當我們利用Shewhart管制圖(Shewhart control chart)或累積和管制圖(Cumulative-sum chart. CUSUM chart)來偵測製程時,通常假設製品係獨立取自一個服從均數μ和標準差為σ的獨立常態分配的管制下進行。但是若產品特性值呈現自相關時,這類管制圖就可能發生誤導的結果。本文利用時間序列模式來解決具相關變數的管制圖問題。並考慮利用非線性時間序列模式及特別原因管制圖(special-cause control chart)來檢視台灣經濟景氣指標是否處於控制中的狀態。並討論特別原因管制圖的連串長度分佈(run length distribution)。在最後的實例分析中,介紹自動控制的觀念。 / Traditionally, in the quality control process, such as: Shewhart control chart or CUSUM chart, it is assumed that the observation process follows an i.i.d normal distribution. If the assumption for independence fails, that is when the process exhibits type of autocorrelation, we need to find a more reliable decision method. In this paper, we will apply the time series analysis and structure changed concept to slove the serial correlation problem. The idea of automatic control can be applied in the explanation of this nonlinear process. Finally, a time series about the monitoring indicators of Taiwan is discussed in detail as an example.

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.

本論文提出利用機率平賭性質由選擇權市場價格還原風險中立機率測度的雙目標規劃模型。假設對應同一標的資產且不同履約價的選擇權均為歐式選擇權，到期時標的資產的狀態為離散點且個數有限。若市場不存在套利機會時，建構出最小化離差總和及最大化平滑的雙目標規劃模型。將此雙目標規劃模型利用權重法轉換成單一目標之非線性模型，即可還原風險中立機率測度，並利用此風險中立機率測度評價選擇權的公平價格。最後，我們以台指選擇權(TXO)為例，驗證此模型的評價能力。 / This thesis proposes a biobjective nonlinear programming model to derive risk-neutral probability distribution of underlying asset. The method are used to choose probabilities that minimize the deviation between the observed price and the theoretical price as well as maximize the smoothness of the resulting probabilities. A weighting method is used to covert the model into a single objective model. Given a non-arbitrage observed option price, a risk-neutral probability distribution consistent with the observed option can be recovered by the model. This risk-neutral probability is then utilized to evaluate the fair price of options. Finally, an empirical study applying to Taiwan’s market is given to verify the pricing ability of this model.

意識的議題古老而難解，但是近年來認知神經科學領域對此議題的探討已經熱烈展開，本研究之主要目的即在探索視覺意識與大腦功能性連結之間的關係。 根據一項人臉知覺的實驗結果，本研究依照線性對非線性、局部對整體等兩項條件所構成的四個取向，分別擬定用以反映視覺意識的腦電波指標。結果發現，線性的局部指標—即γ波的強度，以及線性的整體指標—即γ波的相位耦合程度，兩者皆無法有效反映視覺意識。然而，非線性的局部指標—即吸子的相關維度，在特定通道上可以反映視覺意識；至於非線性的整體指標—即廣義的同步化程度，乃為四者中最能穩定反映視覺意識的指標。 除了得到上述若干可以有效反映視覺意識的腦電波指標之外，本研究實質上整合了認知神經科學、非線性動力系統理論、小波轉換理論以及小世界理論等當代思維，因此文中亦做出大量而深入的理論探討，並且提出對現有相關研究在邏輯或方法上的改進與澄清。 / Consciousness is an ancient and puzzling mystery. Until recently, scientists have made little significant progress on it. This study is aimed to search for the neural correlates of visual awareness. / Based on empirical data from an experiment of face perception, this study explores linear vs. nonlinear and local vs. global human EEG indexes of visual awareness. The results indicate that neither linear local index, i.e. γ-band power, nor linear global index, i.e. γ-band phase coherence, can reveal the participant’s state of awareness validly. However, nonlinear local index, i.e. correlation dimension of attractor, can be a valid index of visual awareness, but only on specific channels. Last but not least, nonlinear global index, i.e. generalized synchrony, can be the most valid and efficient index of visual awareness. / In addition to the empirical findings listed above, this study, an interdisciplinary combination of cognitive neuroscience, chaos theory, wavelet transform and small-world theory, also presents numerous theoretical discussions and modifications to other related studies logically or methodologically.

