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SUMMARY:Discrete Fourier transform methods in the analysis of nonstationar
 y time series - Suhasini Subba Rao\, Texas A&amp\;M University
DTSTART:20130531T150000Z
DTEND:20130531T160000Z
UID:TALK45566@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:The Discrete Fourier Transform (DFT) is often used to analysis
  time series\,\nusually under the assumption of (second order) stationarit
 y of the time\nseries. One of the main reasons for using this transformati
 on is that the\nDFT tends to uncorrelate the original time series. Thus th
 e DFT can be\ntreated as an almost uncorrelated complex random variable\, 
 and standard\nmethods for independent data can be applied to the DFT. It c
 an be shown that\nthis useful uncorrelation property does not hold for non
 stationary time\nseries. This would suggest that the DFT is no longer a he
 lpful tool for\nnonstationary time series analysis. However\, the purpose 
 of this talk is to\ndemonstrate that correlations between the DFTs contain
  useful information\nabout the nonstationary nature of the underlying time
  series. We will\nexploit the starkly contrasting correlation\nproperties 
 between stationarity and nonstationarity DFTs to construct a test\nfor sec
 ond order stationarity and\, if time permits\, to construct an\nestimator 
 of the time-varying spectral density.\n
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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