Search results for: conditional mean time to failure

Authors: Sule Sahin, Basak Bulut Karageyik

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This paper introduces a hazard rate function for the time of ruin to calculate the conditional probability of ruin for very small intervals. We call this function the force of ruin (FoR). We obtain the expected time of ruin and conditional expected time of ruin from the exact finite time ruin probability with exponential claim amounts. Then we introduce the FoR which gives the conditional probability of ruin and the condition is that ruin has not occurred at time t. We analyse the behavior of the FoR function for different initial surpluses over a specific time interval. We also obtain FoR under the excess of loss reinsurance arrangement and examine the effect of reinsurance on the FoR.

Keywords: conditional time of ruin, finite time ruin probability, force of ruin, reinsurance

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Authors: Hachmi Ben Ameur, Jean Luc Prigent

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We propose an extension of the CPPI method, which is based on conditional floors. In this framework, we examine in particular the TIPP and margin based strategies. These methods allow keeping part of the past gains and protecting the portfolio value against future high drawdowns of the financial market. However, as for the standard CPPI method, the investor can benefit from potential market rises. To control the risk of such strategies, we introduce both Value-at-Risk (VaR) and Expected Shortfall (ES) risk measures. For each of these criteria, we show that the conditional floor must be higher than a lower bound. We illustrate these results, for a quite general ARCH type model, including the EGARCH (1,1) as a special case.

Keywords: CPPI, conditional floor, ARCH, VaR, expected ehortfall

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Authors: Amit Ghosh, Chanchal Kundu

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Recently, the notion of past cumulative inaccuracy (CPI) measure has been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order α (alpha) and study the proposed measure for conditionally specified models of two components failed at different time instants called generalized conditional CPI (GCCPI). We provide some bounds using usual stochastic order and investigate several properties of GCCPI. The effect of monotone transformation on this proposed measure has also been examined. Furthermore, we characterize some bivariate distributions under the assumption of conditional proportional reversed hazard rate model. Moreover, the role of GCCPI in reliability modeling has also been investigated for a real-life problem.

Keywords: cumulative past inaccuracy, marginal and conditional past lifetimes, conditional proportional reversed hazard rate model, usual stochastic order

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Authors: Zubdahe Noor, Haseeb Athar

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In this article, first a relation for conditional expectation is developed and then is used to characterize a general class of distributions F(x) = 1-e^(-ah(x)) through conditional expectation of difference of pair of generalized order statistics. Some results are reduced for particular cases. In the end, a list of distributions is presented in the form of table that are compatible with the given general class.

Keywords: generalized order statistics, order statistics, record values, conditional expectation, characterization

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Authors: Lela Mirtskhulava, Mariam Khunjgurua, Nino Lomineishvili, Koba Bakuria

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Software reliability prediction gives a great opportunity to measure the software failure rate at any point throughout system test. A software reliability prediction model provides with the technique for improving reliability. Software reliability is very important factor for estimating overall system reliability, which depends on the individual component reliabilities. It differs from hardware reliability in that it reflects the design perfection. Main reason of software reliability problems is high complexity of software. Various approaches can be used to improve the reliability of software. We focus on software reliability model in this article, assuming that there is a time redundancy, the value of which (the number of repeated transmission of basic blocks) can be an optimization parameter. We consider given mathematical model in the assumption that in the system may occur not only irreversible failures, but also a failure that can be taken as self-repairing failures that significantly affect the reliability and accuracy of information transfer. Main task of the given paper is to find a time distribution function (DF) of instructions sequence transmission, which consists of random number of basic blocks. We consider the system software unreliable; the time between adjacent failures has exponential distribution.

Keywords: exponential distribution, conditional mean time to failure, distribution function, mathematical model, software reliability

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Authors: Akram Khaleghei, Ghosheh Balagh, Viliam Makis

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In this paper, we investigate the residual life prediction problem for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model with unknown parameters. The parameter estimation procedure based on an EM algorithm is developed and the formulas for the conditional reliability function and the mean residual life are derived, illustrated by a numerical example.

Keywords: partially observable system, hidden Markov model, competing risks, residual life prediction

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Authors: Panudet Saengseedam, Nanthachai Kantanantha

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This paper proposes a linear mixed model (LMM) with spatial effects to forecast rice and cassava yields in Thailand at the same time. A multivariate conditional autoregressive (MCAR) model is assumed to present the spatial effects. A Bayesian method is used for parameter estimation via Gibbs sampling Markov Chain Monte Carlo (MCMC). The model is applied to the rice and cassava yields monthly data which have been extracted from the Office of Agricultural Economics, Ministry of Agriculture and Cooperatives of Thailand. The results show that the proposed model has better performance in most provinces in both fitting part and validation part compared to the simple exponential smoothing and conditional auto regressive models (CAR) from our previous study.

