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題名 區間時間序列預測及其準確度分析
Time series analysis and forecasting evaluation with interval data
作者 徐惠莉
Hsu, Hui-Li
貢獻者 吳柏林
Wu, Berlin
徐惠莉
Hsu, Hui-Li
關鍵詞 區間時間序列
模糊統計
區間預測
區間均方誤差
平均相對區間誤差
XOR平均比率
模糊相關係數
相關係數區間
interval time series
fuzzy statistics
interval forecasting
mean squared error of interval
mean relative interval error
mean ratio of exclusive-or
fuzzy correlation coefficient
correlation coefficient interval
日期 2008
上傳時間 8-十二月-2010 11:53:13 (UTC+8)
摘要 近年來隨著科技的進步與工商業的發展，預測技術的創新與改進愈來愈受到重視。相對地，對於預測準確度的要求也愈來愈高。尤其在經濟建設、經營規畫、管理控制等問題上，預測更是決策過程中不可或缺的重要資訊。然而僅用單一數值形式收集來的資料，其建立的模式是不足以描述每日或每月的發展趨勢。因為有太多模糊且不完整訊息，以致於無法用傳統以點資料建構的系統來進行預測。基於點預測的不確定性，因此嘗試以區間資料來建構模式並進行預測。本論文探討區間時間序列之動態走勢及預測結果之效率性，共三部份，分別為區間時間序列之分析與預測、區間預測準確度之探討和計算區間資料的相關係數。
第一部份，利用區間具有糢糊數的特質，將其分解成區間平均數及區間長度，提出區間時間數列建構過程及預測方法，如區間移動平均、區間加權移動平均、ARIMA區間預測等方法。並藉由模擬方式設計出數組穩定及非穩定之區間時間數列，再利用本文所提出的區間預測方法進行預測。根據這些計算預測結果效率性的方法，發現ARIMA區間預測，提供了較傳統的預測方法更為準確及具有彈性的預測結果。
第二部份，我們特別針對區間預測結果的準確度提出效率性的分析，如平均區間預測誤差平方和、平均相對區間誤差及平均XOR比率。而在預測效率性的實證分析上，平均XOR比率能給與決策者更正確的資訊，做出更客觀的判斷。
第三部份，在探討如何將區間資料應用在計算相關係數。利用單一數值資料的收集 ，並以傳統的相關係數r來說明兩變數之間是否相關? 是較為便利且易懂的統計方法。但資料是否足以代表母體特性？這樣求出來的相關係數值會不會太主觀?有鑑於此，以區間就是模糊數的概念，建構模糊相關係數。最後舉出應用實例，比較模糊相關係數與傳統的相關係數的差異性，在說明兩變數關係的強弱程度，模糊相關係數提供了一個較有彈性的統計分析方法。
Point forecasting provides important information during decision-making processes, especially in economic developments, population policies, management planning or financial controls. Nevertheless, the forecasting model constructed only by single values may not demonstrate the whole trend of a daily or monthly process. Since there are so many unpredictable and continuous fluctuations on the process to be predicted, the observed values are discrete instantaneous values which are insufficient to represent the true process. Therefore, the collected information is generally vague and incomplete so that the real number system is not sufficient to express the forecasting model. In additional, due to the business marketing is full of uncertainty and the continuous fluctuations, intervals are used to express and establish the forecasting model to estimate the prediction values.
This dissertation investigates the dynamic trend of interval time series and the performance evaluation of interval forecasting. It consists of three parts: the analysis and forecasting of interval time series, the evaluation of forecasting performance for interval data, and the calculation of the fuzzy correlation coefficient.
First of all, we propose the conception of fuzzy for interval and propose interval forecasting approaches, such as the interval moving average, the weighted interval moving average, and ARIMA interval forecasting. The soft computing technique as well as the model simulation is used to carry out the interval forecasting. The forecast results are compared by the mean squared interval error and the mean relative interval error. Finally, we take two practical cases study. By the comparison of forecasting performance, it is found that ARIMA interval forecasting provides more efficiency and flexibility than the traditional ones do.
