Survey/Tutorial lecture - Locally stationary processes

Wednesday, September 7, 2011 - 2:00pm - 3:00pm
Keller 3-180
Rainer Dahlhaus (Ruprecht-Karls-Universität 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.

Furthermore we discuss the estimation of instantaneous frequencies for processes with a nonlinear phase.