Nonlinear Innovations and Impulse Responses with Application to VaR Sensitivity
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)
York University - Department of Economics
Les Cahiers du CREF of HEC Montréal Working Paper No. 03-08
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.
Number of Pages in PDF File: 42
Keywords: Nonlinear Dynamics, Gaussian Innovations, Volterra Expansion, Impulse Response, ACD Model, Value at Risk
JEL Classification: C10, C22, C52, G11
Date posted: July 18, 2005
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