同時比較多個樣本間的差異，可用ANOVA來檢定，但ANOVA只能得到樣本間有差異的訊息，無法明確指出是哪些樣本間有差異，需要使用多重比較找出樣本間的差異。本文主要探討相關的離散型資料的多重比較，以型I誤差與檢定力兩指標找出最適的多重比較法。本文依序探討獨立的連續型資料、相關的連續型資料、獨立的離散型資料、相關的離散型資料，並針對相關型的資料提出修正法。綜合型I誤差與檢定力兩指標來看，在樣本間的平均差異小時，Shaffer’s first procedure Test (1986)、Procedure 4 by Bergmann and Hommel (1988)為兩兩比較下較佳的修正法，Hochberg Test (1988)為多對ㄧ比較下較佳的修正法；樣本間平均差異大時，Bonferroni 為兩兩比較下較佳的修正法，Hochberg (1988)、Simes (1986)為多對ㄧ比較下較佳的修正法。 / Analysis of variance (ANOVA) is usually applied to check whether there are differences among more than two treatments. However, even there are differences, multiple comparison procedures are still needed to determine which pair(s) of treatments are different. In this study, we use simulation to compare the frequently used multiple comparison procedures, including many-to-one and pair-wise, and type-I error and power are used to measure the performance of procedures. Two types of data were considered, independently and correlated distributed data. If the differences among treatments are small, Shaffer’s first procedure test (1986) and Procedure 4 by Bergmann and Hommel (1988) are the best in pair-wise case, and Hochberg test (1988) is the best in many-to-one case. If the differences among treatments are large, the Bonferroni procedure is the best in pair-wise case, and the procedures by Hochberg (1988) and Simes (1986) are the best in many-to-one case.

本文將模糊理論的觀念，應用在估計、檢定及時間數列分析上。研究重點包括離散型及連續型模糊樣本的定義與度量，模糊參數的最佳估計，模糊排序方法應用於無母數檢定，模糊相似度的定義、性質，以及如何將其應用於辨識不同時間數列間的落差l期相似程度等。我們首先將常見的模糊資料分為離散型及連續型，並針對不同類型的資料，給定對應的模糊平均數、模糊變異數等模糊參數的概念與一些重要性質。接著我們提出幾種估計方法，針對不同的模糊參數進行最佳估計並提出可行的評判準則。進一步地，我們將模糊排序方法應用於無母數檢定推論。最後我們提出模糊相似度的定義與度量。經由系統性的模擬與分析，我們建立兩時間數列間模糊相似度演算法則。實證分析方面，我們利用提出的方法對台灣的股價加權指數、個股股價進行估計及檢定；同時，針對台灣歷年GDP、民間消費、毛投資間的相似性進行偵測，以驗證我們提出的模糊參數估計、模糊無母數檢定及模糊相似度演算法的效率性與實用性。 / In this paper, we apply fuzzy theory in estimation, nonparametric test, and time series analysis. Our focus is on: How to define and measure the discrete type fuzzy data and continuous one? How to find the optimal estimators for fuzzy parameters? How to apply fuzzy ranking methods in nonparametric test when the data is vague? How to define and find the degree of fuzzy similarity between two time series? First, fuzzy data is classified according to its type, discrete or continuous. Then we give some definitions and properties on fuzzy mean, fuzzy variance for different type of fuzzy data. Next, we proposed some estimating methods and evaluation rules. Moreover we apply fuzzy ranking methods in nonparametric test, such as Sign test, Wilcoxon signed rank test, Wilcoxon rank sum test, and so on. Finally, we suggest the definitions as well as the algorithm for computing the degree of fuzzy similarity between two time series. We also give some simulate and empirical examples to illustrate the techniques and to analyze fuzzy data. Results show that fuzzy statistics with soft computing are more realistic and reasonable for the social science research.

