Description Details References See Also

The Rfssa package provides the collection of necessary functions to implement functional singular spectrum analysis (FSSA) for analysing functional time series (FTS) data. FSSA is a novel non-parametric method to perform decomposition and reconstruction of FTS.

The use of the package starts with the decomposition
of functional time series (`fts`

) objects using `fssa`

.
Then a suitable grouping of the principal compomnents is required for reconstruction which can be done heuristically by looking at
the plots of the decomposition (`plot`

).
Alternatively, one can examine the weighted correlation (w-correlation) matrix
(`fwcor`

). The final step is the reconstruction of the
principal components into additive `fts`

objects
whose sum approximates the original univariate or multivariate functional time series (`freconstruct`

).

This version of the Rfssa package includes updates to existing functions including `fssa`

, `plot`

, `wplot`

, and
`freconstruct`

. Multivariate functional singular spectrum analysis (mfssa) was added to the package in `fssa`

to allow
the user to perform embedding and decomposition of a multivariate FTS. The reconstruction stage in `freconstruct`

was also updated
to allow for reconstruction (including Hankelization) of multivariate FTS objects
using multivariate FSSA objects that come from mfssa. Plotting options for FSSA objects in `plot`

were also updated
so that the user can now plot left singular functions, right singular vectors, left singular function heat diagrams, and periodograms. FSSA plotting
options also allow the user to specify which particular components they want to plot. For example, a user can specify that they want to see a paired-plot of only the
third and fourth component. The 'meanvectors' and 'meanpaired' options were removed as these are satisfied with 'paired' and 'vectors' options. The 'efunctions'
and 'efunctions2' options were also removed in lieu of the addition of the left singular function heat map option. The user can also specify the 'cuts' parameter in
`wplot`

to make visualization of the w-correlation matrix easier.

This version of the Rfssa package also includes new functions
for converting functional data (FD) objects to FTS objects, arithmetic, indexing, correlation, and plotting of FTS data.
The user is able to convert an FD object to an FTS object using `fts`

. The user can also perform addition,
subtraction, and multiplication of FTS objects with other FTS objects or FTS objects with scalars
by using '+', '-', and '*' respectively. The package also
allows for indexing of FTS objects by using '['. The user can also measure the unweighted correlation
between FTS objects by using `cor.fts`

. The plotting of FTS objects can be performed using `plot`

which uses the plotly package for visualization.

The package update also includes a new shiny app (`launchApp`

) that can be used for demonstrations of univariate or multivariate FSSA
depending on the type that is specified.
The app allows the user to explore FSSA with simulated data, data that is provided on the server, or data that the user provides.
It allows the user to change parameters as they please, gives visual results of the methods, and also allows the user to compare FSSA results to other
spectrum analysis methods such as multivariate singular spectrum analysis. The tool is easy to use and can act as a nice starting point for a user that wishes to
perform FSSA as a part of their data analysis.

Haghbin H., Najibi, S.M., Mahmoudvand R., Trinka J., Maadooliat M. (2019). Functional singular spectrum Analysis. Manuscript submitted for publication.

`fssa`

, `freconstruct`

,
`fwcor`

, `wplot`

, `fts`

, `plot.fts`

, `plot.fssa`

,
`cor.fts`

, `launchApp`

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