Transformed Polynomials for Nonlinear Autoregressive Models of the Conditional Mean

Abstract

This paper proposes a new set of transformed polynomial functions that provide a flexible setting for nonlinear autoregressive modeling of the conditional mean while at the same time ensuring the strict stationarity, ergodicity, fading memory and existence of moments of the implied stochastic sequence. The great flexibility of the transformed polynomial functions makes them interesting for both parametric and semi-nonparametric autoregressive modeling. This flexibility is established by showing that transformed polynomial sieves are sup-norm-dense on the space of continuous functions and offer appropriate convergence speeds on Holder function spaces.