Most indexes use a cap-weighted strategy as the asset allocation method. Many researchers suggest that although the cap-weighted strategy often serves as an appropriate surrogate to the market portfolio, it cannot consistently outperform other portfolio weighting strategies. The main reasons behind it would be related to the market movement and the underlying volatility. It is possible to narrow down the scope of the research by focusing on an industry index as was done in this research. The focus would be on the mining index of Indonesia. Comparisons will be done between the established index to other portfolio weighting schemes, namely the equally weighted portfolio and the minimum variance portfolio. The results of the research was that the index was not quite efficient, both on the returns and the Sharpe or information ratio aspect. There are many possible reasons behind this, but the most possible reasons would be that the stocks included do not contribute to diversification, over focus on the coal industry, lack of rebalancing or restructuring, in addition to the market itself. The implication of this research would be that stock exclusion might also contribute to risk minimization.

隨著世界金融的改革開放，國際匯率、利率、股票、債券以及相關衍生性金融商品的突破創新，為企業提供充裕且分散的資金管道，但亦對於企業風險之控管投下一顆不定時的炸彈。基於風險控管的必要性，風險值(VaR)技術與觀念，也就應運而生。VaR可以明確量化風險大小為絕對金額，即使不同的金融商品也可利用其相關性加以整合，因此匯率、利率、股票及各式衍生性金融商品的投資組合皆可用整合的技巧算出。 　本研究利用歷史模擬、Bootstrap、Delta-Normal、Gamma、Hull & White混合常態、Cronish-Fisher偏峰態修正、Barone 整合法(Unified)等模型，分別計算股票、外匯、債券、及權證等個別資產投組，再運用Basle提出的回溯測試(Back Test)與前向測試(Forward Test)、Kupiec的LR test、Hendricks提出的評比方法以及Lopez提出的驗證方法，共十二種測定指標，進行各投資組合VaR模型優劣之區分。 　最後再運用較優之VaR模型估計與驗證同時持有股票、外匯、權証三種資產投資組合，以及股票、外匯、權証、債券等四種資產投資組合的總投資組合VaR，尋求最適切、簡易且不失精確的模型，在考慮各種資產間相關性下，統合計算所持有之多元化金融資產較精確、客觀的風險值。 　本研究結論如下： 一、 認購權証資產屬於右偏，即負報酬機率較高，使用CronishFisher偏態修正模型，可以得到較適切估計值；但其他資產有時準確有時不準確。 　二、 台灣認購權証市場，隱含波動度往往大於歷史波動度1至3倍，且用隱含波動度所求算的VaR驗證結果不佳，但利用歷史波動度實證結果佳。 　三、 Hull&White混合常態轉換模型在外匯資產上表現較股票資產精確，這可能受到股票投組報酬率分配較外匯投組具不確定性的影響。 　四、 債券資產投組，隨著持有存續期間越長，債券價格報酬率標準差越高，則債券投組的持有風險也隨之增加，亦即VaR估計值會趨於保守。 　五、 使用Delta-Gamma法，估計非線性資產（認購權証、債券）之VaR與Delta- Normal模型驗證結果相近，故吾人在估計一天之VaR，不需考慮二階風險。 　六、 不同VaR模型受到不同之資產特性、最適衰退因子、信心水準假設、歷史窗口長度等因素影響，導致各VaR模型準確性的差異，本研究選取單資產投組中較佳且易擴充於多資產，考慮相關性的Unified（整合）模型進行多資產投組VaR的估計與驗證，其驗證結果易優。 　七、 在多資產投組VaR的估計上，應考量資產間的相關性，根據證實Unified(div)考慮相關模型表現較未考慮相關模型Unified(undiv)佳。

資產配置乃是將資金分散投資到主要的資產類別中，諸如股票、債券、現金等。傳統的均數/變異數方法在資產配置上早已被廣泛的運用。但是，現今的金融情勢多變，多期配置的需求提高，傳統均數/變異數方法只處理單一期間的資產配置，且反應未來的能力不佳，顯然已經不適用。 本論文提供一種多期動態的資產配置，可以改良過去單點估計值的缺點，同時能夠將未來情境納入考量，使多期資產配置更富策略性。並實證在兩期的情況下，期中調整資產組合與不調整的差異性。從而瞭解持續的動態規劃，方能提升資產配置的效率性。 / Asset allocation is the process of dividing an investment fund among major asset classes such as equities, bonds, cash, etc. Traditional mean-variance portfolio selection is widely used for asset allocation. However, as time goes by, the financial condition changes rapidly. The method of mean-variance analysis has some limitations. It not only can’t deal with multiperiod asset allocation, but also cannot reflect future economic circumstances, especially for long-term investments. This research tries to use the method of multi-stage dynamic programming for asset allocation. This method can improve the pits of single estimate in using mean-variance analysis, and take future scenarios into account so that the model will become more useful in practice. The two-period empirical results have shown that using continuous dynamic programming to build strategic asset allocation decision can improve the efficiency of asset allocation.

