在本篇文章中，我們採用長期記憶模型來估計S&P500、Nasdaq100和Dow Jones Industrial Index三個股票指數期貨的日收盤價的風險值。為了更準確地計算風險值，本文採用常態分配、t分配以及偏斜t分配來做模型估計以及風險值之計算。有鑒於大多數探討風險值的文獻只考慮買入部位的風險，本研究除了估計買入部位的風險值，也估計放空部位的風險值，以期更能全面性地估算風險。實證結果顯示，ARFIMA-FIGARCH模型配合偏斜t分配較其他兩種分配更能精確地估算樣本內的風險值。基於ARFIMA-FIGARCH模型配合偏斜t分配在樣本內風險值計算的優異表現，我們利用此模型搭配來實際求算樣本外風險值。結果如同樣本內風險值一般，ARFIMA-FIGARCH模型配合偏斜t分配在樣本外也有相當好的風險預測能力。 / In this thesis, we estimate Value-at-Risk (VaR) for daily closing price of three stock index futures contracts, S&P500, Nasdaq100, and Dow Jones, using the double long memory models. Due to the existence of a long-term persistence characterized in our data, the ARFIMA-FIGARCH models are used to compute the VaR. In order to investigate better, three kinds of density distributions, normal, Student-t, and skewed Student-t distributions, are used for estimating models and computing the VaR. In addition to the VaR for the long trading positions which most researches focus on to date, the VaR for the short trading positions are calculated as well in this study. From the empirical results we show that for the three stock index futures, the ARFIMA-FIGARCH models with skewed Student-t distribution perform better in computing in-sample VaR both in long and short trading positions than symmetric models and has a quite excellent performance in forecasting out-of-sample VaR as well.

金融自由化後，金融商品交易的多樣性在活絡金融市場方面佔有很重的份量，也使得投資者有更多樣化的投資管道及標地。投資者購買金融商品除了追求較高的報酬外，對於投資風險的管理也是不容乎視。2007年，美國的次級房貸subprimemortgage風爆使得雷曼兄弟和AIG集團爆發財務危機，正是投資者追求高報酬之後，在風險管理上並未妥善管理所造成。 　　 　　衡量風險時，通常會使用變異數或標準差當做衡量指標，即在衡量其波動性，因此波動性裏含有許多訊息。在本論文中，我們將探討波動性所透露出來的兩個訊息，一個是風險值(VaR)，文中將分別使用二種衡量可解釋長期記憶的GARCH模型探討台股指數期貨及新加坡的摩台股指數期貨這兩個期貨市場的VaR。另外則是試圖尋找出這兩個期貨市場殘差值的波動性之間的長期共整合關係。 本論文主要由三篇文章組成，第一篇是利用Baillie, Bollerslev, and Millelsen (1996) 所提出的長期記憶模型FIGARCH來計算台指期貨的風險值（VaR）；第二篇也是利用長期記憶模型來計算新加坡的摩台指期貨的風險值，但這次的長期記憶模型增加一個由Tse (1998)　提出的可以考慮不對稱性波動的FIAPARCH模型。 　　這兩個模型都搭配三種不同的分配來計算VaR，分別是Normal, Student-t和skewed Student-t分配；實證結果顯示，這兩個期貨市場報酬的波動皆具有長期記憶，表示之前影響指數期貨報酬率的因素對未來指數期貨報酬率會有較長時間的影響力。而在傳統認為差殘值服從常態分配的假定下所計算出的VaR的配適情況較以Student-t分配計算出的VaR的配適情況不具效率，這除了說明傳統的常態分配假說在計算此兩個指數期貨報酬率是不適用之外，亦得出他們是具有肥尾（厚尾）的現象。 　　第三篇則是結合前兩篇的結果來探討此兩個指數期貨報酬率之間的波動性是否具有長期關係。因為台指期貨報酬率與摩台指期貨報酬率的波動性皆具有長期記憶，故在此部分，利用Engle-Granger (1987) 的兩階段共整合模型來求此兩個指數期貨報酬率之間的波動性是否存在長期關係。實證結果顯示，他們確實存在長期共整合關係，且摩台指期貨報酬率的波動性較台指期貨報酬率的波動性強，因此我們可以在台指期貨市場買入期指，而在新加坡的摩台指期貨市場避險 / The finance commodity exchange's multiplicity holds the very heavy component in the detachable money market aspect, after the financial liberalization. It also enables the investor to have many chances and commodities of investment. The investor purchases the financial commodity besides the higher reward, and does not allow regarding investment risk's management to regard. In 2007, the securitization commodity violation of US's subprimemortgage explodes causes Lehman Brothers and the AIG group erupts the financial crisis. This is precisely the investor pursues the high reward, and their administration centers have not created properly in the risk management. When we measure risks, we usually adopt the variance or the standard deviation. That is to weight its property of volatilities. There is much information in the volatilities. In this thesis, we discussed two kinds of information which the property of volatilities discloses. One is the value at risk (VaR hereafter). In this article, we use long-term memory's GARCH model to explain that the VaR of Taiwan stock index futures returns and Singapore's MSCI Taiwan index futures returns. Moreover, we attempts to seek for whether there are long relationship of the residuals volatilities between these two futures markets. This thesis was combined by three essays. The first essay employed the FIGARCH model of Baillie, Bollerslev, and Millelsen (1996) to calculated the VaR of Taiwan stock index futures returns. The second essay employed the FIGARCH model and FIAPARCH model of Tse (1998) to calculated the VaR of Singapore's MSCI Taiwan index futures returns. We calculated the VaRs of the different two futures markets by using the FIGARCH and FIAPARCH models with three different distributions-normal, student-t and skewed student-t. The empirical results showed the two futures markets both has long memory. It is not efficient to calculated the VaRs by using the traditional normal distribution. The Student-t distribution fitted the model better than the normal distribution. The third essay, we employed the Engle-Granger (1987) two-step cointegration model to test whether there are long relationship of the residuals volatilities between the Taiwan stock index futures returns and Singapore's MSCI Taiwan index futures returns. The empirical results showed that there was fractional cointegration between the two futures markets and the volatility in Taiwan stock index futures market is about 83% of that in MSCI Taiwan Index Futures market.

