approach 75
5.2 Transformation based on Smoothing Fitted Functions 80
5.2.1 Introduction to Nonparametric Regression 80
5.2.2 k-Nearest Neighbor Smoothing Estimator 84
5.2.3 Kernel Density Estimator and Kernel Regression 87
5.2.4 Selection of Bandwidth 92
CHAPTER 6. NUMERICAL EXAMPLES AND DISCUSSION 98
6.1 Prediction of Taiwan Stock Index 98
6.1.1 Relative Outcomes of Series and Factors Analysis 99
6.1.2 Predictive Results of Various Models 105
6.1.3 Predictive Results with Factors Adjustment 114
6.1.4 Analysis and Discussion 121
6.2 Prediction of Cold Drink’s Sales 122
6.2.1 Numerical Results 124
6.2.2 Analysis and Discussion 127
CHAPTER 7. CONCLUSIONS 138
REFERENCES 140
APPENDIX A STOCK PRICE OF STOCK EXCHANGE MARKET IN TAIWAN 145
APPENDIX B SURVEY OF FACTORS RELATED WITH STOCK EXCHANGE MARKET IN TAIWAN 148
APPENDIX C SUMMARY OF OCCURRED FACTORS IN STOCK EXCHANGE MARKET 157

[1] Chang, B. R., “ Alternative View of Grey Relational Analysis,” The Journal of Grey System, Vol. 13 (1), p.p. 31-40, 2001.
[2] Chang, B. R., “An Optimal Grey Relational Measurement,” Proceedings of International Joint Conference on Neural Networks, p.p. 1609-1614, 2001.
[3] Chang, B. R., “ Novel Grey Relational Measurements,” Proceedings of International Joint Conference on Neural Networks, p.p.1615-1619.
[4] Chang, D. Y., “ Applications of the Extent Analysis Method on Fuzzy AHP,” European Journal of Operational Research, Vol. 95, p.p. 649-655, 1996.
[5] Chang, H. C. and Wu, John H., “A Study on The Relation Between Adaptive Factor and Grey Prediction,” The 2000 Fifth National Conference on Grey Theory and Application, p.p. 289-298, 2000.
[6] Chang, P. T., “Fuzzy Seasonality Forecasting,” Fuzzy Set and Systems, Vol. 90, p.p. 1-10, 1997.
[7] Chang, T. C., Wen K. L., Chang H. T. and You M. L., “Inverse Approach to Find An Optimum a for Grey Prediction Model.” IEEE International Conference on System, Man and Cybernetics, p.p. 309-313, 1999.
[8] Chu, C. K., “Bandwidth Selection in Nonparametric Regression with General Errors,” Journal of Statistical Planning and Inference, Vol.44 (3), p.p. 265-275, 1995.
[9] Chen, H. S. and Chang, W. C, “A Study of Optimal Grey Model GM(1,1),” Journal of The Chinese Grey System Association, Vol. 1 (2), p.p.141-145, 1998.
[10] Chen, J. Y. and Lin, Y. H., “Design of Fuzzy Sliding Mode Controller with Grey Predictor,” The Journal of Grey System, Vol. 8 (2), p.p.147-164, 1996.
[11] Cheng, C. B. and Lee, E. S., “ Nonparametric Fuzzy Regression－k-NN and Kernel Smoothing Techniques,” Computers and Mathematics with Application, Vol. 38, p.p. 239-251, 1999.
[12] Cheng, C. H., “Evaluating Navel Tactical Missile Systems by Fuzzy AHP based on the Grade Value of Membership Function,” European Journal of Operational Research, Vol. 96, p.p. 343-350, 1996.
[13] Chiao, J. Y., Wang, W. Y. and Lu, M. J., “ A Study for Applying Grey Forecasting to Improve the Reliability of Product,” The 1997 Second National Conference on Grey Theory and Applications, p.p.66-71, 1997.
[14] DeLurgio S. A, Forecasting Principles and Applications, McGraw Hill College Div: Boston, 1997.
[15] Deng, J. L., “Introduction to Grey System Theory,” The Journal of Grey System, Vol. 1 (1), p.p. 1-24, 1989.
[16] Deng J. L. The Theory and Application of Grey System, Kao-Li Books Inc.: Taipei, 2000.
[17] Deng, J. L., Kuo, H., Wen, K. L., Chang, T. C., and Chang, W. C., Methods and Applications of Grey Prediction Model, Kao-Li Books Inc.: Taipei, 2000.
