A Fully Nonlinear Structural Vector Autoregressive Model Identified via Independent Innovation Analysis

This paper develops a fully nonlinear structural vector autoregressive model whose contemporaneous mapping can be nonlinear and non-additive. It identifies mutually independent structural shocks by combining exogenous-variable-induced changes in their conditional distributions with contrastive learning and a structured exponential-family specification. The initial componentwise transformation ambiguity is reduced to a one-parameter transformed-scale map and, under a logistic parameterization of the natural parameters, further to permutation and componentwise sign changes. Feed-forward neural networks estimate the resulting nonlinear SVAR. An application examines U.S. industrial production responses to real oil-price shocks, while the accompanying R package iiasvar implements the methods.