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第五章 結論
在時間數列的分析過程中，統計數值資料本身的不確定性與模糊性，可說是 傳統時間數列模型不易建構的困難所在，Manski (1990)曾指出，數值資料有過度 解釋的危險。倘若我們利用此假性的精確值，來作因果分析或計量度量，可能造 成因果判定偏差、決策模式誤導或擴大預測結果和實際狀態之間的差異。人類的 思維模式中，計量過程本身即充滿著模糊性，這似乎是單純化的結果，但過分單 純化又會阻礙計量方法與標準的客觀性。若能結合較穩健性與符合實際狀況的模 糊統計分析，應能避免這樣的情況發生。
自從 Zadeh 教授在 1965 年提出了模糊集合的概念，做為測試不明確隸屬度 函數的工具以來，許多的模糊研究嘗試以此方法設定理論架構，並試圖以此一理 論作為建構更為先進模糊理論的基礎。雖然，過去模糊理論的應用範疇，大部份 侷限在計算機科學領域裡的專家系統研究中。但近來，由於人文社會科學的測度 理論發展過程裡，複雜的人文社會科學現象，無法以傳統數值模型充分合理解 釋，進而導致模糊統計與模糊相關性日漸受到重視，這應是一種自然的發展結 果。有鑑於此，目前將模糊理論應用在人文社會科學研究中的情形已相當普遍。
模糊分類(fuzzy clustering)是一種用來處理資料分類及型態識別的新方法，在 本論文中我們提出以轉折區間的概念來取代傳統時間數列發生結構改變的轉折 點，並提供一套程序來檢測在顯著水準 下時間數列是否存在轉折區間。轉折區 間的存在與否幫助我們可以辨別時間數列是否有結構上的轉變，以本論文中的實 例來看，我們所建議的程序可以有效的檢測出轉折區間。
若是跟傳統的方法相比，本論文所提出的方法具有幾個優點：
1. 時間數列的結構訊息對於本論文的轉折區間檢測程序來說並不需要。
2. 此法亦適用於歷史資料的語意處理，處理過程與本論文所建議十分相 似，只需在步驟 2 加上學者經驗判斷即可。
僅管具有上述的優點，但在本論文中尚有待解決的問題，亦是未來值得研究 的方向，分述如下：
1. 本論文雖提及多變量模糊時間數列模式建構與預測，但由於時間的關 係，並未於文中舉出實例的建構過程。
2. 字詞的語意應該細心地定義以求穩定，像是「轉折點」所代表的究竟是 平均數的改變、變異數的改變、特徵參數的改變或是模式的改變，這點 必須在檢測程序實施前先行做好。
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參考文獻
Balke, N. S. (1993), Detecting level shifts in time series, Journal of Business Economic Statistics, 11(1), 81-92.
Chen, S. M. (1996), Forecasting enrollments based on fuzzy time series, Fuzzy Sets and Systems, 81, 311-319.
Chiang, D., L. Chow, and Y. Wang (2000), Mining time series data by a fuzzy linguistic summary system, Fuzzy Sets and Systems, 112, 419-432.
Clymer, J., P. Corey, and J. Gardner (1992), Discrete event fuzzy airport control, IEEE Transactions on Systems, Man, and Cybernetics, 22(2), 343-351.
Cutsem, B. V., and I. Gath (1993), Detection of outliers and robust estimation using fuzzy clustering, Computational Statistics and Data Analysis, 15, 47-61.
Dubois, D. and H. Prade (1991), Fuzzy sets in approximate reasoning, Part Ⅰ : Inference with possibility distributions, Fuzzy Sets and Systems, 40, 143-202.
Graham, B. P. and R. B. Newell (1989), Fuzzy adaptive control of a first-order process, Fuzzy Sets and Systems, 31, 47-65.
Hathaway, R. J., and J. C. Bezdek (1993), Switching regression models and fuzzy clustering, IEEE Transactions of Fuzzy Systems, 1, 195-204.
Hinkley, D. V. (1971), Inference about the change point from cumulative sum test, Biometria, 26, 279-284.
Hsu, D. A. (1982), A Bayesian robust detection of shift in the risk structure of stock market returns, Journal of the American Statistical Association, 77, 29-39.
Inclan, C. & Tiao, G. C. (1994), Use of cumulative sums of squares for retrospective detection of changes of variance, Journal of the American Statistical Association, 89(427), 913-924.
