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Nonlinear Innovations and Impulse Responses with Application to VaR Sensitivity

Les Cahiers du CREF of HEC Montréal Working Paper No. 03-08

42 Pages Posted: 18 Jul 2005  

Christian Gourieroux

University of Toronto - Department of Economics; Center for Interuniversity Research and Analysis on Organization (CIRANO); Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE); National Bureau of Economic Research (NBER)

Joann Jasiak

York University - Department of Economics

Date Written: November 2003

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 of 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, 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.

Keywords: Nonlinear Dynamics, Gaussian Innovations, Volterra Expansion, Impulse Response, ACD Model, Value at Risk

JEL Classification: C10, C22, C52, G11

Suggested Citation

Gourieroux, Christian and Jasiak, Joann, Nonlinear Innovations and Impulse Responses with Application to VaR Sensitivity (November 2003). Les Cahiers du CREF of HEC Montréal Working Paper No. 03-08. Available at SSRN: https://ssrn.com/abstract=757352 or http://dx.doi.org/10.2139/ssrn.757352

Christian Gourieroux (Contact Author)

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S 3G7
Canada
416-978-4349 (Phone)
416-978-6713 (Fax)

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

2020 rue University, 25th Floor
Montreal, Quebec H3C 3J7
Canada

Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE) ( email )

15 Boulevard Gabriel Peri
92245 Malakoff Cedex
France
33.4117.7666 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Joann Jasiak

York University - Department of Economics ( email )

4700 Keele St.
Toronto, Ontario M3J 1P3
Canada
416-736-2100 EX77045 (Phone)
416-736-5987 (Fax)

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