Functional Singular Spectrum Analysis

Authors

Hossein Haghbin, Persian Gulf University
Seyed Morteza Najibi, Shiraz University
Rahim Mahmoudvand, Bu-Ali Sina University
Jordan Trinka, Marquette University
Mehdi Maadooliat, Marquette UniversityFollow

Document Type

Article

Publication Date

12-2021

Publisher

Wiley

Source Publication

Stat

Source ISSN

2049-1573

Original Item ID

DOI: 10.1002/sta4.330

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.

Comments

Accepted version. Stat, Vol. 10, No. 1 (December 2021). DOI. © 2021 Wiley. Used with permission.

Recommended Citation

Haghbin, Hossein; Najibi, Seyed Morteza; Mahmoudvand, Rahim; Trinka, Jordan; and Maadooliat, Mehdi, "Functional Singular Spectrum Analysis" (2021). Mathematical and Statistical Science Faculty Research and Publications. 111.
https://epublications.marquette.edu/math_fac/111