Credit derivatives are very popular on financial markets in recent days. The most liquid credit derivative is a credit default swap (CDS). In this research we investigate methods for modeling and monitoring of the price process of CDS. We study Hull and White model to calculate CDS spread and have data for our analysis. We consider different methods for monitoring of the price process of CDS. In particular we study CUSUM method. And we calculate more commonly used perfomance measures for this method.

Industrial processes are subject to changes that can adversely affect product quality. A change in the process that increases the variability of the output of the process causes the output to be less uniform and increases the probability that individual items will not meet specifications. Statistical control charts for monitoring process variance can be used to detect an increase in the variability of the output of a process so that the situation can be repaired and product uniformity restored. Control charts that increase the sampling rate when there is evidence the variance has changed gather information more quickly and detect changes in the variance more quickly (on average) than fixed sampling rate procedures. Several variable sampling rate procedures for detecting increases in the process variance will be developed and compared with fixed sampling rate methods. A control chart for the variance is usually used with a separate control chart for the mean so that changes in the average level of the process and the variability of the process can both be detected. A simple method for applying variable sampling rate techniques to dual monitoring of mean and variance will be developed. This control chart procedure increases the sampling rate when there is evidence the mean or variance has changed so that changes in either parameter that will negatively impact product quality will be detected quickly. / Ph. D.

No description available.

No description available.

No description available.

No description available.

Companies routinely perform life tests for their products. Typically, these tests involve running a set of products until the units fail. Most often, the data are censored according to different censoring schemes, depending on the particulars of the test. On occasion, tests are stopped at a predetermined time and the units that are yet to fail are suspended. In other instances, the data are collected through periodic inspection and only upper and lower bounds on the lifetimes are recorded. Reliability professionals use a number of non-normal distributions to model the resulting lifetime data with the Weibull distribution being the most frequently used. If one is interested in monitoring the quality and reliability characteristics of such processes, one needs to account for the challenges imposed by the nature of the data. We propose likelihood ratio based cumulative sum (CUSUM) control charts for censored lifetime data with non-normal distributions. We illustrate the development and implementation of the charts, and we evaluate their properties through simulation studies. We address the problem of interval censoring, and we construct a CUSUM chart for censored ordered categorical data, which we illustrate by a case study at Becton Dickinson (BD). We also address the problem of monitoring both of the parameters of the Weibull distribution for processes with right-censored data. / Ph. D.

Neste trabalho propomos gráficos de controle tipo CUSUM para monitoramento de tempos de sobrevivência. Nossa proposta é desenvolver diferentes estatísticas para o escore do gráfico CUSUM de forma prospectiva. Inicialmente propomos um gráfico CUSUM não paramétrico para monitoramento de populações homogêneas que avalia a variação na estatística log-rank como forma de identificar se há uma mudança significativa no risco de falha ao longo do tempo. Algumas abordagens diferentes foram consideradas e em destaque colocamos o gráfico ZDiff CUSUM, que tem como escore o incremento na estatística Z do teste log-rank em relação à inspeção anterior. Foi constatado, via simulação, que este método é eficiente. Posteriormente investigamos abordagens que levam em conta heterogeneidade na população por meio do modelo de Cox, considerando medidas baseadas na razão de verossimilhanças e em resíduos martingal e deviance. Através de simulações, verificou-se que o método com base na razão de verossimilhanças se mostrou ágil para detectar alteração na taxa de falha, quando se conhece a intensidade da mudança e este valor é informado na construção do teste. Por outro lado, os gráficos CUSUM com base em resíduos são mais simples e se mostraram eficazes para identificar aumentos no padrão da sobrevivência. Estes três métodos e o ZDiff CUSUM foram aplicados a dados de um estudo conduzido no Instituto do Coração (InCor) envolvendo pacientes com insuficiência cardíaca. Foi detectado que ao longo do tempo estes pacientes apresentam sobrevida maior, o que pode estar ligado à melhoria no tratamento e procedimentos realizados no hospital. Como conclusão, sugerimos que os gráficos tipo CUSUM com resíduos do modelo de Cox e o método não paramétrico com teste log-rank podem ser alternativas para utilização na prática em monitoramento de dados de sobrevivência. / In this work we propose CUSUM control charts to monitor survival times. Our proposal is to develop different statistics for the CUSUM chart score in a prospective way, to take into account SA approaches. We initially consider a non-parametric approach to monitor homogeneous populations. This CUSUM evaluates the variation on the log-rank test statistics as a way to identify significant changes in the risk of failure. Some different expressions for this have been considered and, in particular, we propose a ZDiff CUSUM chart computed as the increment on the log-rank test statistics Z at each inspection point in relation to the previous one. Based on simulation studies it was found that this method is efficient. Subsequently we investigated approaches that take into account heterogeneity in the population through the Cox model, considering measures based on the likelihood ratio and on martingal and deviance residuals. Through simulations, it was verified that the method based on the likelihood ratio was agile to detect a change in the hazard rate, when the intensity of the change is known and this value is informed in the construction of the test. On the other hand, CUSUM methods based on residuals are simpler and have been shown to be effective in identifying increases in survival pattern. These three methods and the ZDiff CUSUM were applied to a dataset from a study conducted at the Heart Institute (InCor) on patients with heart failure. It has been found that, over time, these patients have greater survival, which may be linked to improved treatment and procedures performed at the hospital. As a conclusion, we suggest that the CUSUM methods based on Cox model residuals and the nonparametric method on the log-rank test may be alternatives for practice in monitoring survival data.

