點預測為目前使用最多之預測陳述,其效率評估亦多以最小平方和誤差(minimum of sum of square errors)為主。每日或月的經濟或財金指標預測是點預測最常見的例子。但是隨著區間時間數列真正需求與軟計算(soft computing)科技的發展,區間計算與預測愈來愈受重視。本文提出幾種區間時間數列預測的方法,並研究其效率評估。在第三章,我們定義區間誤差和,並將其對應到實數值,以便用傳統的方法計算。最後我們以影響經濟作物的天氣預測,作實證研究分析。考慮在無參數條件下,幾種預測方法作效率評估與準確性探討。天氣預測是區間預測的例子,建立合適的的區間預測方法與效率評估,對各研究領域將會有莫大的幫助。 / Currently, the most use of forecasts is the point forecasting, whose efficiency evaluations are major in the least squares and error (minimum of sum of square errors). The common examples of the point forecasting are daily or monthly economy index or financial estimation. But along with the real demand of interval time series and the development of soft computation (soft computing), the interval computation and the forecasting are more and more important. This article provides some interval time series forecasting methods, and studies the efficiency evaluation. In chapter 3, we define sum errors of interval and correspond them to the real numbers, so as to compute with traditional way. Finally, we decide to use the weather forecasting which can affect the cash crop to be the empirical study analysis. Consider some forecasting methods under the non-parameter condition to be the efficiency evaluations and the accurate discussion. The weather forecasting is an example of interval forecasting. It will be more helpful of each research area if we establish the appropriate interval forecasting method and the efficiency evaluation.

台灣加權股價指數(TAIEX)，可以說是台灣最重要的經濟指數之一。在預測的方法中，時間序列分析一直都是熱門的課題，也是最常被使用來研究股價預測的方法。近年來，模糊理論在生醫、財務、社會、電機等各領域都有不錯的應用與發展 。本研究欲透過模糊區間的預測，主要是以時間序列預測台灣加權股價指數，來作為模糊區間精確度的探討，並針對區間時間序列進行模式的建構診斷和預測。最後我們將以2012年第一季(Q1)，每日交易股價指數的最高價與最低價作為實際研究的例子，同時也比較不同預測方法所得的結果。結果顯示模糊區間預測提供不同於傳統預測方法所得的資訊，希望能提供投資者另一種投資的參考。 關鍵字 : 台灣加權股價指數(TAIEX) 、模糊理論、模糊區間、區間預測 / Taiwan Weighted Stock Index (TAIEX) is one of Taiwan's most important economic indicators. Among the forecasting methods of time series analysis is always a hot issue on the forecasting methods and is also the most commonly used to make the stock price predictions. In recent years , fuzzy theory makes a great of application and development in various fields , such as , biomedical , financial and social …etc.. For this study, through the fuzzy interval forecasting is mainly based on time series forecasting TAIEX as fuzzy interval accuracy of the construction of diagnosis and prediction of the mode and interval time series. Finally, we will take the daily highest / lowest stock index prices data in the first quarter of 2012 (Q1) for actual research example , and will compare different forecasting methods of the results. The results show that the fuzzy interval forecasting differented from the traditional one on the basis of these information. We hope to offer investors an alternative investment advice. Keyword : Taiwan Capitalization Weighted Stock Index (TAIEX) 、 Fuzzy theory 、 Fuzzy interval、Interval forecasting.

時間序列是用來預測未來趨勢的一種重要技術，然而在實務上建構時間序列模型時，參數很難有效估計。原因可能來自於時間序列本身的模糊性質，而導致參數的不確定性使得預測結果產生極大誤差。如果將參數模糊化引進時間序列的模型中，往往過於複雜。本論文提出相對移動率為新的模糊時間序列建構方法，讓原本具有模糊性質的時間序列經由反模糊化(defuzzification)後，以點估計的方式估計起始中心點，經由適當的修正調整為較佳的中心點以及半徑，建立有效的區間時間序列。並將相對移動率引進門檻自廻規模型中，取代原有之門檻值設定，並建立區間時間序列。最後，我們使用台灣加權股價指數為例，以本論文所提出之方法進行區間預測及效率評估。 / The time series is an important technology that is used to predict future trends, however in the real world, parameter is difficult to estimate effectively when we construct a time series model due to the of the fuzzy property of the times series data. The estimated parameters in the time series will cause a big error due to the uncertainty of fuzzy data. It is too complex to introduce the fuzzy parameters into the time series model. In this thesis, we propose relative moving ratio as a new criteria in constructing procedure of an interval time series. We defuzzify a fuzzy data and use point estimation to obtain an initial center, then we adjust the center and radius making it more appropriately. The resulting center and radius is then become an interval time series that can be use to forecast an interval data. We also apply relative moving ratio in threshold autoregressive models by replacing the threshold in constructing interval time series. Finally, in empirical studies chapter, we use Taiwan weighted Stock Index as examples to evaluate the performance of the proposed two methods in building the interval time series.

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.