近幾年，風險值已經成為金融機構風險控管的重要工具。它的明確及簡單易懂是其讓人接受的原因，加上巴塞爾銀行監理委員會在1996提出的巴塞爾協定修正，規定銀行將市場風險因素納入考量，並允許銀行自行發展內部模型，以風險值模型衡量市場風險後，各種風險值的估算方法相繼被提出。 本篇論文是使用部分整合自回歸條件變異數（Fractional Integrated Generalized Autoregressive Conditional Heteroskedasticity，簡稱FIGARCH）計算長期利率期貨多空部位的每日風險值。選取的三支長期利率期貨是在芝加哥期貨交易所掛牌的三十年期美國政府債券期貨（TB）、十年期美國政府債券期貨（TN） 與十年期市政債券指數期貨（MNI）。 利率期貨的研究在過去文獻中，甚少被提及。但隨著利率型商品日新月異的發展，以利率期貨避險的需求也與日遽增。尤其在台灣，利率期貨更是今年新登場的期貨商品。因此，我選擇利率期貨作為研究標的，藉由以FIGARCH模型來配適波動性，提供避險者一個估算風險值的方法。 FIGARCH模型係由Baillie、Bollerslev與Mikkelsen於1996所提出，與傳統GARCH模型所不同的是，FIGARCH模型特別適用於描述具有波動性長期記憶（Long Memory）性質的資料。所謂長期記憶性，是指衝擊所造成的持續性是以緩慢的雙曲線速率衰退。而許多市場實證分析均指出，FIGARCH較適合用來描述金融市場上的波動性。此外，本研究的風險值計算，除了一般實務界常用的常態分配以外，還考慮了t分配與偏斜t分配，以捕捉財務資料常見的厚尾與偏斜的特性。 而實證結果顯示，長期利率期貨報酬率的波動性確實存在長期記憶性，所以FIGARCH(1,d,1)模型可以適切地估算長期利率期貨的每日風險值，不論在樣本內或樣本外的風險值計算均優於傳統GARCH(1,1)模型的計算結果。至於各種不同分配的比較，在樣本內的風險值計算，當α=0.05時，常態分配FIGARCH(1,d,1)模型表現較佳；當α=0.025到0.0025時，t分配與偏斜t分配FIGARCH(1,d,1)模型表現較佳，而偏斜t分配FIGARCH又稍微優於t分配FIGARCH(1,d,1)模型。 而樣本外的風險值預測，則有不同的結果，當α=0.05，t分配與偏斜t分配FIGARCH(1,d,1)模型表現較佳；而α=0.01時，常態分配FIGARCH(1,d,1)模型表現較佳。而且t分配與偏斜t分配FIGARCH(1,d,1)模型在α=0.01會出現太過保守的情形，出現失敗率（failure rate）為零，高估風險值。 / Value-at-Risk (VaR) has become the standard measure used to quantify market risk recently, and it is defined as the maximum expected loss in the value of an asset or portfolio, for a given probability α at a determined time period. This article uses the FIGARCH(1,d,1) models to calculate daily VaR for long-term interest rate futures returns for long and short trading positions based on the normal, the Student-t, and the skewed Student-t error distributions. The U.S. Treasury bonds futures, Treasury notes futures, and municipal notes index futures of daily frequency are studied. The empirical results show that returns series for three interest rate futures all have long memory in volatility, and should be modeled using fractional integrated models. Besides, the in-sample and out-of-sample VaR values generated using FIGARCH(1,d,1) models are more accurate than those generated using traditional GARCH(1,1) models. For different distributions among FIGARCH(1,d,1) models, the normal FIGARCH(1,d,1) models are preferred for in-sample VaR computing whenα=0.05, and the Student-t and skewed Student-t models perform better for in-sample VaR computing whenα=0.025-0.0025. Nonetheless, for out-of-sample VaR, the Student-t and skewed Student-t FIGARCH(1,d,1) models perform better in the case α=0.05 while the normal FIGARCH(1,d,1) models perform better in the case α=0.01. The VaR values obtained by the Student-t and skewed Student-t FIGARCH(1,d,1) models are too conservative whenα=0.01.

