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SUMMARY:Functional time series approach for inference on multifractional p
 artial pseudodifferential equations - Maria Dolores Ruiz-Medina (Universid
 ad de Granada)
DTSTART:20220404T130000Z
DTEND:20220404T140000Z
UID:TALK170063@talks.cam.ac.uk
DESCRIPTION:Long&nbsp\; Range Dependence (LRD) in functional sequences is 
 characterized&nbsp\;in the spectral domain under suitable conditions (see 
 Ruiz-Medina\,2021). Particularly\,&nbsp\; the spectral representation of t
 he discretesampling of the mean-square solution to multifractionalpseudodi
 fferential equations can be approximated by tapering its&nbsp\;continuous 
 spectrum. A multifractionally integrated functionalautoregressive moving a
 verages process (MIFAMA process) family is thenobtained.&nbsp\; For this&n
 bsp\; family\, the&nbsp\; convergence to zero in theHilbert-Schmidt operat
 or norm of the integrated bias of the periodogramoperator is proved. Under
  a Gaussian scenario\, a&nbsp\; weak--consistentparametric estimator of th
 e long--memory operator is then obtained byminimizing\, in&nbsp\; the&nbsp
 \; norm of bounded linear operators\, a divergenceinformation functional&n
 bsp\; loss. Application of these results to asymptoticinference on multifr
 actional processes\, including multifractionalBrownian motion\, are&nbsp\;
  illustrated as well.REFERENCERuiz--Medina\, M.D. (2021). Spectral analysi
 s of long range dependence infunctional time series. ArXiv: 1912.07086v7.
LOCATION:Seminar Room 2\, Newton Institute
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