In multivariate nonlinear time series models, impulse response functions are only partially identified, and identifiable summaries such as pseudo impulse responses depend on the chosen shock definition and universe of variables.
Indeed, the Gaussian VAR(1) is a very special case of dynamic models and such properties are in general, not indicative of what arises in a nonlinear dynamic framework
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Identification of Impulse Response Functions for Nonlinear Dynamic Models
In multivariate nonlinear time series models, impulse response functions are only partially identified, and identifiable summaries such as pseudo impulse responses depend on the chosen shock definition and universe of variables.