券商和投資大眾越來越了解價格風險管理的重要性，但是對於波動度風險管理工具及其重要性的認知卻較為貧乏。論文探討的即是美歐新興的波動度管理工具：波動度交換契約(volatility swaps)和變異數交換契約(variance swaps)。藉著波動度交換契約，交易者就可以將所暴露的不確定風險轉換為固定的風險。 論文的焦點在於變異數交換契約(variance swaps)公平履約價的訂定。文章中所使用的評價方法是複製法(replictions strategy)，在唯一的假設條件下：股價的變動是連續的，用已知的金融商品複製成新的商品，而複製成本也就是變異數交換契約的公平價格。 在完美的市場中，我們用履約價從零到無限大的選擇權複製變異數交換契約，但是現實的情況下並不允許如此，改用有限範圍的選擇權複製其損益。故再加以討論當假設不成立：股價跳空時，以及用有限範圍履約價對複製策略的影響。 而波動度交換契約(volaility swaps)不管在理論上或是實務上的評價、避險的難度都遠高於變異數交換契約，在第七章節中，引用泰勒展開式和Heston的波動度模型，求得波動度交換契約公平履約價Kvol的評價公式。 一、中文部分： 1.、 寶來金融創新雙月刊 p31-p38 ‘波動性風險可以規避嗎？’ 陳凌鶴、林瑞瑤 2 、國際金融市場泛論與分析 陳松男著 3 、選擇權與期貨：衍生性商品 陳松男著 4 、期貨市場分析 朱浩民著 二、英文部分： 1. Black F, and M Scholes, 1973 ‘The pricing of options and Corporate liabilities” Journal of Political Economy 81, pages 637-659. 2. Carr P ,and D Madan, 1999 “Introducing the covariance swaps” Risk February, pages 47-51 3. Chriss N ,and W Morokoff, 1999 “Market risk for variance swaps” Risk October, pages 55-59 4. Derman E, 1999 “Regimes of volatility” Risk April, pages 55-59 5. Demeterfi K, E Derman, M Kamal and J Zou, 1999 “A guide to variance swaps”Risk June, pages 54-49 6. Dupire B, 1993 ” Model art risk” Risk September, pages 118-120 7. Andreas Grynbichler, Francis A, Longstaff, 1995, “Valuing futures and options on volatility”. Journal of Banking & Finance 20. 8. Carr, P., and D. Madan. “Towards a Theory of Volatility Trading.” In R. Jarrow, ed. Volatility: New Estimation Techniques for Pricing Derivatives. London: Risk Books, 1998, pp. 417-427. 9. Brenner, M., and D. Galai 1989, “New Financial Instruments for Hedging changes in Volatility”, Financial Analysis’s Journal , July-August, pp.61-65. 10 Demeterfi K., E. Derman, M. Kamal and J. Z. Zou, 1999”A guide to Volatility and Variance Swaps.” Journal of Derivatives, summer pp.9-32. 11. Derman, E. and I. Kani. “Riding on a Smile.” Risk. 7, No. 2 (1994), pp.32-39. ─. “Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility.” International Journal of Theoretical and Applied Finance, Vol. 1, No. 1 (1998), pp. 61-110. 12 Neuberger, A. “The Log Contract: A New Instrument to Hedge Volatility.” Journal of Porfolio Management, Winter 1994, pages 74-80. 13 Neuberger, A. 1996. “The Log Contract and Other power Contracts “The Handbook of Exotic Options. Chicago: Irwin Professional Publishing, pages 220-212. 