預測技術在決策過程中是不可或缺的重要工具。精確的預測可以提供決策者更多的資訊去做出正確的決策。傳統的點預測方法是目前使用最多的預測方式，其預測模式常需要較嚴格的基本假設，這使得預測模式的建構較為困難。而加權模糊時間數列模式並不需要強烈的基本假設，模式架構較傳統更為簡易，也提供決策者更多的選擇。本研究將傳統的加權模糊時間數列推廣為區間加權模糊時間數列。與常用的幾種區間模糊時間數列做比較，以預測每日台幣對美元的匯率的方式來探討幾種預測方法的效率評估與準確性。 / Forecasting technology has played an important role for the decision makers. Accurate forecasts can provide decision makers more information to make the right decisions. Currently, the most use of forecasts is the traditional point forecasting, whose forecasting model often requires strict assumptions, and this makes it more difficult to construct the forecasting model. Weighted fuzzy time series model does not require so strong assumptions, so the model construction is simpler than traditional ones. It also provides the decision makers more options. In this research, we promote the weighted fuzzy time series model to the interval weighted fuzzy time series model. And we compare it with some commonly used interval fuzzy time series models, to discuss their efficiency evaluations and accuracy by forecasting daily exchange rate for US Dollars to NT Dollars.

股票是許多人採取投資的項目。若能準確預測股價的漲跌，則可以有效地降低投資風險，賺取利潤。然而，有許多因素會影響股票走勢，例如政治因素，匯率變化，天災人禍。因此，股票走勢很難被精確預測。我們嘗試用模糊統計來解決股價預測的問題。本論文藉由模糊相關矩陣來建立多變量模糊時間數列，以便用來預測股票趨勢。實證研究則以台灣加權股價指數為對象，對每日的收盤價進行模糊時間數列分析與預測，還計算誤差與準確率。實證研究顯示，能降低投資者的風險。

近年來，預測技術的創新與改進愈來愈受到重視。對於預測效率評估的要求也愈來愈高。尤其在經濟建設、人口政策、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。目前有關模糊時間數列分析與預測效率評估並不多見。主要是模糊殘差值的測量相當困難。有鑑於此，本文提出以模糊距離來進行效率評估。並且從不同的角度來探討預測的準確度。實證研究顯示，藉由中心點與區間長度的整合測度，可以得到一個合理的評估結果。這對於財務金融的模糊數據分析與未來市場的走勢將深具意義。

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.

投資的獲利多寡並不單單基於預測的準確性，信心度的大小亦攸關獲利的結果。因為信心度愈大，則投資人將會提高投資的金額，而獲得更多的利潤。反之，雖然預測的結果是準確的，但若信心度很小，則投資人將不敢投入較多的金額，如此一來所獲得的利潤就有限了。本文嘗試著應用信心度函數來輔助說明多變量模糊時間數列預測結果，亦即預測模式對預測結果的屬性所具有的信心程度。最後利用多變量模糊時間數列模式，結合加權股價指數的收盤價及成交量兩個變量，針對台灣加權股價指數進行預測及衡量預測屬性的信心度。相信這對於風險控管及提高投資報酬深具意義。

由於電腦革命的成功，在短暫的幾年之間，更加速了經濟的成長，而金融的投資分析，是社會經濟發展的原動力，因此研究這方向的財務數學也相對的提高了專家、學者的研究熱潮。就以股票、匯率市場來說，如果能比别人早一步掌握行情走勢，就能獲得較高的利潤。但影響股價、匯率波動的因素很多，尤其是在複雜多變及不確定性的資訊下。因此；如何進行更精確的趨勢分析與預測，是本文研究的主題。由於，傳統的期望值是二元的邏輯思考(非1即0)，比較無法符合多變與不確定的財金問題，因此本文考慮以模糊統計方法，以模糊期望值的方法來作趨勢分析與預測，期望能對複雜多變的財金體系提共一套更精確合理的投資分析方法，可以提供投資者更多的訊息，做出明確的抉擇。最後；以我國集中市場加權股票指數、台幣對美元匯率及台積電股價為例，做一實例上的詳細探討。 / Based on computer revolutionary coming off, economics grows fast in previous several years, then the investment analyze of finance is the impetus of development of society economic. Therefore, many experts and scholars are interested in the research of financial mathematics. Taking stock market and exchange market for example, if you can predict the future trend of market, you obtain more profit. However, there are many factors that act on stock prices and exchange rate. Especially, the market information is complicated and incomplete. How to go along accurate trend analysis and divination is the important point of the text research. Because traditional expectation value is dibasic logic thought (either 1 or 0), that can’t conform to the highly changeable and uncertain finance problems. For this reason, in this research we propose an integrated procedure for fuzzy expectation value modeling and forecasting through fuzzy relation equations. We apply this technique to construct a fuzzy expectation value model for Taiwan Weighted Stock Index and exchange rate and forecast future trend. We strongly believe that this model will be profound of meaning in forecasting future trend of financial market.

