Nonparametric ML-estimation for nonstationary time series

Wolfgang Polonik, University of California, Davis
(joint work with Rainer Dahlhaus, University of Heidelberg)

Traditionally, time series analysis often assumes stationarity.
In reality, however, this assumption often is violated. Typically
important characteristics of time series, like the variance, change
over time. Real world examples we have in mind are seismographic data of
earthquakes and explosions, or EEG recordings of epileptic seizures.
In this talk we discuss how to estimate such time varying characteristics
nonparametrically via a maximum likelihood (ML) approach in the
framework of  locally stationary processes.

It will be indicated how asymptotic theory for these nonparametric 
ML-estimators
can be based on the (time varying) empirical spectral process, and how in
special instances algorithmic issues can be tackled by exploiting ideas from
isotonic regression.

An approach to classification of seismic time series in earthquakes and 
explosions
is presented as an application of the theoretical work.