14 Oilver Brockaus and Douplas Long 2000 ‘Volatility Swaps Made Simple' Risk , January, pages 118-120 15 Jim Gatheral “Case studies in Financial course Notes” Spring 2000,Merrill Lynch 16 Bemd Rolfes and Eric Henn ,1999 “A vega nation.” Risk December, pages 26-28 17 Whaley R, 1993 “Derivatives on market volatility :hedging tools long overdue.” Journal of Derivatives, fall, pages 71-84 18 Cheryl L.Sulima , 2001 “Volatility and Variance Swaps” Capital Markets .News, Federal Reserve Bank of Chicago,March ,pages 1-4 19 Nina Mehta “Equity Vol Swaps Grow UP.”, Derivatives Strategy Magazine , July 1999 20 Dean Curnutt “The Art of the Variance swaps ” Derivatives Strategy Magazine , February 2000

本研究的目的為研究台灣省在1990年之15-17歲的在學率，在找出可能影響因素並蒐集好相關的資料後，我們將蒐集到的資料分成兩個部份，一個部份用來建造模型，而另一個部份則用來測試所建立出來的模型。主要的過程是：先利用簡單迴歸模型了解各個可能的因素對於15-17歲的在學率的影響程度，經過許多分析及了解後再對這些變數採取可能的變數轉換(variable transformations)，而後再利用三種常用的統計迴歸方法﹝包含有逐步迴歸(stepwise regression)方法、前進選擇(forward selection)方法以及後退消除(backward elimination)方法﹞去發展出一個適當的複迴歸模型(multiple regression model)。對於這個模型，以實際的台灣在學情況來看，我們看不出它有任何的不合理；同時也利用圖形及檢定去驗證模型的假設，其次還做有關迴歸參數的推論(inferences about regression parameters)。再其次，我們運用變異數分析的結果(analysis of variance results)以及新觀察值的預測情形(predictions of new observations)來評估模型的預測能力。最後並利用所得到的最適當的模型，對如何提昇15-17歲青少年的在學率給予適當的建議。 / The objective of this research is to study what factors may affect the schooling rates of 15-17 years old in Taiwan province in 1990. After finding out some possible factors and collecting those data regarding those factors, we separate the data (by stratified random sampling) into two sets. One set is used to construct the model, and the other set shall be used to test the model. The main process to build a regression model is as follows. First, we shall use simple linear regression models to help us to see if each factor may have relation with the schooling rates. With the analysis of residuals and so on, we then make appropriate transformations on each of these factors. Finally, we use three common statistical regression techniques (including stepwise regression, forward selection, and backward elimination methods) to develop a suitable multiple regression model. It seems that, by our understanding of schooling rates in Taiwan, this model is not unreasonable. In addition, we verify the assumptions of the model by graphical methods and statistical tests. We also do the inferences about regression parameters. Furthermore, ye use the results of the analysis of variance and predictions of new observations to evaluate the prediction ability of the model. Finally, we use the most appropriate multiple regression model to give some suggestions to improve (or keep) the schooling rates of 15-17 years old.

