100 research outputs found

    Refining value-at-risk estimates using a Bayesian Markov-switching GJR-GARCH copula-EVT model

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    In this paper, we propose a model for forecasting Value-at-Risk (VaR) using a Bayesian Markov-switching GJR-GARCH(1,1) model with skewed Student’s-t innovation, copula functions and extreme value theory. A Bayesian Markov-switching GJR-GARCH(1,1) model that identifies non-constant volatility over time and allows the GARCH parameters to vary over time following a Markov process, is combined with copula functions and EVT to formulate the Bayesian Markov-switching GJR-GARCH(1,1) copula-EVT VaR model, which is then used to forecast the level of risk on financial asset returns. We further propose a new method for threshold selection in EVT analysis, which we term the hybrid method. Empirical and back-testing results show that the proposed VaR models capture VaR reasonably well in periods of calm and in periods of crisis

    Optimal predictions of powers of conditionally heteroskedastic processes

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    The standard method for estimating powers of conditionally heteroskedastic processes is a two-step procedure in which the volatility is estimated by ga.us-sian quasi-maximum likelihood (QML) in a first step, and an empirical mean of the rescaled innovations is computed in a second step. This paper proposes an alternative one-step procedure, based on an appropriate non-gaussian QML estimation of the model, and establishes the asymptotic properties of the two ap¬proaches. Their performances are compared for finite-order GARCH models and for the ARCH(oo). For the standard GARCH(p, q) and the Asymmetric Power GARCH(p, g), it is shown that the asymptotic relative efficiency of the estimators only depends on the prediction problem and on some moments of the independent process. An application to indexes of major stock exchanges is proposed

    Testing That Some GARCH Coefficients are Equal to Zero

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    The asymptotic distribution of the quasi-maximum likelihood (QML) estimator for generalized autoregressive conditional heteroskedastic (GARCH) processes is not standard when the true parameter have zero coefficients. This asymptotic distribution is the projection of a normal vector distribution onto a convex cone. We show that the QML estimator does not converge to its asymptotic distribution locally uniformly. Using these results, we consider the problem of testing that one or several GARCH coefficients are equal to zero. The null distribution and the local asymptotic powers of the Wald, score and quasi-likelihood ratio tests are derived. The one-sided nature of the problem is exploited and asymptotic optimality issues are addressed

    Threshold Arch Models and Asymmetries in Volatility.

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    This paper attempts to enlarge the class of Threshold Heteroscedastic Models (TARCH) introduced by Zakoian (1991). We show that it is possible to relax the positivity constraints on the parameters of the conditional variance. Unconstrained models provide a greater generality of the paths allowing for non-linearities in the volatility. Cyclical behavior is permitted as well as different relative impacts of positive and negative shocks on volatility, depending on their size. We give empirical evidence using French stock returns. Copyright 1993 by John Wiley & Sons, Ltd.

    Testing That Some GARCH Coefficients are Equal to Zero

    No full text
    The asymptotic distribution of the quasi-maximum likelihood (QML) estimator for generalized autoregressive conditional heteroskedastic (GARCH) processes is not standard when the true parameter have zero coefficients. This asymptotic distribution is the projection of a normal vector distribution onto a convex cone. We show that the QML estimator does not converge to its asymptotic distribution locally uniformly. Using these results, we consider the problem of testing that one or several GARCH coefficients are equal to zero. The null distribution and the local asymptotic powers of the Wald, score and quasi-likelihood ratio tests are derived. The one-sided nature of the problem is exploited and asymptotic optimality issues are addressed

    Merits and Drawbacks of Variance Targeting in GARCH Models

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