Ahmed Ghorbel

Abstract: Control Chart Pattern Recognition (CCPR) is a critical task in Statistical Process Control (SPC). Abnormal patterns exhibited in control charts can be associated with certain assignable causes adversely affecting the process stability. Abundant literature treats the detection of different Control Chart Patterns (CCPs). In fact, numerous CCPR studies have been developed according to various objectives and hypotheses. Despite the widespread literature on this topic, efforts to review and analyze research on CCPR are very limited. For this reason, this survey paper proposes a new conceptual classification scheme, based on content analysis method, to classify past and current developments in CCPR research. More than 120 papers published on CCPR studies within 1991-2010 were classified and analyzed. Major findings of this survey include the following. (1) The most popular CCPR studies deal with independently and identically distributed process data. (2) Some recent studies on identification of mean shifts or/and variance shifts of a multivariate process are based on innovative techniques. (3) The percentage of studies that address concurrent pattern identification is increasing. (4) The majority of the reviewed articles use Artificial Neural Network (ANN) approach. Feature-based techniques, in particular wavelet-denoise, are investigated for improving the recognition performance of ANN. For the same reason, there is a general trend followed by many authors who propose hybrid, modular and integrated ANN recognizer designs combined with decision tree learning, particle swarm optimization, etc. (5) There are two main categories of performance criteria used to evaluate CCPR approaches: statistical criteria that are related to two conventional Average Run Length (ARL) measures, and recognition-accuracy criteria, which are not based on these ARL measures. The most applied criteria are recognition-accuracy criteria, mainly for ANN-based approaches. Performance criteria which are related to ARL measures are insufficient and inappropriate in the case of concurrent pattern identification. Finally, this paper briefly discusses some future research directions and our perspectives.

Abstract: The goal of this paper is to evaluate the hedging strategies performance of a range of copula and traditional methods for three spot and futures oil markets: WTI crude oil, propane and heating oil. Our contribution is two-fold. First, we model dependence structure between spot and futures oil markets using copula theory applied to bivariate standardised residuals data obtained from two fitted univariate FIEGARCH models. To take in consideration the presence of extremes, we model residuals by a generalised Pareto distribution (GPD). This procedure permits to simultaneously capturing asymmetric non-linear behaviour, dependence structure, long memory and occurrence of extreme events. Second, we use this method with different Archimedean copulas functions (Joe, Frank, bb1, bb2, bb6, and Gumbel) to investigate hedging performance and the efficiency of copula methods in risk reduction and return improvement. Empirical results show that copulas methods perform better than tradition hedging strategies in terms of return and variance. bb6 copula provide the best performed hedge ratios for both WTI crude oil and propane markets while Frank copula prove effective risk reducers compared with other copulas and traditional methods for heating oil market.

Abstract: In this work, we use a time varying copula model to investigate the impact of the global financial crisis on dependence between American and each of six major stock markets and on risk management strategies. The model is implemented with a AR- GARCH-t for the marginal distribution and the extreme value copula for the joint distribution, which allow taking into account non linear dependence, tails behaviour and their development over time. We investigate whether there are significant changes in the time-varying dependence structure of market and in VaR and ES measures especially during global financial crises period. Empirical results show that market dependences between U.S, European and Brazilian markets tend to increase considerably during crisis period and this increase started around the beginning of 2008. In the other hand, market volatility registered record levels around the end of 2008 due to the increase of the degree of uncertainty in this period. As a consequence, investors will allow more amounts to cover against negative evolution of portfolio value.

Abstract: Six Sigma is a well-known concept which means perfection. A process of production to three sigma makes 3.4 defaults/million unit, whereas six sigma means for us perfection. We used it now to mean type of specialised training, aiming at the attack of very high objectives for processes improvement. Six Sigma is a method of continuous improvement and elimination of non-quality, passing by cycle DMAIC: to define, measure, analyse, innovate and control carried out by a project team. In this paper, we propose a new practice of Six Sigma for reduction of the number of non-conformities and minimisation of the number of customers' Complaints for KITAMEUBLE industry.

Abstract: In this paper we propose a method to estimate the value-at-risk (VaR) of a portfolio based on a combination of time series, extreme value theory and copula fitting. Given multivariate financial data, we use a univariate ARMA-GARCH model for each return series. We then fit a generalized Pareto distribution to the tails of the residuals to model the distributions of marginal residuals, followed by a bivariate extreme value copula fitting, which is used to estimate portfolio VaR via simulation. As a first step, this method is applied to two portfolios, each composed of two indexes. As a second step, we extend the method to portfolios based on three indexes. In this case dependence between residuals is modeled by using trivariate nested copulas. The reported results demonstrate that conditional extremevalue copula methods provide a better representation of the dependence structure of multivariate data and produce the most accurate estimates of risk, both for standard and for more extreme VaR quantiles. Comparatively, traditional univariate and multivariate methods result in significantly less accurate risk estimates for most cases. In the context of the international financial crises in the year 2008, the predictive performance of all models decreases significantly. Only copula methods provide acceptable VaR predictions.

