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.

動機與目的：傳統的統計迴歸模式假設觀測值的不確定性來自於隨機現象，而模糊迴歸則考慮不確定性來自於多重隸屬現象。不同的模型建構所得到的估計值也不一致。如何衡量模型的優劣程度，至今仍沒有一套嚴謹的標準。 研究方法：本研究以區間模糊數建構模糊迴歸模式，如此一來對樣本的解釋方式將更為貼近現實，並提出一套區間模糊數距離測度，以衡量估計值與實際值之間的差距。實證分析中（懸浮微粒PM_10濃度預測、台灣加權股價指數預測），我們藉由此距離測度衡量二維模糊迴歸與傳統二項最小平方法對於樣本的配適性。 創新與推廣：提出區間模糊數距離衡量估計值與原樣本之差異程度。在符合傳統統計迴歸精神之下，當距離最小就是差異最小的估計，最能符合所抽取的樣本，也是最佳估計。 重要發現：利用本區間模糊數距離測度，我們發現二維模糊迴歸方法比起傳統二項最小平方法更有效率且廣義殘差（generalized residual）將更小。 結論：過去以來，我們對於模糊迴歸架構一直都沒有完整的衡量標準。文中我們定義區間模糊數區間距離與平均距離，並推導賦距空間等性質。結合實例分析及應用，建構一合適模糊迴歸模式，以利統計決策分析參考。 / Objective: This study concerns how to develop effective fuzzy regression models. In the literature, little is addressed on how to evaluate the effectiveness of fuzzy regression models developed with different regression methods. We consider this issue in this work and present a framework for such evaluation. Method: We consider fuzzy regression models developed with different regression approaches. A method to evaluate the developed models is proposed. We then show that the proposed method possesses desirable mathematical properties and it is applied to compare the two-dimensional regression method and the traditional least square based regression method in our case studies: predicating the concentration of and the volatility of the weighted price index of the Taiwanese stock exchange. Innovation: We propose a new metric to define a distance between two fuzzy numbers. This metric can be used to evaluate the performance of different fuzzy regression models. When a prediction from one model is closest to the sample data measured in terms of the proposed metric, it can be recognized as the optimal predication. Results: Based on the proposed metric, it can be obtained that the two-dimensional fuzzy regression method is better than the traditional least square based regression method. Especially, its resulting generalized residual is smaller. Conclusion: In the literature, no unified framework has been previously proposed in evaluating the effectiveness of developed fuzzy regression models. In this work, we present a metric to achieve this goal. It facilitates the work to determine whether a fuzzy regression model suitably fits obtained samples and whether the model has potential to provide sufficient accuracy for follow-up analysis in a considered problem.

波浪理論是由 Nalph Nelson Elliott在1938年所發表的價格趨勢分析工具，它也是近年來技術分析界運用相當廣泛的一種工具。艾略特認為：「不管是股票或是任何商品價格的波動，都與大自然潮汐一樣，具有一種相當程度的規律性。」。其實這個原理和產業周期循環也很接近，運用於越多人參與的市場會越準確，因為人性也是一種大自然的現象。 台灣加權股價指數是以民國55年為基期100來編製，本文雖由民國55年談起，但由於資料繁多，故集中採用民國76年1月至民國95年12月的二十年資料做為資料收集期間，以艾略特波浪理論的原則找出在台灣股市的應用規則，進而推演出未來的走勢。 / Wave Principle is a trend analysis method that was developed by Nalph Elliott in 1938. Today, the principle is one of the most widely adopted methods for technical analysis in finance. Elliott discovered that the ever-changing path of stock market prices reveals a structural design that in turn reflects a basic harmony found in nature. In fact this principle is also similar to industry cycle. When this principle is utilized in a market, especially when a lot of people participate in this market, the principle will be rather accurate, because humanity is also a natural phenomenon. The Taiwan Weighted Stock Index was at 100 in 1966, the base period. Although the discussion in this paper starts from 1966, due to the abundance of the data, I decide to focus my research on the recent twenty years. The purpose of this study is to identify the usability of Eilliott’s Wave Principle by applying it in Taiwan’s stock market and to figure out the trend for the future.

本文主要以時間序列為基礎，透過一般化自我相關條件異質變異模型、介入分析、誤差修正、多元轉換函數及組合預測等方法，來建立台灣加權股價指數的預測模型。 從預測精確度之結果顯示，多元轉換函數納入介入分析模型為單一預測模式的最佳預測模型，且其預測績效具有穩定性，而透過最小誤差迴歸組合預測模型可以再改善預測模型在MSPE、RMSPE、MAPE及Theil’s U等量的預測績效。 從多元轉換函數納入介入分析模型中發現，台灣加權股價指數會受到美國道瓊工業指數、台幣兌美元之匯率及消費者物價指數等經濟變數所影響。由於股票市場是重要景氣領先指標，因而當台灣或美國股票市場發生重大事件時，將會對台灣經濟發展產生衝擊，而從本文研究發現，政府可藉由短期政策的施行，產生另一股力量來平衡股市的波動，進而穩定台灣整體經濟發展。 / This research introduces GARCH, ECM, transfer function, and combined forecasting model to predict the changes of TAIEX, and to evaluate the forecasting performance of different models. The results show that the intervention analysis integrated into transfer function yields an accurate prediction model, and the forecasting performance is stable. According to the weighted average of forecasts by minimizing regression error, the resulting forecasting performance such as MSPE, RMSPE, MAPE and Theil’s U will be improved. The intervention analysis integrated into transfer function model shows that the TAIEX is affected by external factors, INDU, exchange rate, and consumer price index. The stock market is one of the major leading indictor, when the Taiwan or U.S. stock market had been impacted, and then Taiwan’s economic development will also be fluctuated. This paper shows that short-term implementation of policies could result in another force to balance the fluctuations in the stock market, and to stabilize the economic development in Taiwan.

有別於國內現有相關研究文獻，本研究首度將台灣50股價指數報酬率及區分多頭市場、空頭市場後之每日台灣加權股價指數報酬率、台灣50股價指數報酬率分別與相對應之每日外資買賣超金額納入研究，並以2002年1月至2008年12月底止之這一段時間為研究期間，從其間所經歷之數個多頭、空頭起伏波段，以瞭解外資之累積性淨買超或淨賣超行為對台灣股價指數報酬率所產生之影響，藉由實證數據探知外資於我國股市是否有洞燭先機，居證券市場領先者之能力，抑或僅是市場之追隨者。 經以因果關係檢定發現，就研究期間內所有樣本資料而言，在台灣加權股價指數方面，台灣加權股價指數報酬率與外資買賣超金額間呈具反饋互為因果之關係，但在落後期數加長後，加權股價指數報酬率對於外資買賣超金額仍維持相當顯著之影響關係，而外資買賣超金額對於加權股價指數報酬率影響之顯著性則有減弱現象。在台灣50股價指數部分，檢定結果則與台灣加權股價指數報酬率之情形有別，台灣50股價指數報酬率對外資買賣超金額存在著明顯之單向影響關係，即外資買賣超金額係隨著台灣50股價指數報酬率漲跌幅之高低而變動。 若將研究樣本資料分為多頭及空頭兩部分，經因果關係檢定發現，台灣加權股價指數與台灣50股價指數無論是在多頭市場或空頭市場，所呈現之結果均相同，即當市場處於大多頭時，外資買賣超金額單向的隨著加權股價指數報酬率及台灣50股價指數報酬率之變動而變動，但在市場處於小多頭或空頭時，外資買賣超金額與加權股價指數報酬率及台灣50股價指數報酬率間之因果關係並不顯著。