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SUMMARY:Estimation of Noisy Diffusions - Prof Sofia Olhede\, Dept of Stati
 sitcs\, University College London
DTSTART:20100217T141500Z
DTEND:20100217T151500Z
UID:TALK21507@talks.cam.ac.uk
CONTACT:Rachel Fogg
DESCRIPTION:Noisy diffusions are ubiquitous in applications -- such as in 
 physics\, biology\, finance\, and atmosphere/ocean science. Most of the st
 ochastic models that are used in applications involve unknown parameters w
 hich can be\, in principle\, estimated from observations of the Ito proces
 s. In many cases the observations of a diffusion process are contaminated 
 by high-frequency observation error. It is therefore important to develop 
 accurate and efficient statistical inference procedures that take into acc
 ount this contamination of the observed high-frequency data\, to ensure we
 ll-behaved procedures even in the limit of the sampling period tending to 
 zero. Our goal is to address this issue by developing statistical inferenc
 e methodologies in the frequency domain\, in particular for estimating the
  integrated volatility.\n\nWe shall show that intuition and understanding 
 can be found in the frequency domain\, using the Fourier transform of the 
 increments of the observed process. A shrinkage estimator will be proposed
  based on the sampling properties of this Fourier transform. The asymptoti
 c variance of this new estimator will be derived\, and the estimator will 
 be shown to be asymptotically efficient. The estimator also has an interes
 ting interpretation as smoothing the empirical auto-covariance sequence of
  the increments of the observations. The method can easily be generalized 
 to the case of correlated observation error\, and simulation studies illus
 trate a number of interesting properties of the estimation procedure.\n\nS
 ofia Olhede (UCL)\, joint work with Greg Pavliotis and Adam Sykulski\n(Imp
 erial)\n
LOCATION:LR4\, Engineering\, Department of
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