Generalized likelihood ratio (GLR) control charts are investigated for two types of statistical process monitoring (SPC) problems. The first part of this dissertation considers the problem of monitoring a normally distributed process variable when a special cause may produce a time varying linear drift in the mean. The design and application of a GLR control chart for drift detection is investigated. The GLR drift chart does not require specification of any tuning parameters by the practitioner, and has the advantage that, at the time of the signal, estimates of both the change point and the drift rate are immediately available. An equation is provided to accurately approximate the control limit. The performance of the GLR drift chart is compared to other control charts such as a standard CUSUM chart and a CUSCORE chart designed for drift detection. We also compare the GLR chart designed for drift detection to the GLR chart designed for sustained shift detection since both of them require only a control limit to be specified. In terms of the expected time for detection and in terms of the bias and mean squared error of the change-point estimators, the GLR drift chart has better performance for a wide range of drift rates relative to the GLR shift chart when the out-of-control process is truly a linear drift. The second part of the dissertation considers the problem of monitoring a linear functional relationship between a response variable and one or more explanatory variables (a linear profile). The design and application of GLR control charts for this problem are investigated. The likelihood ratio test of the GLR chart is generalized over the regression coefficients, the variance of the error term, and the possible change-point. The performance of the GLR chart is compared to various existing control charts. We show that the overall performance of the GLR chart is much better than other options in detecting a wide range of shift sizes. The existing control charts designed for certain shifts that may be of particular interest have several chart parameters that need to be specified by the user, which makes the design of such control charts more difficult. The GLR chart is very simple to design, as it is invariant to the choice of design matrix and the values of in-control parameters. Therefore there is only one design parameter (the control limit) that needs to be specified. Especially, the GLR chart can be constructed based on the sample size of n=1 at each sampling point, whereas other charts cannot be applied. Another advantage of the GLR chart is its built-in diagnostic aids that provide estimates of both the change-point and the values of linear profile parameters. / Ph. D.

Because on the method of Harris and Shen (2003), we implement the robust estimator of optimal hedge ratio in Taiwan stock market. By using the Taiwan Stock Index and Taiwan Stock Index Futures, we used the robust estimation of optimal hedge ratio. We use two estimators, the rolling window model and the exponentially weighted moving average (EWMA), to estimate the robust optimal hedge ratio. We also compare the hedging effectiveness of the robust hedge ratios and the traditional least- squared hedge ratios. We find that the volatility of the hedged portfolio using robust optimal hedge ratio is substantially lower than that of the portfolio using the traditional hedge ratios. With the less excessive volatility, the transaction cost decrease substantially, and the cost of rebalancing portfolio is lower as well. / Because on the method of Harris and Shen (2003), we implement the robust estimator of optimal hedge ratio in Taiwan stock market. By using the Taiwan Stock Index and Taiwan Stock Index Futures, we used the robust estimation of optimal hedge ratio. We use two estimators, the rolling window model and the exponentially weighted moving average (EWMA), to estimate the robust optimal hedge ratio. We also compare the hedging effectiveness of the robust hedge ratios and the traditional least- squared hedge ratios. We find that the volatility of the hedged portfolio using robust optimal hedge ratio is substantially lower than that of the portfolio using the traditional hedge ratios. With the less excessive volatility, the transaction cost decrease substantially, and the cost of rebalancing portfolio is lower as well.

Taiwan Security Market is a typical order-driven market. The electronic trading system of Taiwan Security Market launched in 1998 significantly reduces the trade matching time (the current matching time is around 20 seconds) and promptly provides updated online trading information to traders. In this study, we establish an online transaction simulation system which can be applied to predict trade prices and study market efficiency. Models are established for the times and volumes of the newly added bid/ask orders on the match list. Exponentially weighted moving average (EWMA) method is adopted to update the model parameters. Match prices are predicted dynamically based on the EWMA updated models. Further, high frequency bid/ask order data are used to find the supply and demand curves as well as the equilibrium prices. Differences between the transaction prices and the equilibrium prices are used to investigate the efficiency of Taiwan Security Market. Finally, EWMA and cusum control charts are used to monitor the market efficiency. In empirical study, we analyze the intra-daily (April, 2005) high frequency match data of Uni-president Enterprises Corporation and Formosa Plastics Corporation.

