Statistical inference for Axiom A attractors

From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying theory that can be used not only for predicting those systems a short time ahead, but also as a basis for statistical inference about their dynamics. The method is applied to prediction of 3 different systems. The statistical inference aspect can be applied to explore and enhance computer models of such systems which in turn can provide feedback for even better prediction and more precise inference.