Keywords: Bayesian method, linear mixed model, multivariate conditional autoregressive model, spatial time series

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Authors: Siqi Qiu, Yijian Zheng, Xin Guo Ming

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In many reliability and risk analysis, failures of components are supposed to be independent. However, in reality, the ignorance of failure dependencies among components may render the results of reliability and risk analysis incorrect. There are two principal ways to incorporate failure dependencies in system reliability and risk analysis: implicit and explicit methods. In the implicit method, failure dependencies can be modeled by joint probabilities, correlation values or conditional probabilities. In the explicit method, certain types of dependencies can be modeled in a fault tree as mutually independent basic events for specific component failures. In this paper, explicit and implicit methods based on BDD will be proposed to evaluate the reliability of systems considering failure dependencies. The obtained results prove the equivalence of the proposed implicit and explicit methods. It is found that the consideration of failure dependencies decreases the reliability of systems. This observation is intuitive, because more components fail due to failure dependencies. The consideration of failure dependencies helps designers to reduce the dependencies between components during the design phase to make the system more reliable.

Keywords: reliability assessment, risk assessment, failure dependencies, binary decision diagram

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Authors: Piotr Fiszeder, Marcin Fałdziński, Peter Molnár

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The dynamic conditional correlation model of Engle (2002) is one of the most popular multivariate volatility models. However, this model is based solely on closing prices. It has been documented in the literature that the high and low price of the day can be used in an efficient volatility estimation. We, therefore, suggest a model which incorporates high and low prices into the dynamic conditional correlation framework. Empirical evaluation of this model is conducted on three datasets: currencies, stocks, and commodity exchange-traded funds. The utilisation of realized variances and covariances as proxies for true variances and covariances allows us to reach a strong conclusion that our model outperforms not only the standard dynamic conditional correlation model but also a competing range-based dynamic conditional correlation model.

Keywords: volatility, DCC model, high and low prices, range-based models, covariance forecasting

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Authors: Golnaz Shahtahmassebi, Jose Maria Sarabia

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In this talk, we introduce a new class of conjugate prior distributions obtained from conditional specification methodology. We illustrate the application of such distribution in Bayesian change point detection in Poisson processes. We obtain the posterior distribution of model parameters using a general bivariate distribution with gamma conditionals. Simulation from the posterior is readily implemented using a Gibbs sampling algorithm. The Gibbs sampling is implemented even when using conditional densities that are incompatible or only compatible with an improper joint density. The application of such methods will be demonstrated using examples of simulated and real data.

Keywords: change point, bayesian inference, Gibbs sampler, conditional specification, gamma conditional distributions

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Authors: S. H. Arnaud Kanga, O. Hili, S. Dabo-Niang

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Spatial prediction is an issue appealing and attracting several fields such as agriculture, environmental sciences, ecology, econometrics, and many others. Although multiple non-parametric prediction methods exist for spatial data, those are based on the conditional expectation. This paper took a different approach by examining a non-parametric spatial predictor of the conditional quantile. The study especially observes the stationary multidimensional spatial process over a rectangular domain. Indeed, the proposed quantile is obtained by inverting the conditional distribution function. Furthermore, the proposed estimator of the conditional distribution function depends on three kernels, where one of them controls the distance between spatial locations, while the other two control the distance between observations. In addition, the almost complete convergence and the convergence in mean order q of the kernel predictor are obtained when the sample considered is alpha-mixing. Such approach of the prediction method gives the advantage of accuracy as it overcomes sensitivity to extreme and outliers values.