Neste trabalho propomos gráficos de controle tipo CUSUM para monitoramento de tempos de sobrevivência. Nossa proposta é desenvolver diferentes estatísticas para o escore do gráfico CUSUM de forma prospectiva. Inicialmente propomos um gráfico CUSUM não paramétrico para monitoramento de populações homogêneas que avalia a variação na estatística log-rank como forma de identificar se há uma mudança significativa no risco de falha ao longo do tempo. Algumas abordagens diferentes foram consideradas e em destaque colocamos o gráfico ZDiff CUSUM, que tem como escore o incremento na estatística Z do teste log-rank em relação à inspeção anterior. Foi constatado, via simulação, que este método é eficiente. Posteriormente investigamos abordagens que levam em conta heterogeneidade na população por meio do modelo de Cox, considerando medidas baseadas na razão de verossimilhanças e em resíduos martingal e deviance. Através de simulações, verificou-se que o método com base na razão de verossimilhanças se mostrou ágil para detectar alteração na taxa de falha, quando se conhece a intensidade da mudança e este valor é informado na construção do teste. Por outro lado, os gráficos CUSUM com base em resíduos são mais simples e se mostraram eficazes para identificar aumentos no padrão da sobrevivência. Estes três métodos e o ZDiff CUSUM foram aplicados a dados de um estudo conduzido no Instituto do Coração (InCor) envolvendo pacientes com insuficiência cardíaca. Foi detectado que ao longo do tempo estes pacientes apresentam sobrevida maior, o que pode estar ligado à melhoria no tratamento e procedimentos realizados no hospital. Como conclusão, sugerimos que os gráficos tipo CUSUM com resíduos do modelo de Cox e o método não paramétrico com teste log-rank podem ser alternativas para utilização na prática em monitoramento de dados de sobrevivência. / In this work we propose CUSUM control charts to monitor survival times. Our proposal is to develop different statistics for the CUSUM chart score in a prospective way, to take into account SA approaches. We initially consider a non-parametric approach to monitor homogeneous populations. This CUSUM evaluates the variation on the log-rank test statistics as a way to identify significant changes in the risk of failure. Some different expressions for this have been considered and, in particular, we propose a ZDiff CUSUM chart computed as the increment on the log-rank test statistics Z at each inspection point in relation to the previous one. Based on simulation studies it was found that this method is efficient. Subsequently we investigated approaches that take into account heterogeneity in the population through the Cox model, considering measures based on the likelihood ratio and on martingal and deviance residuals. Through simulations, it was verified that the method based on the likelihood ratio was agile to detect a change in the hazard rate, when the intensity of the change is known and this value is informed in the construction of the test. On the other hand, CUSUM methods based on residuals are simpler and have been shown to be effective in identifying increases in survival pattern. These three methods and the ZDiff CUSUM were applied to a dataset from a study conducted at the Heart Institute (InCor) on patients with heart failure. It has been found that, over time, these patients have greater survival, which may be linked to improved treatment and procedures performed at the hospital. As a conclusion, we suggest that the CUSUM methods based on Cox model residuals and the nonparametric method on the log-rank test may be alternatives for practice in monitoring survival data.

This study aims at analysing how African oil benchmarks within the OPEC Reference Basket relative to the WTI and Brent benchmarks which are considered as global pricing benchmarks for the period starting from 1997-2008. The Nigerian Bonny Light and Algerian Saharan blend were the two benchmarks used for this study. A time series analysis was applied to the weekly price data series set and with the aid of a breakpoint unit root test and Cusum of Squared test to determine if there was a change in the persistence of the spread of each African benchmark relative to the global benchmarks. The results for from the unit root test indicated the presence of a structural break in the price spread in 2004 for the Bonny Light benchmark and in 2005 for the Saharan blend relative to both global benchmarks. The Cusum Squared test for the four benchmark pairings indicated a change in persistence of the price spreads. The null hypothesis was rejected for the alternative hypothesis of the price spread process having a relatively high persistence value after a while. The Cusum Test results showed a change in persistence for both African benchmarks relative to the WTI benchmark and no change in persistence relative to the Brent benchmark. The results of from the Time series analysis indicated the competitive nature of African benchmarks relative to global benchmarks and this could benefit exporting countries by virtue of setting up derivative markets. The derivative markets would allow for the trade of benchmark spreads, futures contracts, options and other financial instruments for African oil producers.