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Abstract
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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 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.
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