Keywords: conditional quantile, kernel, nonparametric, stationary

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Authors: Rao Fu, Jie Chen, Shutian Zeng, Yiping Zhuang, Agus Sudjianto

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Generative Adversarial Net (GAN) has proved to be a powerful machine learning tool in image data analysis and generation. In this paper, we propose to use Conditional Generative Adversarial Net (CGAN) to learn and simulate time series data. The conditions include both categorical and continuous variables with different auxiliary information. Our simulation studies show that CGAN has the capability to learn different types of normal and heavy-tailed distributions, as well as dependent structures of different time series. It also has the capability to generate conditional predictive distributions consistent with training data distributions. We also provide an in-depth discussion on the rationale behind GAN and the neural networks as hierarchical splines to establish a clear connection with existing statistical methods of distribution generation. In practice, CGAN has a wide range of applications in market risk and counterparty risk analysis: it can be applied to learn historical data and generate scenarios for the calculation of Value-at-Risk (VaR) and Expected Shortfall (ES), and it can also predict the movement of the market risk factors. We present a real data analysis including a backtesting to demonstrate that CGAN can outperform Historical Simulation (HS), a popular method in market risk analysis to calculate VaR. CGAN can also be applied in economic time series modeling and forecasting. In this regard, we have included an example of hypothetical shock analysis for economic models and the generation of potential CCAR scenarios by CGAN at the end of the paper.

Keywords: conditional generative adversarial net, market and credit risk management, neural network, time series

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Authors: Kalai Lamia, Jilani Faouzi

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Measuring and controlling risk is one of the most attractive issues in finance. With the persistence of uncontrolled and erratic stocks movements, volatility is perceived as a barometer of daily fluctuations. An objective measure of this variable seems then needed to control risks and cover those that are considered the most important. Non-linear autoregressive modeling is our first evaluation approach. In particular, we test the presence of “persistence” of conditional variance and the presence of a degree of a leverage effect. In order to resolve for the problem of “asymmetry” in volatility, the retained specifications point to the importance of stocks reactions in response to news. Effects of shocks on volatility highlight also the need to study the “long term” behaviour of conditional variance of stocks returns and articulate the presence of long memory and dependence of time series in the long run. We note that the integrated fractional autoregressive model allows for representing time series that show long-term conditional variance thanks to fractional integration parameters. In order to stop at the dynamics that manage time series, a comparative study of the results of the different models will allow for better understanding volatility structure over the Tunisia stock market, with the aim of accurately predicting fluctuation risks.

Keywords: asymmetry volatility, clustering, stylised facts, leverage effect

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Authors: Aries Nawel, Bentarzi Mohamed

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This paper deals with the study of some probabilistic and statistical properties of a Periodic Integer-Valued Moving Average Model (PINMA_{S}(q)). The closed forms of the mean, the second moment and the periodic autocovariance function are obtained. Furthermore, the time reversibility of the model is discussed in details. Moreover, the estimation of the underlying parameters are obtained by the Yule-Walker method, the Conditional Least Square method (CLS) and the Weighted Conditional Least Square method (WCLS). A simulation study is carried out to evaluate the performance of the estimation method. Moreover, an application on real data set is provided.

Keywords: periodic integer-valued moving average, periodically correlated process, time reversibility, count data

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Authors: Fayaz Moosavi, Saeid Moradyfard

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One of the methods in avoiding management fraud and increasing the quality of financial information, is the notification of qualitative features of financial information, including conservatism characteristic. Although taking a conservatism approach, while boosting the quality of financial information, is able to reduce the informational risk and the cost of capital stock of commercial department, by presenting an improper image about the situation of the commercial department, raises the risk of failure in returning the main and capital interest, and consequently the cost of capital of the commercial department. In order to know if conservatism finally leads to the increase or decrease of the cost of capital or does not have any influence on it, information regarding accepted companies in Tehran stock exchange is utilized by application of pooling method from 2007 to 2012 and it included 124 companies. The results of the study revealed that there is an opposite and meaningful relationship between conditional conservatism and the cost of capital of the company. In other words, if bad and unsuitable news and signs are reflected sooner than good news in accounting profit, the cost of capital of the company increases. In addition, there is a positive and meaningful relationship between the cost of capital and lack of information asymmetry.

Keywords: conditional conservatism, lack of information asymmetry, the cost of capital, stock exchange

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Authors: Gultekin Gurcay

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In this paper, effects and responses of stock were analyzed. This analysis was done periodically. The dimensions of the financial crisis impact on the stock market were investigated by GARCH model. In this context, S&P 500 stock market is modeled with DAX, NIKKEI and BIST100. In this way, The effects of the changing in S&P 500 stock market were examined on European and Asian stock markets. Conditional variance coefficient will be calculated through garch model. The scope of the crisis period, the conditional covariance coefficient will be analyzed comparatively.

