Abstract
In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functionalSSA to analyze functional time series. The new methodology is constructed by integrating ideasfrom functional data analysis and univariate SSA. Specifically, we i ntroduce a trajectory operatorin the functional world, which is equivalent to the trajectory matrix in the regular SSA. In theregular S SA, one needs to obtain the singular value decomposition (SVD) of the trajectorymatrix to decompose a given time series. Since there is no procedure to extract the functionalSVD (fSVD) of the trajectory operator, we introduce a computationally tr actable algorithm toobtain the fSVD components. The effectiveness of the proposed approach is illustrated by aninteresting example of remote sensing data. Also, we develop an efficient and user-friendly Rpackage and a shiny web application to allow interactive exploration of the results.
Seyed Morteza Najibi
Research Fellow in Statistics
My research interests include statistical machine learning, directional statistics, Bayesian modeling, and non-parametric modeling.