Made available in DSpace on 2010-04-20T20:14:42Z (GMT). No. of bitstreams: 0 Previous issue date: 2000-04-04T00:00:00Z / Faz revisão teórica dos modelos de value-at-risk (VAR). Revisa principais estudos anteriores sobre VAR no Brasil e no exterior. Testa o desempenho de cinco metodologias de VAR, a saber: metodologia Paramétrica com uso da Volatilidade Histórica, Paramétrica com uso da Volatilidade EWMA, Paramétrica com uso da Volatilidade GARCH(1,1), Simulação Histórica e uma Metodologia Híbrida proposta por BOUDOUKH e taI (1998). Aplica as metodologias a carteiras teóricas compostas por proporções diversas de ações e títulos de renda fixa de 30 dias no mercado financeiro brasileiro. O trabalho encontra evidências da superioridade da Metodologia Híbrida com fator de caimento de 0,99 e da Simulação Histórica, sendo esta apenas marginalmente inferior, Estes resultados se coadunam com evidências encontradas nas séries em estudo de não normalidade, heterocedasticidade e autocorrelação. / This work analyses the performance of five value-at-risk methodologies, namely the Parametric Methodology making use of Historic Volatility, Parametric Methodology making use of Exponencial Weighting Moving Average (EWMA), Parametric Methodology making use of GARCH( 1,1), Historic Simulation and a Hybrid Methodology proposed by BOUDOUKH et aI. (1998). These models were applyied to the return time series of Ibovespa and 30-day fixed rate bonds, setting up five theoretic portfolios with varying weights of these two assets. Evidences in the studied period showed a superior performance of the Hybrid Methodology using a decay facto r of 0,99, followed closely by Historic Simulation. These results agree with the main time series characteristics, that is, non-normality, autocorrelation and heteroskedasticity of returns. Considering the remaining Parametric Methodologies, the EWMA volatility with decay factor of 0,99 achieved better results than GARCH (1, 1) and historic volatility. The worst results were provided by historic volatility. The initial hypothesis of this work, refering to a possible relationship between the performance of different VAR methodologies and the volatility level of the portfolio, that is, high/low volatility assets could have a major/minor response to methodology change, was not sustained by empirical evidences.

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / The work aims to build , using the BEM (Blade Element Moment) theory , and test three wind rotors , each one consisting of three blades, which were constructed and used for assembling three SWT (Small Wind Turbine) with TSR (Tip Speed Ratio) equal to seven. The three rotors with blades of 2 meters length, distinguished themselves in their geometries as follows: 1) blades without any correction, 2) blades with only tip correction, 3) blades with only root correction. The NREL S809 airfoil developed by the U.S. National Renewable Energy Laboratory (NREL) was used. This airfoil is characterized by having been specially developed for wind turbines. The airfoil experimental data, such as the lift and drag coefficients as a function of angle of attack, were obtained based on wind tunnel test results for Reynolds number of 3 x 105. Also, field tests were conducted to collect torque in the main shaft of the wind rotor [N ∙ m], angular velocity [rad/s] and wind speed [m/s] data, using proper instrumentation and a data collection system. The data collected in the field for each turbine, were analyzed by statistical inference. The power coefficient data were grouped by TSR ranges, and was observed that the data of the last two ranges were the only intervals that showed a normal distribution of data of the Cp . These data were subjected to a one-way ANOVA. And the results showed no significant difference between the average of the rotors SC and CP. Already the data did not exhibit a normal distribution were analyzed by Exponentially Weighted Moving Average (MMEP). It was also observed that the three rotors showed no difference between the power coefficients, of the statistical point of view. An important finding of the experiments was that the CR blades had higher average values of power coefficients for each band TSR. / O trabalho visou construir, atravÃs da Teoria do BEM (Blade Element Moment), e testar trÃs rotores eÃlicos, cada um destes constituÃdos de trÃs pÃs, as quais foram construÃdas e aplicadas na montagem de trÃs TEPP (Turbinas EÃlicas de Pequeno Porte) com TSR (Tip Speed Ratio de projeto igual a sete. Os trÃs rotores, com pÃs de 2 metros de comprimento, distinguiram-se, em suas geometrias, do seguinte modo: 1) pÃs sem correÃÃo alguma, 2) pÃs com correÃÃo somente na ponta e 3) pÃs com correÃÃo somente na raiz. O aerofÃlio aplicado foi o NREL S809, desenvolvido pelo laboratÃrio norte americano de energias renovÃveis (NREL). Este aerofÃlio à caracterizado por ter sido projetado para uso especÃfico em turbinas eÃlicas. Os dados experimentais do aerofÃlio, como os coeficientes de sustentaÃÃo e arrasto em funÃÃo do Ãngulo de ataque, foram obtidos com base nos resultados de testes em tÃnel de vento para um nÃmero de Reynolds de 3 x 105. Realizou-se, tambÃm, testes em campo, utilizando-se de uma instrumentaÃÃo necessÃria para a coleta de dados de torque no eixo principal do rotor eÃlico [N.m], velocidade angular do rotor [rad/s], e velocidade do vento, por meio de um sistema de coleta de dados. Os dados colhidos em campo, de cada turbina, foram analisados por inferÃncia estatÃstica. Os dados de Cp foram agrupados por faixas de TSR, e observou-se que os dados das duas Ãltimas faixas foram os Ãnicos intervalos que apresentaram uma distribuiÃÃo normal de probabilidade dos dados de Cp . Estes dados foram submetidos a uma ANOVA com um fator. E os resultados mostraram que nÃo hà uma diferenÃa significativa entre as mÃdias dos rotores SC e CP. Jà os dados que nÃo apresentaram uma distribuiÃÃo normal foram analisados pela MÃdia MÃvel Exponencialmente Ponderada (MMEP). Verificou-se tambÃm que os trÃs rotores nÃo apresentaram diferenÃa entre os coeficientes de potÃncia, do ponto de vista estatÃstico. Uma importante constataÃÃo dos experimentos realizados foi a de que as pÃs CR apresentaram valores mÃdios de Cp superiores para cada faixa de TSR.