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.

本文嘗試以模糊理論的觀念，應用到時間數列分析上。研究重點包括模糊關係、模糊規則庫和模糊時間數列模式建構與預測等。我們首先給定模糊時間數列模式的概念與一些重要性質。接著提出模糊規則庫的定義，以及模式建構的流程，並以模糊關係方程式的推導，提出模糊時間數列模式建構方法。最後，利用提出的方法，對台灣地區加權股票指數建立模糊時間數列模式，並對未來進行預測，且考慮以平均預測準確度來做預測效果之比較。這對於財務金融的未來走勢分析將深具意義。 / The paper has attempted to apply the concept of fuzzy method on the analysis of time series. This reserch is also to include fuzzy relation, fuzzy rule base, fuzzy time series model constructed and forecasting. First, we'll define the concept of fuzzy time series model and some important properties. Next, the definition of fuzzy rule base will also be put forward, along with procedure of model constructed, the formation of fuzzy relation polynomial, and the methods to construct fuzzy time series model. At last, with the above methods, we'll build up fuzzy time series model on Taiwan Weighted Index and predict future trend while examine the predictive results with average forecasting accuracy. This shall carry profund signifigornce on the analysis of future trend in terms of financialism.

對於一個具有結構性改變性質的非線性時間數列，通常很難判斷何處為轉 捩點，或者何處為所謂的轉型期。雖然長久以來已有不少偵查轉捩點的方 法被提出，但是對於轉捩區間以及對於一些語言性的時間數列資料問題（ 例如：景氣指標的紅綠燈時間數列），都很少被提出來。本論文中，我們 首先引用Zadeh於1965年提出來的模糊理論的觀念來介紹糢糊時間數列（ FTS）。進而定義出在□水準下的模糊點（FP）和模糊轉捩區間（FCP）， 並且證明了一些有用的性質。最後再以台灣地區出生率資料為例，說明□ 水準的模糊轉捩區間的判定方法，並列出了詳細的執行步驟。實驗結果更 證明出我們的模糊檢驗法非常具有實用性及有效性。 / As far as structural change of a non-linear time series is concerned, it is hard to tell when the change point or the fuzzy change period occurs. Though many methods are used for the task of detecting, most of them primarily deal with the case of change point, and few examine the problem of fuzzy change period and linguistic time series ( for example, the index of prosperity represented by red or green light ). In this article, we adopt the theory of fuzzy which is proposed by Zedeh ( 1965 ) to introduce the concept of fuzzy time series ( FTS ). Furthermore, we define the □level of fuzzy point (FP) as well as fuzzy change period (FCP), and prove some useful properties. Finally we explain the method we proposed in detecting the □level of fuzzy change period in terms of the data of Taiwan birth rate and provide step-by-step procedures. Experimental results show that the proposed method of fuzzy detecting is available and practical in detecting the □level of fuzzy change period.

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，同樣地，對於預測準確度的要求也愈來愈高。尤其在經濟建設、人口政策、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。有鑑於此，本論文嘗試應用模糊關係方程式，提出多變量模糊時間數列建構過程及轉折區間檢測模式理論架構。另一方面，多變量模糊時間數列模式建構過程，研究者曾提出很多轉折點之偵測與檢定方法，然而在實際的例子中，時間數列之結構改變所呈現出來的是一種緩慢的改變過程，即轉折點本身就是模糊不確定。這個概念在建構不同模式分析各國經濟活動數據時更顯重要。本論文針對轉折區間之檢測提出一個完整的認定程序。多變量時間數列系統中的隸屬度函數等於在計算成果指標群時的群集中心。應用本論文提出的方法，我們以德國、法國及希臘之總體經濟指標GDP為例，考慮通貨膨脹率、GDP成長率及投資率來進行轉折區間的檢測。 / In recent years, along with the technological advancement and commercial development, the creation and improvement of forecasting techniques have more and more attention. Especially at the economic developments, population policy, management planning and control, forecasting gives necessary and important information in the decision-making process. Regarding stock market as the example, these numerals of closing price are uncertain and indistinct. Again, the factors of influence on quantity are numerous, such as turnover, exchange rate etc. Therefore, if we consider merely the closing price of front day to build and forecast, we will not only misestimate the future trend, but also will cause unnecessary damage. Owing to this reason, we propose the procedure of multivariate fuzzy time series model constructed and theory structure by fuzzy relation equation. Combining closing price with turnover, we apply our methods to build up multivariate fuzzy time series model on Taiwan Weighted Index and predict future trend while examine the predictive results with average forecasting accuracy. A fuzzy time series is defined on averages of cumulative fuzzy entropies of the tree time series. Finally, an empirical study about change periods identification for Germany, France and Greece major macroeconomic indicators are demonstrated.