Secondly, we concentrated on the forecasting performance evaluation for interval data. The evaluation techniques are developed to determine the validity of the forecast results. The forecast results are compared by three criteria which are the mean squared error of interval, mean relative interval error, and the mean ratio of exclusive-or. It is found that the empirical studies show that the mean ratio of exclusive-or can provide a more objective suggestion in interval forecasting for policymakers.
The third part considers the evaluation of the correlation coefficient interval by collecting sample data whose types are real and interval. When an interval is considered as a fuzzy number, the aspect of fuzzy can be utilized to construct the fuzzy correlation coefficient for interval data. As compared with the traditional correlation coefficient, the fuzzy correlation coefficient can demonstrate conservative correlation coefficient and provide an objective statistical method for discovering the correlation between two variables.
參考文獻 [1] Abraham, B., Ledolter, J. Statistical Methods for Forecasting, John Wiley & Sons, New York, 1983.
[2] Akaike, H., Fitting autoregressive models for prediction, Annals of the Institute of Statistical Mathematics, vol. 21, no. 1, pp. 243–247, 1969.
[3] Arnold, S., Mathematical Statistics, Prentice Hall Inc, London, 1990.
[4] Berry, D. and Lindgren, B., Statistics, 2nded, Wadsworth Publishing Company: Belmont, California, 1996.
[5] Box, G. E. P., Jenkins, G. M., and Reinsel, G. C., Time Series Analysis: Forecasting and Control, 4th edn., John Wiley, New York, 2008.
[6] Bustince, H. and Burillo, P., Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and System, vol. 74, no. 2, pp. 237-244, 1995.
[7] Chatfield, C., The Analysis of Time Series, 6th ed., Chapman and Hall, London, 2004.
[8] Chatfield, C., Calculating interval forecasts, Journal of Business and Economic Statistics, vol. 11, no. 2, pp. 121–135, 1993.
[9] Chatfield, C., Model uncertainty and forecast accuracy, Journal of Forecasting, vol. 15, no. 7, pp. 495508, 1996.
[10] Chiang, D. A. and Lin, N. P., Correlation of Fuzzy Set, Fuzzy Sets and Systems, vol. 102, no. 2, pp. 221-226, 1999.
[11] Denœux, T. and Masson, M. H., Multidimensional scaling of interval-valued dissimilarity data, Pattern Recognition Letters, vol. 21, no. 1, pp. 83–92, 2000.
[12] Faraway, J. and Chatfield, C., Time-series forecasting with neural networks: a comparative study using the airline data, Journal of the Royal Statistical Society: Series C (Applied Statistics), vol. 47, no. 2, pp. 231–250, 1998..
[13] Gerstenkorn, T. and Manko, J., Correlation of intuitionistic fuzzy sets. Fuzzy Sets and Systems, vol. 44, no. 1, pp. 39-43, 1991.
[14] Hasuike, T. and Ishii, H., Portfolio Selection Problems Considering Fuzzy Returns of Future Scenarios, International Journal of Innovative Computing Information and Control, vol. 4, no. 10, pp. 2493-2506, 2008.
[15] Hayes, B., A Lucid Interval, American Scientist, vol. 91, no. 6, pp. 484488, 2003.
[16] Hébert, P. A., Masson, M. H. and Denœux, T., Fuzzy multidimensional scaling, Computational Statistics & Data Analysis, vol. 51, no. 1, pp. 335–359, 2006.
[17] Hong, D. H. and Hwang, S. Y., Correlation of intuitionistic fuzzy sets in probability space. Fuzzy Sets and Systems, vol. 75, no. 1, pp. 77-81, 1995.
