Functional singular spectrum analysis
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/80051918-66f6-4f6c-921a-27cf862babeb
- author
- Haghbin, Hossein ; Najibi, Seyed Morteza LU ; Mahmoudvand, Rahim ; Trinka, Jordan and Maadooliat, Mehdi
- organization
- publishing date
- 2021
- 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}}, }