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Time Varying Empirical Spectral Processes With Application to Maximum Whittle Likelihood Estimation
Applied Math| Speaker: | Wolfgang Polonik, Dept. of Statistics, UC Davis |
| Location: | 693 Kerr |
| Start time: | Fri, Dec 7 2001, 4:10PM |
Description
Stochastic processes are considered that admit a time-varying
spectral representation, and hence are only locally stationary.
The statistical problem under consideration is the nonparametric maximum
Whittle-likelihood estimation of characteristics of locally stationary
time series. An example is the estimation of the time varying variance of an
AR-time series which, for instance, has interesting applications in
seismology.
From a theoretical perspective the time varying empirical spectral process
comes into play. The reason is, that the frequency domain is used as a
vehicle to
tackle the underlying statistical problem.
We present some mathematical theory for the time varying empirical spectral
process that parallels modern empirical process theory
(which is based on independent data) . We then indicate how this theory can be
utilized for deriving asymptotic properties of our (function) estimators of
the time
varying characteristics.
We will also show that in special instances algorithmic issues can be tackled
by exploiting ideas from isotonic regression.
This is joint work with R. Dahlhaus from University of Heidelberg, Germany.
Coffee and cookies in 693 Kerr