近年來，非線性時間數列分析是一個快速發展的課題，其中最為人所矚目 的是門檻模式。從過去許多文獻得知，一個簡單門檻模式對於某些型態時 間數列的描述，如結構性改變的行為趨勢，比一般線性ARMA模式更能解釋 實際情況。在本篇論文中，我們將討論有關門檻模式及結構性改變分析的 問題。對於模式的建立，我們提出一個轉型期的觀念，替代傳統尋求一個 轉捩點的方法，進而提出一個結構性改變ARIMA模式有效建立的程序。最 後，我們以台灣出生率當作應用分析的範例，並且利用建立的結構性改變 ARIMA模式，及其他傳統門檻TAR模式，傳統線性分析方法等進行預測分析 及比較。 / Non-linear time series analysis is a rapidly developing subject in recent years. One of special families of non-linear models is threshold model. Many literatures have shown that even simple threshold model can describe certain types of time series, such as structural change behavior, more faithful than using linear ARMA models. In this paper, we discuss some problems about the threshold model and structural change analysis. Instead of finding the change point, we present the change period concepts on the model- building. An efficient algorithem on constructing the structure change ARIMA models is proposed. Finally, we demonstrate an example about the birth rate of Taiwan, and the comparison of forecasting performance for the structure change ARIMA model with alternative models are also made.

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.