Aldrig har det varit lika aktuellt med hållbar teknologi som idag. Behovet av bättre miljöpåverkan inom alla områden har snabbt ökat och energikonsumtionen är ett av dem. En enkel lösning för automatisk kontroll av energikonsumtionen i smarta hem är genom mjukvara. Med dagens IoT teknologi och maskinlärningsmodeller utvecklas den mjukvarubaserade hållbara livsstilen allt mer. För att kontrollera ett hushålls energikonsumption måste plötsligt avvikande beteenden detekteras och regleras för att undvika onödig konsumption. Detta examensarbete använder en tidsserie av temperaturdata för att implementera detektering av anomalier. Fyra modeller implementerades och testades; en linjär regressionsmodell, Pandas EWM funktion, en EWMA modell och en PEWMA modell. Varje modell testades genom att använda dataset från nio olika lägenheter, från samma tidsperiod. Därefter bedömdes varje modell med avseende på Precision, Recall och F-measure, men även en ytterligare bedömning gjordes för linjär regression med R^2-score. Resultaten visar att baserat på noggrannheten hos varje modell överträffade PEWMA de övriga modellerna. EWMA modeller var något bättre än den linjära regressionsmodellen, följt av Pandas egna EWM modell. / Today's society has become more aware of its surroundings and the focus has shifted towards green technology. The need for better environmental impact in all areas is rapidly growing and energy consumption is one of them. A simple solution for automatically controlling the energy consumption of smart homes is through software. With today's IoT technology and machine learning models the movement towards software based ecoliving is growing. In order to control the energy consumption of a household, sudden abnormal behavior must be detected and adjusted to avoid unnecessary consumption. This thesis uses a time-series data set of temperature data for implementation of anomaly detection. Four models were implemented and tested; a Linear Regression model, Pandas EWM function, an exponentially weighted moving average (EWMA) model and finally a probabilistic exponentially weighted moving average (PEWMA) model. Each model was tested using data sets from nine different apartments, from the same time period. Then an evaluation of each model was conducted in terms of Precision, Recall and F-measure, as well as an additional evaluation for Linear Regression, using R^2 score. The results of this thesis show that in terms of accuracy, PEWMA outperformed the other models. The EWMA model was slightly better than the Linear Regression model, followed by the Pandas EWM model.

<p>This thesis is submitted by Weiping Tang on August 2, 2011.</p> / <p>Several control schemes for monitoring process mean shifts, including cumulative sum (CUSUM), weighted cumulative sum (WCUSUM), adaptive cumulative sum (ACUSUM) and exponentially weighted moving average (EWMA) control schemes, display high performance in detecting constant process mean shifts. However, a variety of dynamic mean shifts frequently occur and few control schemes can efficiently work in these situations due to the limited window for catching shifts, particularly when the mean decreases rapidly. This is precisely the case when one uses the residuals from autocorrelated data to monitor the process mean, a feature often referred to as forecast recovery. This thesis focuses on detecting a shift in the mean of a time series when a forecast recovery dynamic pattern in the mean of the residuals is observed. Specifically, we examine in detail several particular cases of the Autoregressive Integrated Moving Average (ARIMA) time series models. We introduce a new upper-sided control chart based on the Exponentially Weighted Moving Average (EWMA) scheme combined with the Fast Initial Response (FIR) feature. To assess chart performance we use the well-established Average</p> <p>Run Length (ARL) criterion. A non-homogeneous Markov chain method is developed for ARL calculation for the proposed chart. We show numerically that the proposed procedure performs as well or better than the Weighted Cumulative Sum (WCUSUM) chart introduced by Shu, Jiang and Tsui (2008), and better than the conventional CUSUM, the ACUSUM and the Generalized Likelihood Ratio Test (GLRT) charts. The methods are illustrated on molecular weight data from a polymer manufacturing process.</p> / Master of Science (MSc)

