Abstract In time series analysis, we often find the trend of dynamic data changing with time. Using the traditional model fitting can't get a good explanation for dynamic data. Therefore, many scholars developed various methods for model construction. The major drawback with most of the methods is that personal viewpoint and experience in model selection are usually influenced in them. Therefore, this paper presents a new approach on genetic-based modeling for the nonlinear time series. The research is based on the concepts of evolution theory as well as natural selection. In order to find a leading model from the nonlinear time series, we make use of the evolution rule: survival of the fittest. Through the process of genetic evolution, the AIC (Akaike information criteria) is used as the adjust function, and the membership function of the best-fitted models are calculated as performance index of chromosome. Empirical example shows that the genetic model can give an efficient explanation in analyzing Taiwan exchange rates, especially when the structure change occurs.

時間數列分析過程，常常發現其走勢，隨著時間過程而演變，應用傳統的線性模式來配適，往往很難獲得合適預測值。因此近幾年來，非線性時間數列結構性改變的研究越來越受到重視，也一直是時間數列及計量經濟學學者所熱衷的研究主題之一。本文利用模糊理論的觀念，以模糊炳找出配適ARCH模式數列之轉折區間，分別以轉折區問起始點及結束點作為截取點，去配適ARCH(1)模式，稱之為截取式自迴歸條件變異數分析法(Trimmed ARCH(1) model)。針對台幣對美元銀行間每日收盤匯率，分別以單變量ARIMA、ARCH(1)、Trtmmed ARCH(1)來建構模式，並做比較分析。比較結果發現，以轉折區間結束點作為截取點之Trimmed ARCH(1)模式，其預測值最為準確，大為改善了原來ARCH(1)模式之預測水準。 / In time series analysis, we often find the trend of which changing with time. Using the traditional model fitting can't get a good prediction. Hence the research of structure change of non-linear time series is attentive in recent years, and non-linear time series analysis is a research topic which the scholars of time series and econometrics are intent on. This article tries to use the theory of fuzzy ,to recognize the structure change period by the fuzzy classification, let the first point and the last point of the structure change period be the cute points, to fit ARCH(1) mod ie which we called the Trimmed ARCH(1) model. We use the data of the exchange rate between N.T dol liars and U.S dollars to compare the ARIMAwith ARCH(1) and Trimmed ARCH(1), the forcasting performance shows that Trimmed ARCH(1) model takes a better prediction result.

近幾年來，非線性時間數列轉折點的研究愈來愈受到重視，學者們也提出許多關於轉折點的偵測及檢定方法。若考慮實際資料走勢轉變的情形，“轉折區間”的概念更可以解釋結構改變的現象。但文獻中對於如何找尋時間數列結構改變之轉折區間的研究並不多。本文擬以時間數列統計模式及模糊學理論的角度來研究，並結合遺傳演算的規則而提出主導模式的概念，來架構出時間數列遺傳模式，再藉由轉折區間決策法則來找出數列的轉折區間。其中，我們以統計模式為遺傳演化過程中的染色體，而以候選模式之隸屬度函數為衡量染色體適應能力的指標。最後，我們舉出臺灣股價收盤指數之實例，分別以我們所提出的方法及其他方法找出數列的轉折區間及轉折點，並做比較。 / For recent years, the research of change point in nonlinear time series has been considered to be more and more important. Scholars have proposed a lot of detecting and testing methods about change points.If considering the trend of real situation, the concept of change period will show the phenomena of structure change.But there are not many researches about how to find change period in time series.My paper is based on the points of time series models and fuzzy theory.Besides,it combines the rules of genetic algorithm and provides the concepts of leading model to construct time seriep genetic model and to find out change period by decision rule.ln this paper, we use time series statistical models as chromosome in procedure of genetic evolution, and we also use membership function of selected models as pereformance: index of chromosome.Finally, the empirical application about change periods and change points detecting by our method and other's for Taiwan stock closing prices is demonstrated and make a comparision with these results.