本篇論文檢驗聯準會模型在六個亞洲市場：中國大陸、印度、馬來西亞、新加坡、台灣和泰國是否成立。我們首先檢驗共整合檢定來觀察變數之間長期的關係；另外，針對線性的指標模型，我們則檢測其是否具有非線性的門檻自回歸情形。實證結果顯示，於共整合檢定下，六個國家的股票價格、股票報酬和十年期債券殖利率具有長期共整合關係；而在非線性的TAR模型配適下，其解釋能力優於線性的AR模型。 / This paper studies the Fed Model in six Asia countries, China, India, Malaysia, Singapore, Taiwan, and Thailand. We examine the cointegraiton test for the long-run relationship and build a nonlinear threshold autoregressive model (TAR) between the long -term government bond yield, the stock index and the earning s index. Our empirical results show that such a long-run relationship indeed exists for those countries. In addition, the explanatory power of TAR model is better than linear AR model.

在全球經貿體系自由化下，國際資金流通快速，匯率變動也非常頻繁，廠商的產銷決策與營運，面對匯率風險更加難以掌控。如何掌握匯率的變動，並採取有效的避險措施，是廠商從事貿易必須面臨之重要課題。本研究採用自我迴歸整合移動平均模式、倒傳遞類神經網路及混合式自我迴歸整合移動平均模式及倒傳遞類神經網路模型進行未來即期匯率報酬率之預測。試圖找出合適的新台幣兌美元即期匯率之預測模型，並將其應用於外匯避險操作。 研究結果顯示，關於預測誤差的績效表現，整體來說，以自我迴歸整合移動平均及倒傳遞類神經網路混合式模型表現最佳，顯示傳統時間序列模型捕捉匯率報酬率走勢之能力，藉由倒傳遞類神經網路捕捉其線性預測誤差中非線性的部分，可更符合資料的特性，加強匯率報酬率預測的準確性。考慮預測方向的正確性，在兩個不同的準則下(SR、PT)，皆以自我迴歸整合移動平均模型表現最差，代表其在進行匯率報酬率之預測時正確率較為不足。而在PT檢定當中，倒傳遞類神經網路模型及混合式模型皆達到顯著。因此利用人工智慧模型對報酬率之方向進行預測是有效的，又以自我迴歸整合移動平均及倒傳遞類神經網路混合式模型表現最好。總結來說，利用倒傳遞類神經網路模型針對自我迴歸整合移動平均模型做非線性的調整，同時涵蓋未來匯率報酬率線性與非線性的部分，使得自我迴歸整合移動平均模型之預測誤差、方向準確性皆得到改善，藉由倒傳遞類神經網路捕捉其線性預測誤差中非線性的部分，可更符合資料的特性，加強匯率報酬率預測的準確性。

本創作嘗試發展一套結合音樂與故事元素的數位繪本，以非線性敘事為架構，融入音樂敘事元素，以「帶走一首曲子」的閱讀形式，創造一種新的繪本閱讀經驗。在閱讀繪本的過程中，讀者可以透過選擇場景中的角色，在閱讀完該角色故事後，獲得代表角色的音樂元素。隨著多次選擇互動，背景的音樂元素也慢慢增加，讀完故事的最後，可以得到一首完整的曲子。根據讀者的選擇不同，將得到不同的音樂結果，此結果也詮釋了每一次的故事經驗。 本繪本創作以「心弦之歌」為主題，透過主角與城市人物的互動，產生聽覺和視覺的變化。本創作期望創造一個由單一至豐富的閱讀體驗，透過音樂、人物與故事的結合，加深作品所要傳達的訊息，並結合音樂和繪本的療癒特性，來達到滿足的效果。 創作完成後進行作品實測與評估，施測對象根據目標對象及評估目標，由21-30歲具繪本閱讀經驗者及潛在讀者、具數位繪本或音樂相關互動App使用經驗者、具音樂背景者所組成，分別就內容及形式兩個面向，透過作品實測、問卷和深入訪談的方式來評估是否達成創作目的，並針對問卷及訪談的結果進行歸納分析，最後提出結論和建議。 / The purpose of this research is to develop an interactive digital picture book app which combines musical and narrative elements by adding musical narration into non-linear narrative structure. This digital project, “Song of Heartstrings”, is aimed at creating a new reading experience of picture book by designing the reading form: “Bring Back a Song”. “Song of Heartstrings” shows auditory and visual changes through the interactions between protagonist and other characters. Through the reading process, audience can select one or more characters among all, and collect corresponding soundtrack after finishing the character’s storyline. The goal of this app is evaluated by readers’ experiences test, questionnaires and in-depth interviews. After that, we use inductive approach to analyze the result of questionnaires and in-depth interviews, and make conclusion and recommendation.

