Statistical inference for locally stationary processes - an overview

Rainer Dahlhaus, University of Heidelberg

Locally stationary processes are models for nonstationary time series
whose behaviour can locally be approximated by a stationary process.
In this situation the classical characteristics of the process such
as the covariance function at some lag k, the spectral density at
some frequency lambda, or eg the parameter of an AR(p)-process are
curves which change slowly over time. The theory of locally
stationary processes allows for a rigorous asymptotic treatment of
various inference problems for such processes. Although technically
more difficult many problems are related to classical curve estimation
problems.

We give an overview over different methods of nonparametric curve
estimation for locally stationary processes. We discuss stationary
methods on segments, wavelet expansions, local likelihood methods
and nonparametric maximum likelihood estimates.

In addition we give an overview over other results for locally stationary
processes.