近幾年來，非線性時間數列分析有快速的發展。其中的門檻自迴歸模式(SETAR)，以具有許多線性ARIMA模式所不能配適的特性而受到重視。但是，自1978年Tong建立SETAR模式以來，門檻參數估計的問題一直是SETAR模式在發展應用上的一個瓶頸。本文將探討以實數編碼遺傳演算法，結合統計學上的模式選取準則，建構SETAR模式門檻與延遲參數估計程序的可行性。並從這個基礎上，進一步地研究較精確的門檻參數估計法。 / Non-linear time series analysis has rapidly developed in recent years. Self-exciting threshold autoregression(SETAR) model of non-linear time series models is attentive, because it has some characters which linear ARIMA model fail to fit. But, It has not yet been applied widely because the question of estimation of threshold parameter limits its development and application since Tong proposed SETAR model in 1978. In this paper, we will study the feasibility which constructs a procedure of estimation of SETAR's threshod and delay parameters with real-coded genetic algorithm and statistical criterion of model selection, and develop a more precise estimation of threshold parameter in the basis.

近幾年來，非線性時間數列分析一直是時間數列及計量經濟學者所熱衷的研究主題之一，而非線性時間數列結構改變的研究也越來越受到重視。其中的門檻自迴歸模式，雖具有線性模式所不能配適的特性，但模式建構的問題，一直是其在發展應用上的瓶頸。本研究擬以門檻自迴歸模式建構的流程並結合遺傳演算法的最佳化搜尋技術，架構出時間數列遺傳演算法，藉此演算法則及程序，全域性地搜尋最佳的門檻自迴歸模式。 / Non-linear time series analysis is a research topic which the schalors of time series and econometrics are intent on, and the research of structure change of non-linear time series is attentive. Threshold autoregressive model (TAR model) of non-linear time series has some characters which linear model fail to fit while the problem of how to find an appropriate threshold value is still attracted many researchers attention. In this paper, we present about searching the parameters for a TAR model by genetic algorithms.

依時間順序出現之一連串觀測值，通常會呈現某一型態，而根據所產生的 型態可以作為判斷事件發生的基礎。例如，震波形成原因的判斷﹔追查環 境污染源﹔以及在醫學方面，辨識一個正常人心電圖的型態與患有心臟病 的病人其心電圖的型態…等。對於這些問題，傳統之辨識方法常因前提假 設的限制而失去其準確性。在本文中，我們應用神經網路中的逆向傳播演 算法則來訓練網路，並利用此受過訓練的網路來辨別線性時間數列ARIMA 及非線性時間數列 BL(1,0,1,1)。結果發現，網路對於模擬資料中雙線性 係數介於0.2至$0.8$之間的資料有高達$80\%$以上的辨識能力。而在實例 研究中，我們訓練網路來判斷震波形成的原因，其正確率亦高達80\%以上 。同時，我們也將神經網路應用在環境保護方面，訓練網路來判斷二地區 空氣品質的型態。 / A series of observations indexed in time often produces a pattern that may form a basis for discriminatingetween different classes of events. For instance, in theeology, what are the causes of seismic waves? a earthquakesr the nuclear explosions ?in the eathenics, we can use theethod to inquire the source which pollutes the air in somelace, and in the medicine, to distinguish the difference oflectrocardiograms between a health person and an a patient..ect. In this paper, we utilize the back-propagation to trainnetwork and use of the trained networks to judge the linearRIMA(1,0,0) model between the nonlinear BIL(1,0,1,1) model,e can find that the trained network has a good recognitionhose accurate rate is above 80\% for the coefficient of the bilinear model being equal to 0.5 or 0.8. In a living example, we have trained a network to decidehich is the cause of seismic wave, and the trained networkhose accurate rate is larger than 80\%. At the same time, e also applied neural network in environmental protection.