Keywords: conditional variance coefficient, financial crisis, garch model, stock market

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Authors: Fariba Azizi, Firoozeh Haghighi, Viliam Makis

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In this paper, we propose a method to model the relationship between failure time and degradation for a simple step stress test where underlying degradation path is linear and different causes of failure are possible. It is assumed that the intensity function depends only on the degradation value. No assumptions are made about the distribution of the failure times. A simple step-stress test is used to shorten failure time of products and a tampered failure rate (TFR) model is proposed to describe the effect of the changing stress on the intensities. We assume that some of the products that fail during the test have a cause of failure that is only known to belong to a certain subset of all possible failures. This case is known as masking. In the presence of masking, the maximum likelihood estimates (MLEs) of the model parameters are obtained through an expectation-maximization (EM) algorithm by treating the causes of failure as missing values. The effect of incomplete information on the estimation of parameters is studied through a Monte-Carlo simulation. Finally, a real example is analyzed to illustrate the application of the proposed methods.

Keywords: cause of failure, linear degradation path, reliability function, expectation-maximization algorithm, intensity, masked data

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Authors: Abderafi Charki, David Bigaud

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The aim of this oral speach is to present the PVMODREL© (PhotoVoltaic MODule RELiability) new software developed in the University of Angers. This new tool permits us to evaluate the lifetime and reliability of a PV module whatever its geographical location and environmental conditions. The electrical power output of a PV module decreases with time mainly as a result of the effects of corrosion, encapsulation discoloration, and solder bond failure. The failure of a PV module is defined as the point where the electrical power degradation reaches a given threshold value. Accelerated life tests (ALTs) are commonly used to assess the reliability of a PV module. However, ALTs provide limited data on the failure of a module and these tests are expensive to carry out. One possible solution is to conduct accelerated degradation tests. The Wiener process in conjunction with the accelerated failure time model makes it possible to carry out numerous simulations and thus to determine the failure time distribution based on the aforementioned threshold value. By this means, the failure time distribution and the lifetime (mean and uncertainty) can be evaluated. An example using the damp heat test is shown to demonstrate the usefulness PVMODREL.

Keywords: lifetime, reliability, PV Module, accelerated life testing, accelerated degradation testing

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Authors: Maria Laura Alzua, Maria Adelaida Lopera

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This paper measures the relative importance of conditional cooperation and unconditional cooperation in a large public goods experiment conducted in Mali. We use expectations about total public goods provision to estimate a structural choice model with heterogeneous preferences. While unconditional cooperation can be captured by common preferences shared by all participants, conditional cooperation is much more heterogeneous and depends on unobserved individual factors. This structural model, in combination with two experimental treatments, suggests that leadership and group communication incentivize public goods provision through different channels. First, We find that participation of local leaders effectively changes individual choices through unconditional cooperation. A simulation exercise predicts that even in the most pessimistic scenario in which all participants expect zero public good provision, 60% would still choose to cooperate. Second, allowing participants to communicate fosters conditional cooperation. The simulations suggest that expectations are responsible for around 24% of the observed public good provision and that group communication does not necessarily ameliorate public good provision. In fact, communication may even worsen the outcome when expectations are low.

Keywords: conditional cooperation, discrete choice model, expectations, public goods game, random coefficients model

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Authors: Rimmy Yadav, Avtar Singh

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—Ant Colony Optimization (ACO) is a promising modern approach to the unused combinatorial optimization. Here ACO is applied to finding the shortest during communication link failure. In this paper, the performances of the prim’s and ACO algorithm are made. By comparing the time complexity and program execution time as set of parameters, we demonstrate the pleasant performance of ACO in finding excellent solution to finding shortest path during communication link failure.

Keywords: ant colony optimization, link failure, prim’s algorithm, shortest path

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Authors: Mohammadamin Abbasnejad

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The analysis of expression and facial Action Units (AUs) detection are very important tasks in fields of computer vision and Human Computer Interaction (HCI) due to the wide range of applications in human life. Many works have been done during the past few years which has their own advantages and disadvantages. In this work, we present a new model based on Gaussian Conditional Random Field. We solve our objective problem using ADMM and we show how well the proposed model works. We train and test our work on two facial expression datasets, CK+, and RU-FACS. Experimental evaluation shows that our proposed approach outperform state of the art expression recognition.

Keywords: Gaussian Conditional Random Field, ADMM, convergence, gradient descent

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Authors: Nada Jasim Habeeb, Rana Saad Mohammed, Muntaha Khudair Abbass

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For more efficient and fast video summarization, this paper presents a surveillance video summarization method. The presented method works to improve video summarization technique. This method depends on temporal differencing to extract most important data from large video stream. This method uses histogram differencing and Sum Conditional Variance which is robust against to illumination variations in order to extract motion objects. The experimental results showed that the presented method gives better output compared with temporal differencing based summarization techniques.