本文主要是研究浮動匯率期間匯率波動對出口產業的影響。一般認為，匯率波動匯會使出口廠商的利潤風險增加，所以波動對於出口量的影響是為負的效果。不過，由於許多國外的研究的結果並不一定支持這種看法。本文針對台灣1984到1995年的資料進行實證研究，並且分別就不同出口產業對匯率波動的反應程度做討論，包括紡織類，塑膠化學類，電子類，機械類及基本金屬類五種產業，主要分為兩個架構分析： 　　（一）衡量匯率波動因子：對於匯率波動的衡量分成兩種方法：一種是以過去匯率變動的方式來衡量，另一種是以本期匯率預測的誤差來衡量，大部份的文獻都是採用前者。在此，為了將廠商事先避險的行為引入，所以採用後者的方法，將預測到的波動與未預測到的波動分離開來。 　　（二）匯率波動對各產業出口量的影響：將所有符合I(1)性質的變數用Johansen的方法做長期共整合關析的估計，再利用Granger Representation Theorem導出短期誤差修正模型，並將符合I(0)性質的波動因子引入模型當中，以便觀察匯率波動對出口量的影響。結果發現，各產業的出口量皆與匯率波動間存在明顯的負相關，其中以電子產業的影響最顯著，紡織類次之，基本金屬類影響最小，根據產品的特性分析可發現：當出口競爭愈激烈者，或是出口彈性愈大者，相對來講，會對匯率波動的反應較敏感。

本論文是二篇探討與股票價格平均數復歸現象有關的實證文章。在第一篇文章中，我們將探討由於廠商特質所產生資金供需雙方訊息的非對稱，而引發的流動性限制對廠商股票價格行為的潛在影響；在第二篇文章中，我們研究的課題是在漲跌幅限制下，交易量與股票報酬自我相關的關係。 第一篇文章主要在探討由於廠商特質所產生資金供需雙方訊息的非對稱，而引發的流動性限制對廠商股票價格行為的影響。我們利用五個廠商特質－所有權結構、集團企業成員、上市時間、公司規模與現金股利的發放，定義面臨流動性限制的廠商，並使用變異數比率衡量股票價格平均數復歸的現象，由於小樣本的問題，我們將利用拔靴法檢定假說：廠商的流動性限制會強化其股票價格平均數復歸的行為。我們的實證結果並不一致，所有權結構、公司規模和集團企業成員的分組實證結果支持我們的假說，流動性限制會強化平均數復歸的行為；而上市時間與現金股利發放的分組實證結果並不支持我們的假說。 在第二篇文章中，我們使用與Campbell et. al. (1993)相同的實證模型，討論在漲跌幅限制下，交易量與股票日報酬自我相關的關係。由於漲跌幅限制的存在，當股票價格觸及漲跌幅上下限時，即停止交易，而使得真正的股票價格無法觀察到，因而未實現之需求或供給將會傳遞至下一個交易日，將使傳統OLS或其衍生方法的估計產生偏誤，而使用Chou和Chib (1995)與Chou (1995)所提的Gibbs抽樣法則可以成功地克服這些困難。所以，本文將應用Chou和Chib (1995)與Chou (1995)的Gibbs抽樣法來衡量台灣股票市場交易量對股票日報酬自我相關係數的影響，以避免漲跌幅限制的影響。本文採用台灣證交所編製的綜合股價指數所採樣的二十四家公司為樣本，利用日資料進行實證分析，實證結果支持「交易量效果」的存在。且在實證過程中，發現台灣股票市場股票日報酬的正自我相關有可能是漲跌幅限制的存在而造成的。

由於住宅價格變動毫無預警制度，人民往往憑著個人主觀的判斷而決定何時購屋或售屋，而此種主觀判斷住宅市場利多及利空的觀念，對住宅市場的供需會產生失衡現象，因此是否可從經濟面的訊息找到住宅價格變動的答案，使住宅價格在尚未變動前，政府即已掌握資訊，提前做好穩定住宅價格的因應對策，使民眾依其需要而購屋，則是本研究之主要目的。 　　本研究從文獻中整理出影響住宅價格變動的七個總體經濟變數，這些總體經濟變數包含工資、物價、所得、貨幣供給額、股價、匯率及利率等，並利用向量自我迴歸模式(VAR)進行實證，以便較客觀的獲得變數間的落後期數及暸解變數間雙向、單向及領先、同步、落後情形，且進一步探討住宅價格與每一個總體經濟變數間影響程度大小及影響情形，以釐清各變數之間的關係。 　　本研究利用VAR模型進行住宅價格與總體經濟變數關係的研究，經由實證，得到下列的結論： 　　一、實證結果方面 　　本研究之實證主要有因果關係檢定與分析、變異數分解之分析及衝擊反應之分析三方面，其實證結果如下所述。 　　（一）因果關係檢定與分析 　　由因果關係檢定與分析中，得到股價、物價、匯率、貨幣供給額及利率均能做為住宅價格變動的領先指標。 　　（二）變異數分解之分析 　　由住宅價格之變異數分解中，得知住宅價格自身的解釋程度僅占三分之一，另三分之二被其他的總體經濟變數所解釋，顯示住宅價格受總體經濟變數的影響相當大；而從其他總體經濟變數之變異數分解中，得知住宅價格變動會干擾到總體經濟變數，而使總體經濟變數受干擾而變動變動。 　　（三）衝擊反應之分析 　　從總體經濟變數對住宅價格的衝擊反應分析圖中可以明顯看出除工資外，其餘總體經濟變數變動對住宅價格造成的衝擊均相當明顯，但匯率及利率對住宅價格的衝擊是負向的。 　　住宅價格對所得、股價、匯率及利率的衝擊相當明顯，而其對匯率的衝擊是負向。 　　二、政策應用方面 政府的決策過程中常會有時間落後的現象，而本研究實證的目的則是要使政府能事先掌握住宅價格的變動，並提前做好穩定住宅價格的因應對策，減少政府決策過程的時間落後現象，而實證結果應用至政策方面的內容則由以下說明之。 　　（一）藉由因果關係檢定與分析的實證內容，可以縮短政府對住宅價格不合理變動問題認定落後的時間。 　　（二）從變異數分解之分析的實證內容中，可以使決策者在解決住宅價格問題時，將行動落後的時間減少。 　　（三）由衝擊反應之分析中，可以使政府在執行穩定住宅價格政策時，將衝擊落後的時間縮小。 / Since there is no alarm system in the change of housing prices, people often decide when to buy or when to sell based on personal and subjective judgement. Such concept to judge subjectively whether the housing market is bull or bear will cause unequilibrium in the supply and demend of the housing market. There it is possible to find out the answers to the change of housing prices from economic side so that the government can have enough information and can be prepared in the reaction to stabilizing the housing prices, and so that the public can buy house according to their needs is the main purpose of this project. 　　