Nonlinear Innovations and Impulse Responses with Application to VaR Sensitivity

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.