[18] Kubo, Y., Fujita, S., and Sugimoto, S., Estimation and Validation of Integer Ambiguity in Carrier Phase GPS Positioning, International Journal of Innovative Computing Information and Control, vol. 4, no. 2, pp. 153-164, 2008.
[19] Liu, S. T. and Kao, C., Fuzzy measures for correlation coefficient of fuzzy numbers. Fuzzy Sets and Systems, vol. 128, no. 2, pp. 267-275, 2002.
[20] Manski, C., The use of intention data to predict behavior: a best case analysis, Journal of the American Statistical Association, vol. 85, no. 412, pp. 934–940, 1990.
[21] McClave, J., Beson, P. and Sincich, T., Statistics for Business and Economics. 7thed. Prentice Hall Inc, London, 1998.
[22] Montgomery, D. C. and Johnson, L. A., Forecasting Time Series Analysis, New York: McGraw-Hill, 1976.
[23] Nguyen, H. T., Wu, B., Fundamentals of Statistics with Fuzzy Data, Springer-Verlag, New York, 2006.
[24] Shimakawa, M., A Proposal of Extension Fuzzy Reasoning Method, International Journal of Innovative Computing Information and Control, vol. 4, no. 10, pp. 2603-2615, 2008.
[25] Shinkai, K., Decision Analysis of Fuzzy Partition Tree Applying Fuzzy Theory, International Journal of Innovative Computing Information and Control, vol. 4, no. 10, pp. 2581-2594, 2008.
[26] Smith, D., Eggen, M., Andre, R. St., A Transition to Advanced Mathematics, 4th ed., Brooks/Cole, New York, 1997.
[27] Tanak, H., Uejima, S. and Asai, K., Linear Regression Analysis with Fuzzy model, IEEE Trans. Systems Man Cybernet, vol. 12, no. 6, pp. 903-907, 1982.
[28] Wakuya, H., Enrichment of Inner Information Representations in Bi-directional Computing Architecture for Time Series Prediction, International Journal of Innovative Computing Information and Control, vol. 4, no. 11, pp. 3079-3090, 2008.
[29] Wang, T., Chen, Y. and Tong, S., Fuzzy Reasoning Models and Algorithms on Type-2 Fuzzy Sets, International Journal of Innovative Computing Information and Control, vol. 4, no.10, pp. 2451-2460, 2008.
[30] Wu, B., Introduction to Time Series Analysis, HwaTai: Taipei, 1995.
[31] Wu, B., Chen, M., Use fuzzy statistical methods in change periods detection. Applied Mathematics and Computation, vol. 99, pp. 241-254, 1999.
[32] Wu, B. and Hsu, Y.-Y., A new approach of bivariate fuzzy time series: with applications to the stock index forecasting, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, vol. 11, no. 6, pp. 671-690, 2004.
[33] Wu, B. and Tseng, N.-F., A new approach to fuzzy regression models with application to business cycle analysis, Fuzzy Sets and Systems, vol. 130, no. 1, pp.33-42, 2002.
[34] Yang, M. S. and Ko, C. H., On a class of fuzzy c-numbers clustering procedures for fuzzy data, Fuzzy Sets and Systems, vol. 84, no. 1, pp. 49–60, 1996.
[35] Yu, C., Correlation of fuzzy numbers, Fuzzy Sets and Systems, vol. 55, no. 3, pp. 303-307, 1993.
[36] Zadeh, L. A, Fuzzy Sets, Information and Control, vol. 8, no. 3, pp. 338-353, 1965.
[37] Zimmermann, H. J., Fussy Set Theory and Its Applications. Boston: Kluwer Academic, 1991.
[38] Taiwan Stock Exchange Corporation, available at: http://www.twse.com.tw/en/.
[39] Introduction to interval FAQ from Dominque Faudot, available at: http://www.mscs.mu.edu/~georgec/IFAQ/faudot2.html.
[40] Kreinovich, V. Nguyen, H. and Wu, B. , On-line Algorithms for computing mean and variance of interval data and their use in intelligent systems. Information Sciences, vol. 177, no. 16, pp.3228 – 3238, 2007.
