人口政策是政府的重要政策之一，而總人口數則是政府制定政治、經濟、社會及文化發展計畫之主要參考依據，因此如何準確地預測未來的總人口數就成為政府相關部門重要的課題。 本論文試圖為台灣地區總人口數建立時間數列預測模式。我們考慮下列模式：單變量自我迴歸整合移動平均介入模式、時間數列迴歸模式、轉換函數介入模式與指數平滑法，其中轉換函數介入模式中所考慮的投入變數包括育齡婦女總生育率、粗出生率及粗死亡率。我們同時以平均絕對百分誤差 (MAPE) 、根均方百分誤差 (RMSPE) 來評估各模式的預測能力，結果顯示以育齡婦女總生育率為投入變數的轉換函數介入模式最佳，而以粗出生率為投入變數的轉換函數介入模式次之，若以這兩個模式進行未來十年總人口數之預測，並與行政院經建會人力規劃處所作的人口預測中推計值比較，其平均絕對百分誤差分別為0.138%，0.156%，顯示時間數列預測模式有相當佳的預測能力。 / In this thesis, we plan to construct various time series models for the total population in Taiwan. The following time series models are considered: ARIMA intervention model, time series regression model, transfers founction intervention model and exponential smoothing method. The input variable considered in the transfer function intervention model include total fertility rate, crude birth rate and crude death rate. We also compare the prediction performance of these models by using mean absolute percentage error (MAPE) and root mean square percentage error (RNSPE). It turns out that the transfer function intervention model with total fertility rate as input is the best model. While the transfer function intervention model with crude birth rate as input ranks the second best. Finally we forecast the total population of the next ten years by using the above two best models and compare with the middle population projection by Manpower Planning Department in Executive YUAN-Council for Economic Planning and Development. The mean absolute percentage error are 0.138% and 0.165% respectively. This result justifies that the time series model has excellent predictive ability and should be considered for total population prediction.

本研究中，我們計算OGA演化投資策略在五類時間數列模型上之表現，這五類模型分別是線性模型、雙線性模型、自迴歸條件異質變異數模型、門檻模型以及混沌模型。我們選擇獲勝機率、累積報酬率、夏普比例以及幸運係數做為評斷表現之準則，並分別推導出其漸近統計檢定。有別於一般計算智慧在財務工程上之應用，利用蒙地卡羅模擬法，研究中將對各表現準則提出嚴格之統計檢定結果。同時在實証研究中，我們考慮歐元兌美元及美元兌日圓的tick-by-tick匯率資料。故本研究主要的重點之一，乃是對於OGA演化投資策略，於這些模擬及實証資料上的有效性應用，作了深入且廣泛的探討。 / In this study, the performance of ordinary GA-based trading strategies are evaluated under five classes of time series model, namely, linear ARMA model, bilinear model, ARCH model, threshold model and chaotic model. The performance criteria employed are the winning probability, accumulated returns, Sharpe ratio and luck coefficient. We then provide the asymptotic statistical tests for these criteria. Unlike many existing applications of computational intelligence in financial engineering, for each performance criterion, we provide a rigorous statistical results based on Monte Carlo simulation. In the empirical study, two tick-by-tick foreign exchange rates are also considered, namely, EUR/USD and USD/JPY. As a result, this study provides us with a thorough understanding about the effectiveness of ordinary GA for evolving trading strategies under these artificial and natural time series data.

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.

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.