Seven variables in macroeconomics influencing the change of housing prices have been taken from reative literature, including wage, commodity price, income, money supply, stock price, exchange rate, and interest rate. VAR has been employed to verify so that the more objective lagging period among variable can be known, and the bi-directional, uni-directional, leading, contemporaneous, and lagging situation among variables can be understood. Furthermore, the degree and the status of influence of each macroeconomic variable to the housing price will be investigated to clarify the relations among the variables. 　　The present project investigate the relations between housing price and macroeconomic variables. We have the following findings: 　　I、In Empirical Study: 　　The empirical study in this project includes causal relation test and analysis, the analysis of variable decompositon, and the analysis of impact response. The results are shown in the following: 　　(I) Causality Test and Analysis 　　In the causality test and analysis, we find out that stock price, commodity price, exchange rate, money supply and interest rate all can be the leading indicators in the change of housing prices. 　　(II) The Analysis of Variable Decomposition 　　It is learned from the variable decomposition of housing prices that housing price can only explain one third of the cause in its change, the other two thirds are explained by other macroeconomic variables. It shows that housing prices are subject to the influence of macroeconomic variables greatly. 　　From the variable decomposition of other macroeconomic variables, we know that the change in housing prices will affect macroeconomic variables so that the macroeconomic variables will change. 　　(III) The Analysis of Impact Response 　　It can be obviously seen from the analysis figure of the impact response of the macroeconomics to housing prices, all macroeconomic variables will cause obvious impact to housing prices expect for wage. However, both exchange rate and interest rate have negative impact to housing prices. 　　Housing prices' impact to income, stock prices, exchange rate and interest rate is quite obvious, among which, the impact to exchange rate is negative. 　　II、Policy Application 　　It is a common phenomenon that there often will be lagging in time in government's decision making. The purise of the empirical study in this project is to let the government to know in advance the change of housing prices and to let the government to know in advance the change of housing prices and to let the government be prepared in the reaction of stabilizing the housing prices to minimize the lagging in the decision making process. The contents of application of the empirical study to policy are explained in the following: 　　(I) With the empirical results of the change of the causality test and analysis, the time for the government to recognize the unreasonable changes in housing prices can be shortened. 　　(II) With the empirical results of the analysis of variable decomposition, the decision makers' lagging in the action responding to housing pricescan be minimized. 　　(III) With the analysis in impact response, the lagging in impact will be minimized when the government executing her housing price stabilizing policy.