[41] Hsu, H. L. and Wu, B., Evaluating forecasting performance for interval data, Computers and Mathematics with Applications, vol. 56, no. 9, pp.2155－2163, 2008.
描述 博士
國立政治大學
應用數學研究所
91751502
97
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0917515022
資料類型 thesis
dc.contributor.advisor 吳柏林zh_TW
dc.contributor.advisor Wu, Berlinen_US
dc.contributor.author (作者) 徐惠莉zh_TW
dc.contributor.author (作者) Hsu, Hui-Lien_US
dc.creator (作者) 徐惠莉zh_TW
dc.creator (作者) Hsu, Hui-Lien_US
dc.date (日期) 2008en_US
dc.date.accessioned 8-十二月-2010 11:53:13 (UTC+8)-
dc.date.available 8-十二月-2010 11:53:13 (UTC+8)-
dc.date.issued (上傳時間) 8-十二月-2010 11:53:13 (UTC+8)-
dc.identifier (其他 識別碼) G0917515022en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/49461-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 91751502zh_TW
dc.description (描述) 97zh_TW
dc.description.abstract (摘要) 近年來隨著科技的進步與工商業的發展，預測技術的創新與改進愈來愈受到重視。相對地，對於預測準確度的要求也愈來愈高。尤其在經濟建設、經營規畫、管理控制等問題上，預測更是決策過程中不可或缺的重要資訊。然而僅用單一數值形式收集來的資料，其建立的模式是不足以描述每日或每月的發展趨勢。因為有太多模糊且不完整訊息，以致於無法用傳統以點資料建構的系統來進行預測。基於點預測的不確定性，因此嘗試以區間資料來建構模式並進行預測。本論文探討區間時間序列之動態走勢及預測結果之效率性，共三部份，分別為區間時間序列之分析與預測、區間預測準確度之探討和計算區間資料的相關係數。
第一部份，利用區間具有糢糊數的特質，將其分解成區間平均數及區間長度，提出區間時間數列建構過程及預測方法，如區間移動平均、區間加權移動平均、ARIMA區間預測等方法。並藉由模擬方式設計出數組穩定及非穩定之區間時間數列，再利用本文所提出的區間預測方法進行預測。根據這些計算預測結果效率性的方法，發現ARIMA區間預測，提供了較傳統的預測方法更為準確及具有彈性的預測結果。
第二部份，我們特別針對區間預測結果的準確度提出效率性的分析，如平均區間預測誤差平方和、平均相對區間誤差及平均XOR比率。而在預測效率性的實證分析上，平均XOR比率能給與決策者更正確的資訊，做出更客觀的判斷。
第三部份，在探討如何將區間資料應用在計算相關係數。利用單一數值資料的收集 ，並以傳統的相關係數r來說明兩變數之間是否相關? 是較為便利且易懂的統計方法。但資料是否足以代表母體特性？這樣求出來的相關係數值會不會太主觀?有鑑於此，以區間就是模糊數的概念，建構模糊相關係數。最後舉出應用實例，比較模糊相關係數與傳統的相關係數的差異性，在說明兩變數關係的強弱程度，模糊相關係數提供了一個較有彈性的統計分析方法。		zh_TW
dc.description.abstract (摘要) Point forecasting provides important information during decision-making processes, especially in economic developments, population policies, management planning or financial controls. Nevertheless, the forecasting model constructed only by single values may not demonstrate the whole trend of a daily or monthly process. Since there are so many unpredictable and continuous fluctuations on the process to be predicted, the observed values are discrete instantaneous values which are insufficient to represent the true process. Therefore, the collected information is generally vague and incomplete so that the real number system is not sufficient to express the forecasting model. In additional, due to the business marketing is full of uncertainty and the continuous fluctuations, intervals are used to express and establish the forecasting model to estimate the prediction values.