Brigo與Mercurio提出了三種新的資產價格過程，分別是位移CEV過程、位移對數常態過程與混合對數常態過程。在這三種過程中，資產價格的波動度不再是一個固定的常數，而是時間與資產價格的明確函數。而由這三種過程所推導出來的歐式選擇權評價公式，將會導致隱含波動度曲線呈現傾斜曲線或是微笑曲線，且提供了參數讓我們能夠配適市場的波動度結構。本文利用台指買權來實證Brigo與Mercurio所提出的三種歐式選擇權評價公式，我們發現校準結果以混合對數常態過程優於位移CEV過程，而位移CEV過程則稍優於位移對數常態過程。因此，在實務校準時，我們建議以混合對數常態過程為台指買權的評價模型，以達到較佳的校準結果。 / Brigo and Mercurio proposed three types of asset-price dynamics which are shifted-CEV process, shifted-lognormal process and mixture-of-lognormals process respectively. In these three processes, the volatility of the asset price is no more a constant but a deterministic function of time and asset price. The European option pricing formulas derived from these three processes lead respectively to skew and smile in the term structure of implied volatilities. Also, the pricing formula provides several parameters for fitting the market volatility term structure. The thesis applies Taiwan’s call option to verifying these three pricing formulas proposed by Brigo and Mercurio. We find that the calibration result of mixture-of-lognormals process is better than the result of shifted-CEV process and the calibration result of shifted-CEV process is a little better than the result of shifted-lognormal process. Therefore, we recommend applying the pricing formula derived from mixture-of-lognormals process to getting a better calibration.

In this study, linear and nonlinear Granger causality tests are used to examine the dynamics, including return to return and volume to volume relationships, between warrants and their underlying stocks in Taiwan Stock Exchange (TSEC). Results of previous studies are mixed and they only focus on linear relationship between the two markets. Here we take nonlinear relationship into consideration to assist in investigating what the direction of information flow is. We use intraday five-minute high frequency data and the result tells that, overall, for both return to return and volume to volume relations, there is bidirectional but asymmetry linear causality and weak unidirectional nonlinear causality from stock to warrant market between these two markets. Combining the linear and nonlinear results we conclude that the direction of information flow is mainly from stock market to warrant market.

在醫學領域中，磁振造影（Magnetic Resonance Imaging, MRI）因為具有良好的空間解析度及對比度，且不會對人體產生任何輻射性或侵入性的傷害，所以在疾病診斷中為經常被醫師們使用的輔助工具。其中利用磁振造影測量患者腦部血流情形所攝得之對比劑濃度與時間關係曲線圖，更是醫學界在對付腦血管病變（Brain Lesion）時的診斷利器。然而截至目前為止，我們尚未有一個較正確且快速的方法可以用來配適其對比劑濃度與時間關係曲線中的參數。所以在本論文中，我們嘗試以統計上的觀點，利用幾種不同的配適方法，找出與原始觀察值最為接近之估計值。 在本研究中使用的配適方法有—「迴歸分析法」、「Whittaker修勻法」、「非線性函數參數修勻法」及「核修勻法（Kernel Graduation）」。 本論文將以往醫學界慣用的「乘方性誤差項」改變為「加成性誤差項」，再以不同的誤差項，利用電腦模擬出各組假資料（Pseudo Data）後，以上述的四種方式對原始觀察值進行參數配適與函數估計。綜合模擬資料與真實資料所配適的比較結果，我們認為在幾種方法中，最穩健（Robust）的配適法是「Whittaker修勻法」。而在本論文中進行配適的真實資料，應該具有較大的誤差項，才導致非線性函數參數修勻法不能得出很好的估計值。 / With greater resolution, higher contrast and no radiative hurt to human body, Magnetic Resonance Imaging (MRI) is widely used by doctors in diagnosing diseases. The concentration of the contrast agent v.s. time curves which generated by MRI for cerebral blood flowing is very useful to doctors when giving treatments to brain lesion. However, we still have no precise and quick solution for fitting the curve of the concentration of the contrast agent vs. time. Therefore, this essay tries to use some different statistical fitting methods to find the closest estimates to the crude observations. We will use four different fitting methods here—"Regression Analysis", "Whittaker Graduation", "Nonlinear Function Parametric Graduation", "Kernel Graduation". This essaywill change the "multiple error term" which was usually used in the medical field to "additive error term". After using different sizes of error terms to generate pseudo data by computer simulation, we fit the parameters and estimate the values of the function to the crude data we've created with the four fitting methods mentioned above. Comparing the fitting result of the simulation data and the real data, we think the most robust fitting method is " Whittaker Graduation". The real data we have fitted in this essay may contain a greater error term, it would make " Nonlinear Function Parametric Graduation" get inadequate fitting values.