Historical Decompositions for Nonlinear Vector Autoregression Models

The historical decomposition is standard within the vector autogression (VAR) toolkit. It
provides an interpretation of historical fluctuations in the modelled time series through
the lens of the identified structural shocks. The proliferation of nonlinear VAR models
naturally leads to extending the historical decomposition into nonlinear settings. This
article discusses how to calculate an exact historical decomposition for a large class of
popular nonlinear VAR models. In particular, the standard historical decomposition one
obtains from a linear VAR is nested within the nonlinear case. The approach discussed
in this article is sufficiently general to be relevant for many popular variants of nonlinear
VAR models.