This dissertation investigates the dynamic trend of interval time series and the performance evaluation of interval forecasting. It consists of three parts: the analysis and forecasting of interval time series, the evaluation of forecasting performance for interval data, and the calculation of the fuzzy correlation coefficient.
First of all, we propose the conception of fuzzy for interval and propose interval forecasting approaches, such as the interval moving average, the weighted interval moving average, and ARIMA interval forecasting. The soft computing technique as well as the model simulation is used to carry out the interval forecasting. The forecast results are compared by the mean squared interval error and the mean relative interval error. Finally, we take two practical cases study. By the comparison of forecasting performance, it is found that ARIMA interval forecasting provides more efficiency and flexibility than the traditional ones do.
Secondly, we concentrated on the forecasting performance evaluation for interval data. The evaluation techniques are developed to determine the validity of the forecast results. The forecast results are compared by three criteria which are the mean squared error of interval, mean relative interval error, and the mean ratio of exclusive-or. It is found that the empirical studies show that the mean ratio of exclusive-or can provide a more objective suggestion in interval forecasting for policymakers.
The third part considers the evaluation of the correlation coefficient interval by collecting sample data whose types are real and interval. When an interval is considered as a fuzzy number, the aspect of fuzzy can be utilized to construct the fuzzy correlation coefficient for interval data. As compared with the traditional correlation coefficient, the fuzzy correlation coefficient can demonstrate conservative correlation coefficient and provide an objective statistical method for discovering the correlation between two variables.		en_US
dc.description.tableofcontents CHAPTER 1 INTRODUCTION 1
CHAPTER 2 INTERVAL TIME SERIES ANALYSIS AND FORECASTING 4
2.1 INTRODUCTION 4
2.2 THE CHARACTERISTICS OF INTERVAL DATA 6
2.2.1 Why Using Interval? 6
2.2.2 An Interval as a Fuzzy Number 7
2.2.3 The Forecasting Models of Interval Time Series 10
2.3 THE EFFICIENCY ANALYSIS OF INTERVAL TIME SERIES FORECASTING 12
2.3.1 The Mean Squared Error of Interval 13
2.3.2 The Mean Relative Interval Error 14
2.4 SIMULATION ANALYSIS AND DISCUSSIONS 16
2.4.1 Simulations of Interval Time Series 16
2.4.2 Model Construction of Interval Time Series 18
2.4.3 The Comparison and Analysis of the Forecast Results 19
2.5 TWO CASE ANALYSES 24
2.5.1 The Monthly Trading Value of the Stock 24
2.5.2 The Daily Temperatures in Taipei 26
2.6 CONCLUSIONS 29
CHAPTER 3 PERFORMANCE ANALYSIS OF INTERVAL FORECASTING 31
3.1 INTRODUCTION 31
3.2 INTERVAL FORECASTING 32
3.2.1 Time Series Forecasting with Interval Data 32
3.2.2 Some Operations of Interval Data 34
3.2.3 Properties of Interval Time Series 35
3.3 EFFICIENCY EVALUATION FOR INTERVAL FORECASTING 37
3.3.1 The Comparison of MESI and MRIE 37
3.3.2 The Feasibility Analysis of MSEI and MRIE 38
3.4 THE MEAN RATIO OF EXCLUSIVE-OR 40
3.4.1 The Mean Ratio of XOR 40
3.4.2 Discussion of MRXOR in Different Forecasting Situations 41