Keywords: temporal differencing, video summarization, histogram differencing, sum conditional variance

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Authors: Soudabeh Shemehsavar

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In this paper, we consider the situation under a life test, in which the failure time of the test units are not related deterministically to an observable stochastic time varying covariate. In such a case, the joint distribution of failure time and a marker value would be useful for modeling the step stress life test. The problem of accelerating such an experiment is considered as the main aim of this paper. We present a step stress accelerated model based on a bivariate Wiener process with one component as the latent (unobservable) degradation process, which determines the failure times and the other as a marker process, the degradation values of which are recorded at times of failure. Parametric inference based on the proposed model is discussed and the optimization procedure for obtaining the optimal time for changing the stress level is presented. The optimization criterion is to minimize the approximate variance of the maximum likelihood estimator of a percentile of the products’ lifetime distribution.

Keywords: bivariate normal, Fisher information matrix, inverse Gaussian distribution, Wiener process

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Authors: Eduardo C. Guardia, Jose W. M. Lima, Afonso H. M. Santos

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This paper presents a nonparametric method to obtain the hazard rate “Bathtub curve” for power system components. The model is a mixture of the three known phases of a component life, the decreasing failure rate (DFR), the constant failure rate (CFR) and the increasing failure rate (IFR) represented by three parametric Weibull models. The parameters are obtained from a simultaneous fitting process of the model to the Kernel nonparametric hazard rate curve. From the Weibull parameters and failure rate curves the useful lifetime and the characteristic lifetime were defined. To demonstrate the model the historic time-to-failure of distribution transformers were used as an example. The resulted “Bathtub curve” shows the failure rate for the equipment lifetime which can be applied in economic and replacement decision models.

Keywords: bathtub curve, failure analysis, lifetime estimation, parameter estimation, Weibull distribution

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Authors: J. H. Lv, W. Z. Wang, S.W. Liu

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The major concern in the aviation industry is the flight safety. Although great effort has been put onto the development of material and system reliability, the failure cases of fatal accidents still occur nowadays. Due to the complexity of the aviation system, and the interaction among the failure components, the failure analysis of the related equipment is a little difficult. This study focuses on surveying the failure cases in aviation, which are extracted from failure analysis journals, including Engineering Failure Analysis and Case studies in Engineering Failure Analysis, in order to obtain the failure sensitive factors or failure sensitive parts. The analytical results show that, among the failure cases, fatigue failure is the largest in number of occurrence. The most failed components are the disk, blade, landing gear, bearing, and fastener. The frequently failed materials consist of steel, aluminum alloy, superalloy, and titanium alloy. Therefore, in order to assure the safety in aviation, more attention should be paid to the fatigue failures.

Keywords: aerospace, disk, failure analysis, fatigue

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Authors: Souhir Ben Amor, Heni Boubaker, Lotfi Belkacem

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This aims of this paper is to forecast the electricity spot prices. First, we focus on modeling the conditional mean of the series so we adopt a generalized fractional -factor Gegenbauer process (k-factor GARMA). Secondly, the residual from the -factor GARMA model has used as a proxy for the conditional variance; these residuals were predicted using two different approaches. In the first approach, a local linear wavelet neural network model (LLWNN) has developed to predict the conditional variance using the Back Propagation learning algorithms. In the second approach, the Gegenbauer generalized autoregressive conditional heteroscedasticity process (G-GARCH) has adopted, and the parameters of the k-factor GARMA-G-GARCH model has estimated using the wavelet methodology based on the discrete wavelet packet transform (DWPT) approach. The empirical results have shown that the k-factor GARMA-G-GARCH model outperform the hybrid k-factor GARMA-LLWNN model, and find it is more appropriate for forecasts.

