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Nonlinear Innovations and Impulse Responses with Application to VaR Sensitivity

Christian Gourieroux and Joann Jasiak
Annales d'Économie et de Statistique
No. 78 (Apr. - Jun., 2005), pp. 1-31
Published by: GENES on behalf of ADRES
DOI: 10.2307/20079126
Stable URL: http://www.jstor.org/stable/20079126
Page Count: 31
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Nonlinear Innovations and Impulse Responses with Application to VaR Sensitivity
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Abstract

This paper introduces impulse response analysis for nonlinear processes based on the concept of nonlinear innovation. Our approach borrows from the traditional linear impulse response analysis in that we consider shocks to innovations of a process. It also extends the methods of nonlinear impulse response analysis proposed earlier in the literature, in that it eliminates the problem of serial correlation of error terms, allows to examine permanent shocks, i.e. shocks occurring repeatedly in time, and provides straightforward interpretation of transitory or symmetric shocks. In our approach, the impulse responses are represented by the joint distribution of the perturbed and unperturbed paths. The analysis can be applied to processes such as the popular GARCH, or ACD models, and can be used to study shock sensitivity of dynamic financial strategies. As an illustration, we show how impulse responses can determine the Value at Risk and the minimum capital requirement under a dynamic portfolio management. /// Nous introduisons un concept d'innovation adapté à l'analyse des dynamiques non linéaires. Nous expliquons comment le processus initial peut être exprimé en fonction des valeurs présentes et passées de l'innovation, utilisons les résidus associés pour construire des tests de spécification d'une dynamique non linéaire et pour définir des fonctions réponses à des chocs transitoires ou permanents. Il est expliqué pourquoi la distribution jointe des trajectoires perturbées et non perturbées est la représentation adéquate de la fonction réponse. Cette approche est illustrée sur des modèles dynamiques non linéaires du type ACD ou modèles à facteur. Elle est aussi utilisée pour étudier la Valeur à Risque et le capital requis dans le cas d'une stratégie dynamique de gestion de portefeuille.

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