Tolerance Limit-based Estimation of the Proportion of Non-conforming Parts in a Multiple Stream Process

The conventional way to characterize the proportion of non-conforming parts in a process is to calculate process capability indices and transform them into a ratio. These widely used indices are able to give digestible information about the ratio of non-conforming parts if some assumptions are fulfilled. A correct estimation method should be based on the output distribution of the process, and the uncertainty of the parameter estimates should be considered, as well. In this article, a special case of the output distribution is examined: a mixture of normal distributions is considered. In practice, this output distribution appears if a multiple stream process is investigated. The novelty of this study is to apply the tolerance interval-based estimation method for the proportion of non-conforming parts in a case study of a multiple stream process and to qualify the limitations of the proposed estimation method. A simulation study is performed to investigate the bias, mean square error, and root mean square error of the estimates from the two estimation methods (process performance index-based and tolerance interval-based) for different sample sizes for each stream (N ). It was found that, if it may be assumed that the speed of the streams is equal in the case of the sample sizes investigated (N = 25, 50, 100 per head), the proposed (tolerance interval-based) method overestimates the proportion of non-conforming parts while the conventional (process performance index-based) method underestimates it. The tolerance-limit based estimation method has asymptotically better properties than the process performance index-based estimation method

Asymmetric multivariate normal mixture GARCH

An asymmetric multivariate generalization of the recently proposed class of normal mixture GARCH models is developed. Issues of parametrization and estimation are discussed. Conditions for covariance stationarity and the existence of the fourth moment are derived, and expressions for the dynamic correlation structure of the process are provided. In an application to stock market returns, it is shown that the disaggregation of the conditional (co)variance process generated by the model provides substantial intuition. Moreover, the model exhibits a strong performance in calculating out–of–sample Value–at–Risk measures

Multivariate regime–switching GARCH with an application to international stock markets

We develop a multivariate generalization of the Markov–switching GARCH model introduced by Haas, Mittnik, and Paolella (2004b) and derive its fourth–moment structure. An application to international stock markets illustrates the relevance of accounting for volatility regimes from both a statistical and economic perspective, including out–of–sample portfolio selection and computation of Value–at–Risk

Asymmetric Multivariate Normal Mixture GARCH

An asymmetric multivariate generalization of the recently proposed class of normal mixture GARCH models is developed. Issues of parametrization and estimation are discussed. Conditions for covariance stationarity and the existence of the fourth moment are derived, and expressions for the dynamic correlation structure of the process are provided. In an application to stock market returns, it is shown that the disaggregation of the conditional (co)variance process generated by the model provides substantial intuition. Moreover, the model exhibits a strong performance in calculating out–of–sample Value–at–Risk measures.Conditional Volatility, Finite Normal Mixtures, Multivariate GARCH, Leverage Effect

Design Performance Analysis of a Self-Organizing Map for Statistical Monitoring of Distribution-free Data Streams

In industrial applications, the continuously growing development of multi-sensor approaches, together with the trend of creating data-rich environments, are straining the effectiveness of the traditional Statistical Process Control (SPC) tools. Industrial data streams frequently violate the statistical assumptions on which SPC tools are based, presenting non-normal or even mixture distributions, strong autocorrelation and complex noise patterns. To tackle these challenges, novel nonparametric approaches are required. Machine learning techniques are suitable to deal with distributional assumption violations and to cope with complex data patterns. Recent studies showed that those methods can be used in quality control problems by exploiting only in-control data for training (such a learning paradigm is also known as “one-class-classification”). In recent studies, the use of distribution-free multivariate SPC methods was proposed, based on unsupervised statistical learning tools, pointing out the difficulty of defining suitable control regions for non-normal data. In this paper, a Self-Organizing Map (SOM) based monitoring approach is presented. The SOM is an automatic data-analysis method, widely applied in recent works to clustering and data exploration problems. A very interesting feature of this method consists of its capability of providing a computationally efficient way to estimate a data-adaptive control region, even in the presence of high dimensional problems. Nevertheless, very few authors adopted the SOM in an SPC monitoring strategy. The aim of this work is to exploit the SOM network architecture, and proposing a network design approach that suites the SPC needs. A comparison study is presented, in which the process monitoring performances are compared against literature benchmark methods. The comparison framework is based on both simulated data and real data from a roll grinding application

Multivariate Regime–Switching GARCH with an Application to International Stock Markets

We develop a multivariate generalization of the Markov–switching GARCH model introduced by Haas, Mittnik, and Paolella (2004b) and derive its fourth–moment structure. An application to international stock markets illustrates the relevance of accounting for volatility regimes from both a statistical and economic perspective, including out–of–sample portfolio selection and computation of Value–at–Risk.Conditional Volatility, Markov–Switching, Multivariate GARCH

Tail Risk Hedging and Regime Switching

In this paper, we analyze futures-based hedging strategies which minimize tail risk measured by Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR). In par- ticular, we first deduce general characterizations of VaR- and CVaR-minimal hedging policies from results on quantile derivatives. We then derive first-order conditions for tail-risk-minimal hedging in mixture and regime-switching (RS) models. Using cross hedging examples, we show that CVaR-minimal hedging can noticeably deviate from standard minimum-variance hedging if the return data exhibit nonelliptical features. In our examples, we find an increase in hedging amounts if RS models identify a joint crash scenario and we confirm a reduction in tail risk using empirical and EVT-based risk estimators. These results imply that switching from minimum-variance to CVaR- minimal hedging can cut losses during financial crises and reduce capital requirements for institutional investors