政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32559

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32559

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/32559

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/32559

Title:	Use of Partial Cumulative Sum to Detect Trends and Change Periods in Time Series Analysis with Fuzzy Statistics
Authors:	陳力揚
Contributors:	吳柏林陳力揚
Keywords:	模糊時間數列轉折區間趨勢雜訊 fuzzy time series change periods partial cumulative sum trend noise
Date:	2002
Issue Date:	2009-09-17 13:44:58 (UTC+8)
Abstract:	轉折點與趨勢的研究在時間數列分析、經濟與財務領域裡一直是重要的研究主題。隨著所欲研究的物件之結構複雜性日益增加,再加上人類的知識語言因人類本身的主觀意識、不同時間、環境的變遷與研判事件的角度等條件下，可能使得所蒐集到的時間數列資料具某種程度的模糊性。為此,Zadeh[1965]提出了模糊理論,專門解決這一類的問題。在討論時間數列分析中的轉折點與趨勢問題時，常常會遇到時間數列的轉折過程緩慢且不明顯的情況。因此傳統的轉折點研究方法在這種情形下便顯得不足。對此，許多學者提出了轉折區間的概念。然而轉折區間的概念仍然存在一個潛在的困擾：在一個小的時間區間下，一個被認定的轉折區間可能在時間區間拉得很長的情況下，被視為是一個不重要的擾動或雜訊。本文嘗試藉由模糊統計量，提出一個轉折區間與趨勢的偵測方法。與其他轉折區間偵測法不同的是我們所提的方法能藉由控制參數，偵測到合乎使用者需求的轉折區間，進而找到一個趨勢的起點與終點。藉此避免把雜訊當成轉折區間或把轉折區間當成雜訊的困擾。因為使用了模糊統計量,同時也解決了資料的模糊性問題。 Because the structural change of a time series from one pattern to another may not switch at once but rather experience a period of adjustment time, conventional change points detection may be inappropriate to apply under this circumstance. Furthermore, changes in time series often occur gradually so that there is a certain amount of fuzziness in the change point. For this, many research have focused on the theory of change periods detection for a better model to fit. However, a change period in some small observation time interval may seem a neglectable noise in a larger observation time interval. In this paper, we propose an approach to detect trends and change periods with fuzzy statistics through using partial cumulative sum. By controlling the parameters, we can filter the noises and find out suitable change periods. With the change periods, we can further find the trends in a time series. Finally, some simulated data and empirical examples are studied to test our approach. Simulation and empirical results show that the performance of our approach is satisfactorily successful.
Reference:	Balke, N. S. [1993], Detecting level shifts in time series. Journal of Business and Economic Statistics. 11(1), 89-92. Barry, D. and Hartigan, J.A. [1993] A Bayesian analysis for change point problems. Journal of the American Statistics Association. 88(421), 309-319. Bleaney, M [1990], Some comparisons of the relative power of simple tests for structure change in regression models. Journal of Forecasting, 9, 437-444. Broemeling, L. D. and Tsurumi, H. [1987], Econometrics and structural change. Marcel Dekker Inc. Chow, G. C. [1960], Testing for equality between sets of coefficients in two linear regressions. Econometrica, 28, 591-605. Custem, B. V. and Gath, I. [1993], Detection of outliers and robust estimation using fuzzy clustering. Computational Statistics and Data Analysis. 15, 47-61. Hathaway, R. J. and Bezedek, J. C. [1993], Switching regression models and fuzzy clustering. IEEE Transactions on fuzzy systems, 1(3), 195-204. Hinkley, D. V. [1971], Inference about the Change-Point from Cumulative Sum Tests. Biometrika, 58, 509-523. Hsu, D. A. [1979], Detecting shifts of parameter in gamma sequence, with applications to stock price and air traffic flow analysis. Journal of the American Statistics Association, 74, 31-40; [1982], A Beysian robust detection of shift in the risk structure of stock market reterns. Journal of the American Statistical Association, 77, 29-39. Inclan, C. and Tiao, G. C. [1994], Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance. Journal of the American Statistical Association, 89, 913-923. Klir, G. F. and Folger, T. A. [1988] Fuzzy Set, Uncertainty and Information. Englewood Cliffs, NJ Prentice Hall. Lin, C. F. and Rerasirta, T. [1994], Testing the constancy of regression parameters against continuous structural change. Journal of Econometrics, 62, 211-228. Nyblom, J. [1989], Testing the Constancy of Regression Parameters over Time. Journal of the American Statistical Association, 84, 223-230. Page, E. S. [1955], A test for change in a parameter occurring at an unknown point, Biometrika, 42, 523-527. Ploberger, W., Kramer, W., and Kontrus, K. [1989], A new test for structural stability in the linear regression model. Journal of Econometrics, 40, 307-318. Sastri, T., Flores, B., and Valdes, J. [1989], Detecting points of change in time series, Computers Open Research, 16, 271-293. Tsay, R. S. [1988], Outliers, level shift, and variance changes in time series. Journal of forecasting, 7, 1-20. Worsley, K. J. [1986], Confidence regions and tests for a change-point I a sequence of exponential family random variables. Biometrika, 73, 91-104. Wu, B. and Chen, M. [1999], Use of fuzzy statistical methods in change periods detection. Applied Mathematics and Computation, 99, 241-254. Yoshinari, Y., W. Pedrycz, and Hirota, K. [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
Description:	碩士國立政治大學應用數學研究所 89751013 91
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0089751013
Data Type:	thesis
Appears in Collections:	[Department of Mathematical Sciences] Theses

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