Lee, Y. C., C. Hwnag, and Y. P. Shih (1994), A combined approach to fuzzy model identification. IEEE Transactions on Systems, Man, and Cybernetics, 24(5), 736-743.
Lowen, R. (1990), A fuzzy language interpolation theorem, Fuzzy Sets and Systems, 34, 33-38.
Manski, C. (1990), The use of intention data to predict behavior: a best case analysis, Journal of the American Statistical Association, 85, 934-940.
Nguyen, H. and M. Sugeno (1998), Fuzzy Modeling and Control, CRC Press.
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
Page, E. S. (1955), A test for change in a parameter occurring at an unknown point, Biometricka, 42, 523-527.
Park, Y. M., U. C. Moon, and K. Y. Lee (1995), A self-organizing fuzzy logic controller for dynamic systems using fuzzy auto-regressive moving average (FARMA) model, IEEE Transactions on Fuzzy Systems, 3(1), 75-82.
Romer, C., A. Kandel, and E. Backer (1995), Fuzzy partitions of the sample space and fuzzy parameter hypotheses, IEEE Transactions on Systems, Man and Cybernetics, 25(9), 1314-1321.
Ruspini, E. (1991), Approximate reasoning: past, present, future, Information Sciences, 57, 297-317.
Song, Q. and B. S. Chissom (1993a), Forecasting enrollments with fuzzy time series—Part I, Fuzzy Sets and Systems, 54, 1-9.
Song, Q. and B. S. Chissom (1993b), Fuzzy time series and its models, Fuzzy Sets and Systems, 54, 269-277.
Song, Q. and B. S. Chissom (1994), Forecasting enrollments with fuzzy time series—Part II, Fuzzy Sets and Systems, 62, 1-8.
Song, Q., R. P. Leland, and B. S. Chissom (1997) , Fuzzy stochastic fuzzy time series and its models, Fuzzy Sets and Systems, 88, 333-341.
Sugeno, M. and K. Tanaka (1991), Successive identification of a fuzzy model and its applications to prediction of a complex system, Fuzzy Sets and Systems, 42, 315-334.
Tong, R. M. (1978), Synthesis of fuzzy models for industrial processes, International Journal of General Systems, Vol.4, 143-162.
Tsay , R, S. (1991), Detecting and modeling non-linearity in univariate time series analysis, Statistica Sinica, 1(2),431-451.
Tseng, F., G. Tzeng, H. Yu, and B. Yuan (2001), Fuzzy ARIMA model for forecasting the foreign exchange market, Fuzzy Sets and Systems, 118, 9-19.
Tseng, T. and C. Klein (1992), A new algorithm for fuzzy multicriteria decision making, International Journal of Approximate Reasoning, 6, 45-66.
Werners, B. (1987), An interactive fuzzy programming system, Fuzzy Sets and Systems, 23, 131-147.
Wu, B. (1994), Identification environment and robust forecasting for nonlinear time series, Computational Economics. 7, 37-53.
Wu, W. (1986), Fuzzy reasoning and fuzzy relational equations, Fuzzy Sets and Systems,
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
20, 67-78.
Wu, B. and C. Sun (1996), Fuzzy statistics and computation on the lexical semantics, Language, Information and Computation (PACLIC 11), 337-346, Seoul, Korea.
Wu, B. and M. Chen (1999), Use of fuzzy statistical technique in change periods detection of nonlinear time series, Applied Mathematics and Computation, 99, 241-254.
Wu, B. and S. Hung (1999) , A fuzzy identification procedure for nonlinear time series:
with example on ARCH and bilinear models, Fuzzy Sets and Systems, 108, 275-287.
Xu, C. W. and Y. Z. Lee (1987) , Fuzzy model identification and self-learning for dynamic systems, IEEE Transactions on Systems, Man, and Cybernetics, Vol.
SCM-17, 683-689.
Yang, M. (1993), A Survey of Fuzzy Clustering, Mathematical and Computer Modelling, 18(11), 1-16.
Yoshinari, Y., W. Pedrycz, and K. Hirota (1993), Construction of fuzzy models through clustering techniques, Fuzzy Sets and Systems, 54, 157-165.
Zadeh, L. A. (1965), Fuzzy Sets, Information and Control, 8, 338-353.
Zimmermann, H. J. (1991), Fuzzy Set Theory and Its Applications, Boston: Kluwer Academic.