本研究旨在探討「以常用詞根輔以圖像構詞式詞彙教學法」、「常用詞根無圖像構詞式詞彙教學法」及傳統的「詞義說明式詞彙教學法」在學生的詞彙記憶上的差異；本研究亦探討學生的英文詞彙量、構詞察覺度、短期記憶、長期記憶及拼詞能力之間的相關。 本研究的主要發現如下：接受「以常用詞根輔以圖像構詞式詞彙教學法」的學生比接受「常用詞根無圖像構詞式詞彙教學法」及傳統的「詞義說明式詞彙教學法」的學生表現出更好的構詞察覺度、短期記憶、長期記憶及拼詞能力。在這三組中，構詞察覺度較高的學生對生詞有較佳的短期記憶與長期記憶能力，反之亦然；在詞彙記憶方面，短期記憶力較佳則長期記憶力也是較佳，反之亦然；並且，一星期後的後測分數比較高的學生在一個月後的後後測分數也會比較高；再者，詞彙的短期記憶與學生英文詞彙量的差異無關，因為學生所記住的生詞都可以持續短暫的時間，但不一定能長久記憶。 / This study aims to investigate the discrepancy in the use of the iconic-morphological approach via commonly-used roots, the non-iconic morphological approach via commonly-used roots, and the traditional definition-based teaching method in vocabulary memorization. It also explores the correlation between English vocabulary size, awareness of morphology, short-term memory for words, long-term memory for words, and vocabulary spelling abilities. The subjects of this study are 91 third-year students studying at the National Overseas Chinese Experimental Senior High School in Taipei County. They received instruction in the iconic-morphological approach via commonly-used roots, the non-iconic morphological approach via commonly-used roots, and the traditional definition-based teaching method, respectively. In the beginning, the three groups took the same pre-test to examine their vocabulary size. Then, subjects were immediately asked to take post-test 1 to examine their awareness of morphology after receiving different instructions. Later, subjects were asked to memorize forty unknown words within twenty minutes and then to take post-test 2 to investigate their short-term memory for words. A week later, post-test 3 was held to check their long-term memory for words. A month later, they sat for post-test 4, used to explore their longer-term memory for the forty words. In conclusion, the study summarizes the main findings pertinent to the proposed research questions. The students who receive instruction in the iconic-morphological approach via commonly-used roots finally develop higher awareness of morphology, better short-term memory for words, better long-term memory for words, and better spelling ability than those who learn in the traditional definition-based approach or in the non-iconic morphological approach via commonly-used roots. Among the three groups, the students who display higher awareness of morphology have better short-term memory and long-term memory for words, and vice versa. Moreover, those who have better short-term memory have better long-term memory, and vice versa; those who have better one-week long-term memory for words definitely have better one-month long-term memory for words. Interestingly, students can learn words by rote for a short period of time regardless of their vocabulary size. That is, one person’s short-term memory for words is not correlated with his vocabulary size.

本篇文章將採用長期記憶模型之一的HYGARCH模型，搭配1985年廣場協議後的日圓匯率期貨資料來估計日圓期貨匯率買入和放空部位的日報酬風險值，探討控管日圓匯率期貨在使用上的風險。為了更準確地計算風險值，本文採用常態分配、學生t分配以及偏態學生t分配來作模型估計以及風險值之計算。 本文實證的結果將有兩方面的貢獻：首先，實證結果顯示當我們採用厚尾分配估計風險值時，樣本內風險值的估計誤差會與信賴水準的高低呈正比的現象，證明在極端的風險值估計上，厚尾分配均有較佳的表現。其次，與其他使用HYGARCH模型研究日圓匯率的文章相較，本文在風險控管層面上所提供的偏態學生t分配，於估計風險值時，比起只考慮厚尾的對稱學生t分配將來得更為有效，其不但在估計誤差上較小，而且根據Kupiec檢定法，其在樣本內的風險值估計也有較好的表現。此外，本文也將多方證明此資料的偏態分配屬於右偏。 / In order to manage the exposure of the dollar/yen futures returns with regarding the long memory behavior in volatility, we use the HYGARCH(1,d,1) model with the data after the Plaza Accord to compute daily Value-at-Risk (VaR) of long and short trading positions. To take into account the fat-tail situation in financial time series, we estimate the model under the normal, Student-t, and skewed Student-t distributions. The contribution of this article is twofold. First, the empirical results show that the bias of in-sample VaR increases as the confidence level increases when VaR is calculated with a fat-tail distribution. Second, we provide a better distribution, the skewed Student-t innovation, for estimating the HYGARCH model for the Japanese yen in respect of risk management because the bias under the skewed Student-t innovation is smaller than that under the Student-t distribution, and in-sample VaR of the models with a skewed Student-t distribution outperforms based on Kupiec test. In addition, we get the innovation skewed to the right through the in-sample VaR analysis.