  Nonlinear Auto-Regressive eXogenous input (NARX) models are a popular class
of nonlinear dynamical models. Often a polynomial basis expansion is used to
describe the internal multivariate nonlinear mapping (P-NARX). Resorting to
fixed basis functions is convenient since it results in a closed form solution
of the estimation problem. The drawback, however, is that the predefined basis
does not necessarily lead to a sparse representation of the relationship,
typically resulting in very large numbers of parameters. So-called decoupling
techniques were specifically designed to reduce large multivariate functions.
It was found that, often, a more efficient parameterisation can be retrieved by
rotating towards a new basis. Characteristic to the decoupled structure is
that, expressed in the new basis, the relationship is structured such that only
single-input single-output nonlinear functions are required. Classical
decoupling techniques are unfit to deal with the case of single-output NARX
models. In this work, this limitation is overcome by adopting the filtered CPD
decoupling method of Decuyper et al. (2021b). The approach is illustrated on
data from the Sliverbox benchmark: measurement data from an electronic circuit
implementation of a forced Duffing oscillator.