近幾年來，有一些研究提出了只用單一一個管制圖即可同時偵測平均數和變異數。根據此目的，我們提出了加權平均損失管制圖，此管制圖是利用加權平均損失所建立的，在一個製成的目標值和平均數不一定相等時，它可同時監控一個製成的平均數和變異數。此加權平均損失統計量是應用一個加權因子，去調整製程平均和目標值的平方差和變異數的損失比重，所以此管制圖的效能比未經由加權因子調整過的管制圖還好。我們不只建立了固定管制參數(FP)加權平均損失管制圖，也建立了適應性加權平均損失管制圖，包括變動抽樣間隔(VSI)、變動樣本數與抽樣間隔(VSI)、變動管制參數(VP)；我們利用平均連串長度(ARL)來衡量固定管制參數管制圖的偵測績效，利用馬可夫鏈的方法計算偵測出異常訊息所需的平均時間(ATS)來衡量適應性管制圖的績效，並且做比較，我們發現適應性管制圖比固定管制參數管制圖的效能還要好。我們也利用最佳化技術建立最加適應性管制圖，當製成失控時，此最佳化管制圖能使ATS1最小。此外，當平均數和變異數的偏移幅度很小時，我們利用指數加權移動平均法(EWMA)建立EWMA加權平均損失管制圖，使其有較好的偵測力。這些我們所提出的管制圖，是只根據單一一個統計量所建立的，和X bar-S管制圖相比，有較好的效能，且和使用兩個管制圖同時偵測平均數和變異數相比，比較輕易理解且容易執行。 / In recent years, a few researchers had proposed different types of single charts that jointly monitor the process mean and the variation. In this project, we use the weighted average loss (WL) to construct WL control charts for monitoring the process mean and variance simultaneously while the target value may be different from the in-control mean. This statistic WL applied a weighted factor to adjust the weights of the loss due to the square of the deviation of the process mean from the target and the variance change. So the WL charts are more effective than unadjusted loss function charts. We not only construct the fixed parameters (FP) WL chart but also the adaptive WL charts which included variable sampling interval (VSI) WL chart, variable sample size and sampling interval (VSSI) WL chart and variable parameters (VP) WL chart. We calculate the average run length (ARL) for FP WL chart and using Markov chain approach to calculate the average time to signal (ATS) for adaptive WL charts to measure the performance and compare each other. From the comparison, we find the adaptive WL charts are more effective than the FP WL chart. We also proposed the optimal adaptive WL charts using an optimization technique to minimize ATS1 (ARL1) when the process was out-of-control. In addition, in order to detect the small shifts of the process mean and variance effectively, we construct the WL charts using the EWMA scheme. The proposed charts are based on only one statistic and are more effective than the X bar-S chart. And the WL charts are easy to understand and apply than using two charts for detecting the mean and variance shifts simultaneously.

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。

Even though the theory of storage is historically a popular view to explain commodity futures prices, many authors focus on the oil price link. Past studies have shown an increased futures price volatility on Mondays and days when natural gas storage levels are released, which could both implicate that storage levels and temperature data are incorporated in the prices. In this thesis, the U.S. natural gas storage level change is studied as a function of the consumption and production. Consumption and production are furthered segmented and separately forecasted by modelling inverse problems that are solved by least squares regression using temperature data and timeseries analysis. The results indicate that each consumer consumption segment is highly dependent of the temperature with R2-values of above 90%. However, modelling each segment completely by time-series analysis proved to be more efficient due to lack of flexibility in the polynomials, lack of used weather stations and seasonal patterns in addition to the temperatures. Although the forecasting models could not beat analysts’ consensus estimates, these present natural gas storage level drivers and can thus be used to incorporate temperature forecasts when estimating futures prices.