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SUMMARY:Dynamic functional principal components - Siegfried Hörmann\, Uni
 versité libre de Bruxelles
DTSTART:20141128T160000Z
DTEND:20141128T170000Z
UID:TALK54676@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:Data in many fields of science are sampled from processes that
  can most naturally be described as functional. Examples include growth cu
 rves\, temperature curves\, curves of financial transaction data and patte
 rns of pollution data. Functional data analysis (FDA) is concerned with th
 e statistical analysis of such data.\n\nAn important tool in many empirica
 l and theoretical problems related to FDA is the functional principal anal
 ysis (FPCA) which allows to represent or approximate curves in low dimensi
 on. It is certainly the most common approach to obtain dimension reduction
  for functional data. In fact\, it achieves in some sense optimal dimensio
 n reduction if data are independent. However\, it is all but uncommon that
  functional data are serially correlated.\n\nA typical example is if the o
 bservations are segments from a continuous time process (e.g. days). Then\
 , although cross-sectionally uncorrelated for a fixed observation\, the cl
 assical FPC-score vectors have non-diagonal cross-correlations. This means
  that we cannot analyze them componentwise (like in the i.i.d. case)\, but
  we need to consider them as vector time series which are less easy to han
 dle and to interpret. In particular\, a functional principal component wit
 h small eigenvalue\, hence negligible instantaneous impact on some observa
 tion\, may have a major impact on the lagged values. Regular FPCs\, thus\,
  in a time series context\, will not lead to an adequate dimension reducti
 on technique\, as they do in the i.i.d. case. This motivates the developme
 nt of a time series version of functional PCA. The idea is to transform th
 e (possibly infinite dimensional) functional time series\, into a vector t
 ime series (of low dimension 3 or 4\, say)\, where the individual componen
 t processes are mutually uncorrelated\, and explain a bigger part of the d
 ynamics and variability of the original process.\n\nIn this talk we will p
 ropose such a dynamic version of FPCA for general data structures (Hilbert
 ian data) and study its properties. An empirical analysis and a real data 
 example will be given.\n\nThe talk is based on joint work with Lukasz Kidz
 iński (EPFL) and Marc Hallin (ULB).
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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