由於許多經濟指標的定義不明確，或是因為資料蒐集的時間不一，導致代表經濟景氣的數值，實際上即具有相當大的的不確定性。傳統的方法多不考慮這樣的模糊性,而傾向尋找一準確的模式轉折點。本文則以模糊數學的方法,運用模糊分類法以及模糊熵，訂定一個評判的準則。藉以找出一時間數列模式發生變化的轉折區間。最後以台灣經濟景氣指標為例，說明此方法可不需對資料的模式有任何事先的認知，即可得出與傳統方法相近，甚至更為合理的預測結果。 / Unlike conventional change points detecting, which seeks to find a decision boundary between classes for certain structural changed time series, the purpose of this research is to investigate a new approach about fuzzy change period identification. Based on the concept of fuzzy theory, we propose a procedure for the - level of fuzzy change period detecting and prove some useful properties for a fuzzy time series. We use some numerical examples to demonstrate how these procedures can be applied. Finally, experimental results show that the proposed detecting approach for structure change of fuzzy time series is available and practical in identifying the alpha-level of fuzzy change period.

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.

轉折型時間序列在現實生活中常常可見，例如因戰爭、政策改變、罷工或自然界的條件劇變等，而使時間序列的走勢發生明顯的轉變。傳統上，對這種轉折型時間序列資料進行轉折點的偵測時，大部分均從事後的觀點，主觀上先行認定結構轉變發生的時點，而後再以檢定加以確認。但此種方法過於主觀，而且轉型並非一蹴可幾，若以單一的轉折點來解釋轉型的現象，似乎不太恰當。 　　有鑑於此，本文利用模糊轉折區間統計認定法，以事前的觀點，對具有平均數或變異數改變的轉折型時間序列進行轉折區間的認定。並以匯率及貿易餘額的實際例子，利用我們所提出的方法進行單變數及雙變數的模糊分類，進而求出個別及聯合的轉折區間。 / Structure-changing time series are often seen in daily life. For example, war, change of policy, labor strike, or change of natural phenomena result in obvious change of time series. Most of detection of change points for structure-changing time series take place afterwards. In this paper, we pre-sent a change periods detection method for trend time series using the concept of fuzzy logic. Empirical example about exchange rate and balance of international trade is illustrated with detailed analysis.

時間數列分析過程，常常發現其走勢，隨著時間過程而演變，應用傳統的線性模式來配適，往往很難獲得合適預測值。因此近幾年來，非線性時間數列結構性改變的研究越來越受到重視，也一直是時間數列及計量經濟學學者所熱衷的研究主題之一。本文利用模糊理論的觀念，以模糊炳找出配適ARCH模式數列之轉折區間，分別以轉折區問起始點及結束點作為截取點，去配適ARCH(1)模式，稱之為截取式自迴歸條件變異數分析法(Trimmed ARCH(1) model)。針對台幣對美元銀行間每日收盤匯率，分別以單變量ARIMA、ARCH(1)、Trtmmed ARCH(1)來建構模式，並做比較分析。比較結果發現，以轉折區間結束點作為截取點之Trimmed ARCH(1)模式，其預測值最為準確，大為改善了原來ARCH(1)模式之預測水準。 / In time series analysis, we often find the trend of which changing with time. Using the traditional model fitting can't get a good prediction. Hence the research of structure change of non-linear time series is attentive in recent years, and non-linear time series analysis is a research topic which the scholars of time series and econometrics are intent on. This article tries to use the theory of fuzzy ,to recognize the structure change period by the fuzzy classification, let the first point and the last point of the structure change period be the cute points, to fit ARCH(1) mod ie which we called the Trimmed ARCH(1) model. We use the data of the exchange rate between N.T dol liars and U.S dollars to compare the ARIMAwith ARCH(1) and Trimmed ARCH(1), the forcasting performance shows that Trimmed ARCH(1) model takes a better prediction result.

資料分類的應用在時間數列的分析與預測過程相當重要。而模糊資料近年來更受到重視，其應用的範圍包含：財金、社會、生醫、電機等各個領域。本研究欲運用模糊資料分類法，對區間時間數列的轉折偵測與模式建構做一個深入探討。主要應用平均累加模糊熵(average of the sum of fuzzy entropies)， 找出其結構性改變的區間。並針對區間型時間數列進行模式建構診斷與預測。最後我們以單身人口數與失業率為實列做一個詳細的探討。結果顯示，失業率對單身人口數有顯著的影響而孤鸞年的效應並不顯著。 / The application of data classifications in time series analysis and forecasting is rather important. The fuzzy data classification has received much attention recently. It can be applied on various fields such as finance, sociology, biomedicine, electrical engineering and so on. This study is to use the fuzzy data classification to perform an intensive research on the change periods detection and model construction of the interval time series. We use average of the sum of fuzzy entropies to find out interval of the structural changes. Focusing on the time series of intervals, we build a model and make prediction about it. At the end, based on the case study on the population of singles versus, we thoroughly discuss this topic. The result shows that the unemployment rate does significantly correlate with the population of singles, but the "widow's year" does not .