Abstract: This paper conducts a comparative evaluation of the predictive performance of various Value-at-Risk (VaR) models. Special emphasis is paid to two methodologies related to the Extreme Value Theory (EVT): The Peaks Over Threshold (POT) and the Block Maxima (BM). We apply both unconditional and conditional EVT models to management of extreme market risks in stock markets. They are applied on daily returns of the BVMT and CAC 40 indices with the intention to compare the performance of various estimation methods on markets with different capitalisation and trading practices. The results we report demonstrate that conditional POT EVT method produces the most accurate forecasts of extreme losses both for standard and more extreme VaR quantiles. The conditional block maxima EVT method is less accurate.

Abstract: This work studies the links existing between the six largest stock markets in the world (USA , Japon, United Kingdom, Germany, France and Canada) in terms of return and volatility. We find that conditional heteroskedasticity is present in every market. In order to properly take account of this phenomena, we estimate a series of bivariate AR(1)-GARCH(1,1) models to measure the links existing between stock markets. The results indicate that the US market has the strongest influence on the other markets in terms of returns. The influence of the other markets on the american market is relatively weak. In term of volatility, the conditional variance of a domestic market is affected not only by the volatility surprises of its own markets, but also by those of foreign markets. The volatility spillover is not unidirectional from the US to foreign markets.

Abstract: In this paper, we investigate the effect of the Reserve Bank of Australia on the $US/$A volatility in the period 1983-1995, which can be broken into four distinct phases. Equally, we investigate the changing effectiveness of daily intervention into various separate components. We test the existence of a long memory behaviour i.e. a finite persistence of volatility. To this aim, we rely on a new mesure of volatility implied by the FIGARCH model that outperforms the traditionnally used GARCH one. We find contemporaneous positive correlation between the direction of intervention and the conditional mean and variance of exchange rate returns. The FIGARCH model implies a long memory behaviour.

Abstract: This work studies the links existing between the six largest stock markets in the world (USA , Japon, United Kingdom, Germany, France and Canada) in terms of return and volatility. We find that conditional heteroskedasticity is present in every market. In order to properly take account of this phenomena, we estimate a series of bivariate AR(1)-GARCH(1,1) models to measure the links existing between stock markets. The results indicate that the US market has the strongest influence on the other markets in terms of returns. The influence of the other markets on the american market is relatively weak. In term of volatility, the conditional variance of a domestic market is affected not only by the volatility surprises of its own markets, but also by those of foreign markets. The volatility spillover is not unidirectional from the US to foreign markets.

Abstract: This work is concerned with the statistical modelling of the dependence structure between three energy commodities markets (WTI crude oil, natural gas and heating oil) using the concept of copulas and proposes a method for estimating the Value at risk (VaR) of energy portfolio based on the combination of time series models with models of the extreme value theory before fitting a copula. Each return series is modelled by AR-(FI) GARCH univariate model. Then, we fit the GPD distribution to the tails of the residuals to model marginal residuals distributions. The extreme value copula to the iid residuals is fitted and we simulate from it to construct N portfolios and estimate VaR. As a first step, the method is applied to a two-dimensional energy portfolio. In second step, we extend method in trivariate context to measure VaR of three-dimensional energy portfolio. Dependences between residuals are modelled using a trivariate nested gumbel copulas. Methods proposed are compared with various univariate and multivariate conventional VaR methods. The reported results demonstrate that garch-t, conditional EVT and FIGARCH extreme value copula methods produce acceptable estimates of risk both for standard and more extreme VaR quantiles. Generally, copulas methods are less accurate compared with their predictive performances in the case of portfolio composed of exchange market indices.

Abstract: Dans ce travail, nous proposons une méthode d’estimation de la VaR d’un portefeuille basée sur la combinaison des modèles de séries temporelles, la théorie des valeurs extrêmes et la théorie des copules. Chaque série des rendements est alors modélisée par un modèle ARMA- GARCH univarié. Les queues des distributions marginales des résidus issus de ces modèles sont modélisées par une distribution de Pareto généralisée. La dépendance entre les résidus est modélisée par une copule de valeurs extrêmes la plus appropriée et à partir de laquelle, on simule des nouvelles séries des résidus pour construire N portefeuilles et estimer la VaR. Dans une première étape, la méthode est appliquée pour deux portefeuilles composés chacun de deux indices. Dans une deuxième étape, nous généralisons la méthode dans un contexte trivarié pour la mesure de risque d’un portefeuille composé de trois indices. Dans ce cas, la dépendance est modélisée par une copule nested trivariée. Les résultats trouvés montrent que les méthodes basées sur les copules de valeurs extrêmes conditionnelles permettent de mieux modéliser la structure de dépendance et offrent des estimations des risques meilleures par comparaison aux méthodes conventionnelles univariées et multivariées. En introduisant la période de la crise financière mondiale 2008 dans l’analyse, les proportions des violations augmentent significativement pour toutes les méthodes et la qualité des prévisions se détériore. Uniquement, les méthodes basées sur les copules continuent à donner des prévisions VaR statistiquement acceptables.

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