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SUMMARY:Factor models for high-dimensional functional time series
DTSTART:20211015T151500
DTEND:20211015T170000
DTSTAMP:20260408T052525Z
UID:a6813f6de685c47d24741bf2c0e2ff36aca7cc3d05d18f204befbe20
CATEGORIES:Conferences - Seminars
DESCRIPTION:Shahin Tavakoli\, Research Center for Statistics\, Geneva Scho
 ol of Economics and Management\nWe setup the theoretical foundations for a
  high-dimensional functional factor model approach in the analysis of larg
 e cross-sections (panels) of functional time series (FTS). We first establ
 ish a representation result stating that\, under mild assumptions on the c
 ovariance operator of the cross-section\, we can represent each FTS as the
  sum of a common component driven by scalar factors loaded via functional 
 loadings\, and a mildly cross-correlated idiosyncratic component. Our mode
 l and theory are developed in a general Hilbert space setting that allows 
 for mixed panels of functional and scalar time series.\n\nWe then turn to 
 the identification of the number of factors\, and the estimation of the fa
 ctors\, their loadings\, and the common components. We provide a family of
  information criteria for identifying the number of factors\, and prove th
 eir consistency. We provide average error bounds for the estimators of the
  factors\, loadings\, and common component\; our results encompass the sca
 lar case\, for which they reproduce and extend\, under weaker conditions\,
  well-established similar results.\nUnder slightly stronger assumptions\, 
 we also provide uniform bounds for the estimators of factors\, loadings\, 
 and common component\, thus extending existing scalar results.\n\nOur cons
 istency results in the asymptotic regime where the number N of series and 
 the number T of time observations diverge thus extend to the functional co
 ntext the “blessing of dimensionality” that explains the success of fa
 ctor models in the analysis of high-dimensional (scalar) time series. We p
 rovide numerical illustrations that corroborate the convergence rates pred
 icted by the theory\, and provide finer understanding of the interplay bet
 ween N and T for estimation purposes.\nWe conclude with an application to 
 forecasting mortality curves\, where we demonstrate that our approach outp
 erforms existing methods.\n\nThis is joint work with Gilles Nisol (ULB) an
 d Marc Hallin (ULB)\n\n 
LOCATION:ELD 020 https://plan.epfl.ch/?room==ELD%20020 https://epfl.zoom.u
 s/j/68610986326
STATUS:CONFIRMED
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