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Functional singular spectrum analysis

Haghbin, Hossein ; Najibi, Seyed Morteza LU orcid ; Mahmoudvand, Rahim ; Trinka, Jordan and Maadooliat, Mehdi (2021) In Stat 10(1).
Abstract
In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA, one needs to obtain the singular value decomposition (SVD) of the trajectory matrix to decompose a given time series. Since there is no procedure to extract the functional SVD (fSVD) of the trajectory operator, we introduce a computationally tractable algorithm to obtain the fSVD components. The effectiveness of the proposed approach is... (More)
In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA, one needs to obtain the singular value decomposition (SVD) of the trajectory matrix to decompose a given time series. Since there is no procedure to extract the functional SVD (fSVD) of the trajectory operator, we introduce a computationally tractable algorithm to obtain the fSVD components. The effectiveness of the proposed approach is illustrated by an interesting example of remote sensing data. Also, we develop an efficient and user‐friendly R package and a shiny web application to allow interactive exploration of the results. (Less)
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author
; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Functional SVD, Functional time series, Hilbert space, Singular spectrum analysis
in
Stat
volume
10
issue
1
article number
e330
pages
15 pages
publisher
Wiley-Blackwell
external identifiers
  • scopus:85121816310
ISSN
2049-1573
DOI
10.1002/sta4.330
language
English
LU publication?
yes
id
80051918-66f6-4f6c-921a-27cf862babeb
date added to LUP
2021-02-25 00:49:47
date last changed
2022-04-27 19:15:46
@article{80051918-66f6-4f6c-921a-27cf862babeb,
  abstract     = {{In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA, one needs to obtain the singular value decomposition (SVD) of the trajectory matrix to decompose a given time series. Since there is no procedure to extract the functional SVD (fSVD) of the trajectory operator, we introduce a computationally tractable algorithm to obtain the fSVD components. The effectiveness of the proposed approach is illustrated by an interesting example of remote sensing data. Also, we develop an efficient and user‐friendly R package and a shiny web application to allow interactive exploration of the results.}},
  author       = {{Haghbin, Hossein and Najibi, Seyed Morteza and Mahmoudvand, Rahim and Trinka, Jordan and Maadooliat, Mehdi}},
  issn         = {{2049-1573}},
  keywords     = {{Functional SVD; Functional time series; Hilbert space; Singular spectrum analysis}},
  language     = {{eng}},
  number       = {{1}},
  publisher    = {{Wiley-Blackwell}},
  series       = {{Stat}},
  title        = {{Functional singular spectrum analysis}},
  url          = {{http://dx.doi.org/10.1002/sta4.330}},
  doi          = {{10.1002/sta4.330}},
  volume       = {{10}},
  year         = {{2021}},
}