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 ARCH-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.
In order to investigate the structure of such processes and to investigate the properties of estimators we use the idea of a stationary approximation and a stationary derivative process. We define derivative processes and a Taylor type expansion for locally stationary processes and show how these techniques can be used for investigating the statistical properties of estimators for such processes. As an application we study in particular nonlinear processes.
Keywords: Locally stationary processes; Approximations; Expansions
Biography: Rainer Dahlhaus has received his PhD and his Habilitation from the University of Essen. Since 1988 he is Professor at the University of Heidelberg.