3.5 EMPIRICAL STUDIES 43
3.5.1 The Efficiency Analysis of Three Forecasting Situations 44
3.5.2 The Forecasting Performance of Temperature 46
3.6 CONCLUSIONS 49
CHAPTER 4 AN INNOVATIVE APPROACH ON FUZZY CORRELATION COEFFICIENT WITH INTERVAL DATA 51
4.1 INTRODUCTION 51
4.2 CORRELATION COEFFICIENT 52
4.2.1 Traditional Correlation Coefficient 52
4.2.2 Correlation Coefficient Interval 53
4.3 FUZZY CORRELATION COEFFICIENT 56
4.3.1 An approximation approach for a correlation coefficient interval 56
4.3.2 Comparison with the Traditional Correlation Coefficient 58
4.4 EMPIRICAL STUDIES 59
4.4.1 Calculus Score and Online Hour 60
4.4.2 Temperature and Relative Humidity 62
4.5 CONCLUSIONS 65
REFERENCES 67		zh_TW
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dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0917515022en_US
dc.subject (關鍵詞) 區間時間序列zh_TW
dc.subject (關鍵詞) 模糊統計zh_TW
dc.subject (關鍵詞) 區間預測zh_TW
dc.subject (關鍵詞) 區間均方誤差zh_TW
dc.subject (關鍵詞) 平均相對區間誤差zh_TW
dc.subject (關鍵詞) XOR平均比率zh_TW
dc.subject (關鍵詞) 模糊相關係數zh_TW
dc.subject (關鍵詞) 相關係數區間zh_TW
dc.subject (關鍵詞) interval time seriesen_US
dc.subject (關鍵詞) fuzzy statisticsen_US
dc.subject (關鍵詞) interval forecastingen_US
dc.subject (關鍵詞) mean squared error of intervalen_US
dc.subject (關鍵詞) mean relative interval erroren_US
dc.subject (關鍵詞) mean ratio of exclusive-oren_US
dc.subject (關鍵詞) fuzzy correlation coefficienten_US
dc.subject (關鍵詞) correlation coefficient intervalen_US
dc.title (題名) 區間時間序列預測及其準確度分析zh_TW
dc.title (題名) Time series analysis and forecasting evaluation with interval dataen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] Abraham, B., Ledolter, J. Statistical Methods for Forecasting, John Wiley & Sons, New York, 1983.zh_TW
dc.relation.reference (參考文獻) [2] Akaike, H., Fitting autoregressive models for prediction, Annals of the Institute of Statistical Mathematics, vol. 21, no. 1, pp. 243–247, 1969.zh_TW
dc.relation.reference (參考文獻) [3] Arnold, S., Mathematical Statistics, Prentice Hall Inc, London, 1990.zh_TW
dc.relation.reference (參考文獻) [4] Berry, D. and Lindgren, B., Statistics, 2nded, Wadsworth Publishing Company: Belmont, California, 1996.zh_TW
dc.relation.reference (參考文獻) [5] Box, G. E. P., Jenkins, G. M., and Reinsel, G. C., Time Series Analysis: Forecasting and Control, 4th edn., John Wiley, New York, 2008.zh_TW
dc.relation.reference (參考文獻) [6] Bustince, H. and Burillo, P., Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and System, vol. 74, no. 2, pp. 237-244, 1995.zh_TW
dc.relation.reference (參考文獻) [7] Chatfield, C., The Analysis of Time Series, 6th ed., Chapman and Hall, London, 2004.zh_TW
dc.relation.reference (參考文獻) [8] Chatfield, C., Calculating interval forecasts, Journal of Business and Economic Statistics, vol. 11, no. 2, pp. 121–135, 1993.zh_TW
dc.relation.reference (參考文獻) [9] Chatfield, C., Model uncertainty and forecast accuracy, Journal of Forecasting, vol. 15, no. 7, pp. 495508, 1996.zh_TW
dc.relation.reference (參考文獻) [10] Chiang, D. A. and Lin, N. P., Correlation of Fuzzy Set, Fuzzy Sets and Systems, vol. 102, no. 2, pp. 221-226, 1999.zh_TW
dc.relation.reference (參考文獻) [11] Denœux, T. and Masson, M. H., Multidimensional scaling of interval-valued dissimilarity data, Pattern Recognition Letters, vol. 21, no. 1, pp. 83–92, 2000.zh_TW
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