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.

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.

【第一篇論文中文摘要】 本文檢測公司負債合約中的利差是否可被最終的違約後償還率所解釋。透過1962年至2007年間在美國金融市場上發行但最後卻違約的負債合約資料來進行實證，發現違約後償還率的確有反映在發行時的利差上，且此關聯性會隨著美國開放商業銀行進行證券承銷業務後隨之更加顯著。我們並且進一步發現此償還率的資訊能更加有效反映原因與發行公司的資訊不對稱程度降低有關。此外，我們同時又發現此負債合約中的利差與違約後償還率的關聯性對於公司治理較差、以及非投資等級的發行公司會更為顯著。最後，我們的實證結果在考量內生問題、潛在可能遺漏解釋變數、以及其他模型設定後，仍同樣具有堅實性。 【第二篇論文中文摘要】 本文使用臺指選擇權的日內資料來探討選擇權提前交易期間是否具有資訊內涵與價格發現的功能。就作者所知，我們是第一篇透過選擇權資料探討提前交易期間資訊內涵的研究。首先，我們分別透過價、量、與高階動差三類資訊變數指標來衡量提前交易期間的資訊內涵。實證結果顯示：選擇權提前交易期間不只能有效反映隔夜資訊 (公開資訊)，且具有預測當日現貨指數開盤後5分鐘內股價指數移動的能力 (反應私有資訊)，說明提前交易期間的確具有資訊內涵與價格發現的功能。此外，我們進一步發現價平選擇權包含最強的資訊內涵，此應與投資人尋求交易流動性最高的價平選擇權來迅速實現其利潤以反映其資訊有關。最後，本研究亦發現前一日海外市場 (美國) 投資人情緒傳染效果的強度會影響提前交易期間選擇權的資訊內涵，而前一日是否交易 (週末效果與假日效果)則不會影響此資訊內涵。 / 【第一篇論文英文摘要】 We investigate whether the spread of corporate debt contacts can be explained by their ultimate recovery rates. Using the actual realized recovery rates of defaulted debt instruments issued in the U.S. from 1962 to 2007, we find that recovery rate is reflected in the spread at issuance, and that this relationship has become more significant since commercial banks were allowed to underwrite corporate securities. Our further investigation indicates that the enhanced informativeness of recovery rate can be attributed to the lowering of information asymmetry of individual firms. Besides, the relation between the spread at issuance and the recovery rate is stronger for weak corporate governance and non-investment grade issuers. Our conclusions are found to be robust to endogeneity issues, potentially omitted variables and alternative model specifications. 【第二篇論文英文摘要】 This study uses tick-by-tick data to examine the information content and price discovery of TAIEX option trading during the pre-opening period. To the best of our knowledge, this is the first study that focuses on the options market. We construct three groups of information variables to measure the information content of the pre-opening period, including the price, volume, and high moment information variables. We find that option trading during the pre-opening period not only can reflect the overnight information (public information) but also predict the 5-minute intraday returns after the opening of spot market (private information), showing the information content and price discovery of option trading during the pre-opening period. We also find that at-the-money options contain the strongest richness of information content, which may result from its highest liquidity. Finally, we also find that the empirical results would be stronger depending on the intensity of investor sentiment from overseas (U.S. market) of last day but not the length of hours without trading (weekend and holiday effect).