On Mon, 1 Feb 1999, T.Sapatinas wrote:
Institute of Mathematics and Statistics,
University of Kent at Canterbury,
Statistics Seminar -- Lent Term 1999
Thursday, 18th February 1999
2:00pm Dr Guy Nason (Bristol University)
"Time-Scale Analysis"
ABSTRACT
Many are familiar with the periodogram as a device that estimates the
power contained within a stationary time series as a function of
frequency. For certain kinds of
non-stationary time series more sophisticated tools exist that estimate
frequency characterstics evolving through time. Instead of looking at the
frequency properties of time
series we examine series behaviour at different operating scales - this
can be extremely appropriate for certain classes of time series.
This talk exhibits a complete suite of theory, methodology and software
for time-scale modelling and analysis of non-stationary time series. We
assume our time series fall
into a class of models generated by a particular and flexible wavelet
representation. This permits us to develop an "evolutionary wavelet
spectrum" (EWS) that measures the
power of a time series at a particular time and scale (or lag). We also
introduce a time-dependent autocovariance function that is the inverse
wavelet transform of the EWS
(in much the same way as the autocovariance of a stationary time series
is the inverse Fourier transform of the spectrum). Estimation of the EWS
is performed by a "smoothed wavelet periodogram" which can be shown to
have good theoretical properties.
We demonstrate the utility of our new methodology on infant heart rate
data recorded by colleagues of the Institute of Child Health, Royal
Hospital for Sick Children, Bristol.
The time-scale power of these non-stationary time series can be estimated
and shows excellent interpretability and can be related to other,
independent, physiological
variables such as sleep-state. Such information is not readily apparent
using other established time-frequency approaches.
This is a joint work with Rainer von Sachs, Institute of Statistics, UCL,
Louvain-la-Neuve, Belgium, and Gerald Kroisandt, Department of
Mathematics, University of
Kaiserslautern, Germany.
Further details of the seminar programme and abstracts of
forthcoming talks are available from:
http://www.ukc.ac.uk/IMS/statistics/people/T.Sapatinas/Seminars/
seminars.html
All are very welcome. The Statistics Seminars will be held in
Mathematics Lecture Theatre in the Institute of Mathematics and
Statistics, Cornwallis Building.
The following WWW page contain details of how to get to the campus,
and how to find your way around:
http://www.ukc.ac.uk/ukc/location.html
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Dr Theofanis Sapatinas,
Lecturer in Statistics,
Postal Address: Institute of Mathematics and Statistics,
University of Kent at Canterbury,
Canterbury, Kent CT2 7NF,
United Kingdom.
Tel: ++(44)-1227-827253
Fax: ++(44)-1227-827932
E-mail: [log in to unmask]
Web: http://www.ukc.ac.uk/IMS/statistics/people/T.Sapatinas/
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