  Empirical modelling often aims for the simplest model consistent with the
data. A new technique is presented which quantifies the consistency of the
model dynamics as a function of location in state space. As is well-known,
traditional statistics of nonlinear models like root-mean-square (RMS) forecast
error can prove misleading. Testing consistency is shown to overcome some of
the deficiencies of RMS error, both within the perfect model scenario and when
applied to data from several physical systems using previously published
models. In particular, testing for consistent nonlinear dynamics provides
insight towards (i) identifying when a delay reconstruction fails to be an
embedding, (ii) allowing state dependent model selection and (iii) optimising
local neighbourhood size. It also provides a more relevant (state dependent)
threshold for identifying false nearest neighbours.