Keywords: electricity price, k-factor GARMA, LLWNN, G-GARCH, forecasting

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Authors: Francisco Fernandez de Castro

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The Conditional Cash Transfer (CCT) model gives monetary transfers to beneficiary families on the condition that they take specific education and health actions. According to the economic rationale of CCTs the poor need incentives to invest in their human capital because they are trapped by a lack of information and misleading beliefs. If left to their own decision, the poor will not be able to choose what is in their best interests. The basic assumption of the CCT model is that the poor need incentives to take care of their own education and health-nutrition. Due to the incentives (income cash transfers and conditionalities), beneficiary families are supposed to attend doctor visits and health talks. Children would stay in the school. These incentivized behaviors would produce outcomes such as better health and higher level of education, which in turn will reduce poverty. Based on a grounded theory approach to conduct a two-year period of qualitative data collection in northern Mexico, this study shows that this explanation is incomplete. In addition to the information failure and inadequate beliefs, there are structural barriers in everyday life of households that make health-nutrition and education investments difficult. In-depth interviews and observation work showed that the program takes for granted local conditions in which beneficiary families should fulfill their co-responsibilities. Data challenged the program’s assumptions and unveiled local obstacles not contemplated in the program’s design. These findings have policy and research implications for the CCT agenda. They bring elements for late programming due to the gap between the CCT strategy as envisioned by policy designers, and the program that beneficiary families experience on the ground. As for research consequences, these findings suggest new avenues for scholarly work regarding the causal mechanisms and social processes explaining CCT outcomes.

Keywords: conditional cash transfers, incentives, poverty, structural barriers

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Authors: Johan Loeckx, Joeri Bultheel

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Recently, the application of deep learning to music has gained popularity. Its true potential, however, has been largely unexplored. In this paper, a new idea for representing the dynamic behavior of music is proposed. A ”forward” conditional RBM takes into account not only preceding but also future samples during training. Though this may sound controversial at first sight, it will be shown that it makes sense from a musical and neuro-cognitive perspective. The model is applied to reconstruct music based upon the first notes and to improvise in the musical style of a composer. Different to expectations, reconstruction accuracy with respect to a regular CRBM with the same order, was not significantly improved. More research is needed to test the performance on unseen data.

Keywords: deep learning, restricted boltzmann machine, music generation, conditional restricted boltzmann machine (CRBM)

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Authors: Salman Mohamadi, Seyed Mohammad Ali Tayaranian Hosseini, Hamidreza Amindavar

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In this paper, we provide a procedure to analyze and model EEG (electroencephalogram) signal as a time series using ARIMA-GARCH to predict an epileptic attack. The heteroskedasticity of EEG signal is examined through the ARCH or GARCH, (Autore- gressive conditional heteroskedasticity, Generalized autoregressive conditional heteroskedasticity) test. The best ARIMA-GARCH model in AIC sense is utilized to measure the volatility of the EEG from epileptic canine subjects, to forecast the future values of EEG. ARIMA-only model can perform prediction, but the ARCH or GARCH model acting on the residuals of ARIMA attains a con- siderable improved forecast horizon. First, we estimate the best ARIMA model, then different orders of ARCH and GARCH modelings are surveyed to determine the best heteroskedastic model of the residuals of the mentioned ARIMA. Using the simulated conditional variance of selected ARCH or GARCH model, we suggest the procedure to predict the oncoming seizures. The results indicate that GARCH modeling determines the dynamic changes of variance well before the onset of seizure. It can be inferred that the prediction capability comes from the ability of the combined ARIMA-GARCH modeling to cover the heteroskedastic nature of EEG signal changes.

Keywords: epileptic seizure prediction , ARIMA, ARCH and GARCH modeling, heteroskedasticity, EEG

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Authors: Longqing Li

Abstract:

The paper addresses the inefficiency of the classical model in measuring the Value-at-Risk (VaR) using a normal distribution or a Student’s t distribution. Specifically, the paper focuses on the one day ahead Value-at-Risk (VaR) of major stock market’s daily returns in US, UK, China and Hong Kong in the most recent ten years under 95% confidence level. To improve the predictable power and search for the best performing model, the paper proposes using two leading alternatives, Extreme Value Theory (EVT) and a family of GARCH models, and compares the relative performance. The main contribution could be summarized in two aspects. First, the paper extends the GARCH family model by incorporating EGARCH and TGARCH to shed light on the difference between each in estimating one day ahead Value-at-Risk (VaR). Second, to account for the non-normality in the distribution of financial markets, the paper applies Generalized Error Distribution (GED), instead of the normal distribution, to govern the innovation term. A dynamic back-testing procedure is employed to assess the performance of each model, a family of GARCH and the conditional EVT. The conclusion is that Exponential GARCH yields the best estimate in out-of-sample one day ahead Value-at-Risk (VaR) forecasting. Moreover, the discrepancy of performance between the GARCH and the conditional EVT is indistinguishable.

Keywords: Value-at-Risk, Extreme Value Theory, conditional EVT, backtesting

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