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The polynomial NARMAX (Nonlinear AutoRegressive Moving Average model witheXogenous input) is a model that represents the dynamics of physical systems.This polynomial contains information from the past of the inputs and outputs ofthe process, that is, it is a recursive model. In digital computers thisgenerates the propagation of the rounding error. Our procedure is based on theestimation of the maximum value of the lower bound error considering anarbitrary number of pseudo-orbits produced from different natural intervalextensions, and a posterior Lyapunov exponent calculation. We appliedsuccessfully our technique for two identified models of the systems: sine mapand Duffing-Ueda oscillator

The Lower Bound Error for polynomial NARMAX using an Arbitrary Number of Natural Interval Extensions