Title: Towards a general theory for non-linear locally stationary processes,
Abstract: In this paper some general theory is presented for locally stationary
processes based on the stationary approximation and the stationary derivative.
Laws of large numbers, central limit theorems as well as deterministic and
stochastic bias expansions are proved for processes obeying an expansion in
terms of the stationary approximation and derivative. In addition it is shown
that this applies to some general nonlinear non-stationary Markov-models. In
addition the results are applied to derive the asymptotic properties of maximum
likelihood estimates of parameter curves in such models.