動態資料往往隨著時間區間取法或測量工具的不同而有差異,此種不確定的特質我們稱為模糊性。但是傳統的時間數列仍是以確定的觀察值來記錄具有模糊性的動態資料。為了更完整的表示一個動態過程,我們考慮模糊時間數列(fuzzy time series)以具有不確定性的模糊集合來取代明確的數值,保持原來的模糊性。 本文探討模糊時間數列中模糊自我迴歸模式(fuzzy autoregressive model簡寫為 FAR 模式)的建構過程,並分別利用此模式來預測中央政府總預算和匯率。FAR 模式乃根據Box-Jenkins(1970)所提出的 ARMA 三階段模式建立的流程並推廣Zadeh(1965)所提出的模糊集合理論而來。在這過程中 ,我們考慮人類思維方法,使FAR 模式更具有彈性且適合未來預測時的需要。而對於所討論的動態過程,也不需要任何模式上的假設(例如:線性或穩定 ),因此 FAR 模式的適用範圍極為廣泛,更不會因為模式的誤判而導致預測時的嚴重錯誤。最後,我們將 FAR 模式的預測結果與傳統 ARMA 模式做比較。 文中關於模糊時間數列的一些性質,例如:模糊趨勢(fuzzy trend)和模糊穩定(fuzzy stationary),由於傳統文獻中沒有加以討論,本文亦提出定義和新的看法。 / Representations of dynamic data are always different as the time interval or measuring tool change. We call these characteristics of uncertainty fuzziness. But traditional time series use crisp observations to record a fuzzy dynamic process. To completely represent, we consider fuzzy time series replacing the crisp numbers with fuzzy sets and preserve original fuzziness. In this paper, the fuzzy autoregressive model (FAR model) of fuzzy time series is studied and used to forecast the Central government expenditure and exchange rates, respectively. The modeling process is according to Box- Jenkins' (1970) method of ARMA model and merged with the fuzzy set theory proposed by Zadeh (1965). Reasonable human judgements and ways of thinking are taken into consideration throughout the modeling process to make the FAR model more elastic and appropriate for forecasting. Unlike certain incorrectly identified models which lead to inaccurate forecasts, the FAR model can be widely applied due to its not having any assumptions on the original time series (e.g., linearity and stationarity). Finally, the performances of the FAR model to Central government expenditure and exchange rates are compared with that of the traditional ARMA model. Additionally, some properties about fuzzy time series, e.g., fuzzy trend and fuzzy stationary, have not been studied in the literature, and we propose definitions and new opinions.

本文將模糊理論的觀念，應用到時間數列分析上。研究重點包括模糊自相似度的定義與度量，模糊自迴歸係數的分析，模糊相似度辨識與自迴歸階次認定、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。接著提出模糊相似度的定義與度量，以及模式建構的流程。經由系統性的模擬與分析，我們建立階次認定的演算法則與認定程序。藉著詳細的演算比較這些類型的模糊時間數列。並以模糊關係方程式推導，提出合適的模糊時間數列模式建構方法。並利用提出的方法對台灣的景氣對策信號，及台灣結婚率建立模糊時間數列模式。最後，使用所建構的模糊時間數列模式對未來進行預測，以驗證所建構模糊時間數列模式的效率性與實用性。 / In modeling a time series the accuracy of various model constructions and forecasting techniques, certain rules and models are adhered to. Traditional methods on the model construction for a time series are based on the researchers' experience by choosing a "good" model, which will satisfactorily explain its dynamic behavior, from a model-base. But a fundamental question that often arises is: does the data exhibit the real case honestly? In this research we show how fuzzy time series construction be applied for this purpose. An order detection process for fuzzy time series is presented. Simulation has been used extensively to explore general properties of statistical procedures, and the approach is particularly useful in fuzzy time series construction. Statistical strategies typically consist of sequences of rules used repeatedly on the same data set. This paper is organized as follows: In Chapter 2 we will discuss about the definition of fuzzy time series as well as certain important properties. In Chapter 3, We use the similarity comparison process to decide the order of a fuzzy time series. Simulations and analysis with the results about various types of autocorrelation are experienced in Chapter 4. Finally, we apply our methods to three empirical examples, Taiwan business cycle index, marriage rate and numbers of students enrollment in Chapter 5. Chapter 6 is the conclusion and the discussion of future researches.