  The polynomial NARMAX (Nonlinear AutoRegressive Moving Average model with
eXogenous input) is a model that represents the dynamics of physical systems.
This polynomial contains information from the past of the inputs and outputs of
the process, that is, it is a recursive model. In digital computers this
generates the propagation of the rounding error. Our procedure is based on the
estimation of the maximum value of the lower bound error considering an
arbitrary number of pseudo-orbits produced from different natural interval
extensions, and a posterior Lyapunov exponent calculation. We applied
successfully our technique for two identified models of the systems: sine map
and Duffing-Ueda oscillator
