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