[18] Deibold, F. X., Elements of Forecasting, 2nd ed. South-Western: Cincinnati, 2001.
[19] Eubank, R. L., Nonparametric Regression and Spline Smoothing, 2nd ed. Marcel Dekker, Inc.: New York, 1999.
[20] Faucher, D., Rasmussen, P. F. and Bobée B., “A Distribution Function based Bandwidth Selection Method for Kernel Quantile Estimation,” Journal of Hydrology, Vol. 250, p.p. 1-11, 2001.
[21] Fernholz, L. T., “ Reducing the Variance by Smoothing,” Journal of Statistical Planning and Inference, Vol. 57, p.p. 29-38, 1997.
[22] Friedman, M. and Kandel, A., Introduction to Pattern Recognition: Statistical, Structural, Neural, and Fuzzy Logic Approaches, World Scientific Publishing: Singapore, 1999.
[23] Hanke, J. E. and Reitsch, A. G., Business Forecasting, 6th ed., Prentice-Hill International: London, 1998.
[24] Hsin, J. Y. and Tasi, Y. P., “ The Research of Superposition Method for Value in Grey Forecasting,” The 2000 Fifth National Conference on Grey Theory and Application, p.p. 305-308, 2000.
[25] Hsu, Y. T., Cheng, H. C. and Lin, C. B., “A Long-Term Prediction Using GMs,” The Journal of Grey System, Vol. 12 (1), p.p. 41-54, 2000.
[26] Lee, C. M., “ A Stabilized Bandwidth Selection Method for Kernel Smoothing of the Periodogram,” Signal Processing, Vol. 81, p.p. 419-430, 2001.
[27] Leong, k., “Seasonal Integration in Economic Time Series,” Mathematics and Computers in Simulation, Vol. 43, p.p. 413-419, 1997.
[28] Loftsgaarden, D. O. and Quesenberry, G. P., “A Nonparametric Estimate of a Multivariate Density Function,” Annals of Mathematical Statistics, Vol. 36, p.p. 1049-1051, 1965.
[29] Shin, N. Z. and Liou, D. K., “An Evaluation Study of Future Indexes Hedging Strategies in Grey System — Applied on Volume Weighted Index and Future Index,” The 1997 Second National Conference on Grey Theory and Applications, p.p.16-33, 1997.
[30] Tanaka, H., Uejima, S. and Asai, K., “Fuzzy Linear Regression Model,” IEEE Trans. System, Man and Cybernetics, Vol. 12, p.p. 903-907, 1982.
[31] Tseng, F. M., Yu, H. C. and Tzeng, G. H., “Applied Hybrid Grey Model to Forecast Seasonal Time Series,” Technological Forecasting and Social Change, Vol. 67, p.p. 291-302, 2001
[32] Tseng, F. M., Yu, H. C. and Tzeng, G. H., “Forecast Seasonal Time Series by Comparing Five Kinds of Hybrid Grey Models,” The Journal of Chinese Fuzzy System, Vol.5 (2), p.p. 45-55, 1999.
[33] Wen, K. L., Chang, T. C., Chang H. T. and You M. L., “The Adaptive a in GM(1,1) Model,” IEEE International Conference on System, Man and Cybernetics, p.p. 304-308, 1999.
[34] Wu, John H. and Lau, C. R., “ A Study to Improve GM(1,1) via Heuristic Method,” The Journal of Grey System, Vol. 10 (3), p.p.183-192, 1998.
[35] Wand, M. P. and Jones, M. C., Kernel Smoothing, Chapman & Hall: London, 1995.
[36] Wu, John H., Chen, C. B., “An Alternative Form for Grey Relational Grades,” The Journal of Grey System, Vol. 11 (1), p.p. 7-12, 1999.
[37] Wu, C. C., Regression Analysis: Theory and Application, 13th ed., Fu-Wen Bookstore: Tainan City, 1995.
[38] Xiao, X. P. “On Parameters in Grey Models,” The Journal of Grey System, Vol. 11 (4), p.p. 315-324, 1999.
[39] Yang, C.Y. and Chou, J.J., “Entropy on Grey Relational Analysis,” The Journal of Grey System, Vol. 13 (4), p.p. 313-320, 2001.
[40] Zhu, K. J., Jing, Y., and Chang, D. Y., “ A Discussion on Extent Analysis Method and Applications of Fuzzy AHP,” European Journal of Operational Research, Vol. 116, p.p.450-456, 199