The Rfssa package provides the collection of necessary functions to implement functional singular spectrum analysis (FSSA)-based methods for analyzing univariate and multivariate functional time series (FTS). Univariate and multivariate FSSA are novel, non-parametric methods used to perform decomposition and reconstruction of univariate and multivariate FTS respectively. In addition, the FSSA-based routines may be performed on FTS whose variables are observed over a one or two-dimensional domain. Finally, one may perform FSSA recurrent or fssa vector forecasting of univariate or multivariate FTS observed over one-dimensional domains. Forecasting of FTS whose variables are observed over domains of dimension greater than one is under development.
The use of the package starts with the decomposition of functional time
fts) objects using the
fssa routine. Then a suitable grouping of the
principal components is required for reconstruction (
fforecast) which can be done heuristically by looking at the
plots of the decomposition. Once a suitable grouping is chosen,
one may perform reconstruction where the sum of all the elements between the disjoint
groups approximates the original FTS. One may also choose to perform
forecasting after a grouping is chosen which returns future observations in
each FTS specified by the groups.
This version of the package leverages a new S4 object for FTS objects (
Along with providing the raw, sampled data, the new object may be specified using a provided basis and grid, a requested
basis and grid, or a mixture of provided and requested elements. We note that
the FTS object may be univariate or multivariate and variables may be observed
over one or two-dimensional domains. Validity checking of the S4 object
constructor inputs was also added to help guide the user. The plotting of FTS
objects was also updated to allow the user to plot FTS variables
observed over two-dimensional domains. Next, the FSSA routine (
updated to perform faster by leveraging the RSpectra and RcppEigen R packages,
and the Eigen C++ package. We achieved a roughly 20 times speed up for
certain data examples. We updated the plotting of fssa objects to
allow for plotting of left singular functions that correspond with FTS
variables observed over a two-dimensional domain.
We updated FSSA reconstruction
freconstruct to handle
FTS whose variables are observed over one or two-dimensional domains. We also
updated FTS arithmetic (such as FTS addition, FTS subtraction, etc.) to allow
the user to perform scalar-FTS arithmetic on different variables of a
multivariate FTS. In addition, we also now host the
Montana datasets on GitHub to significantly decrease the size of the package. In
order to load the data, one simply needs to use the
load_github_data function. This same
function can also be used to load data from any other public GitHub repository.
The first piece of new functionality that has been added is that the user
may now specify univariate or multivariate FTS comprised of variables observed
over one or two-dimensional domains. In addition, forecasting of univariate
and multivariate FTS observed over one-dimensional domains by FSSA/MFSSA
recurrent forecasting and FSSA/MFSSA vector forecasting has also been added.
We have also added in a new data set (
Montana) which provides the data for a
multivariate FTS observed over different dimensional domains.
The package update also includes updates to the 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., Morteza Najibi, S., Mahmoudvand, R., Trinka, J., and Maadooliat, M. (2021). Functional singular spectrum analysis. Stat. e330 STAT-20-0240.R1.
Trinka J., Haghbin H., Maadooliat M. (Accepted) Multivariate Functional Singular Spectrum Analysis: A Nonparametric Approach for Analyzing Multivariate Functional Time Series. In: Bekker A., Ferreira, J., Arashi M., Chen D. (eds) Innovations in Multivariate Statistical Modeling: Navigating Theoretical and Multidisciplinary Domains. Emerging Topics in Statistics and Biostatistics. Springer, Cham.
Trinka J. (2021) Functional Singular Spectrum Analysis: Nonparametric Decomposition and Forecasting Approaches for Functional Time Series [Doctoral dissertation, Marquette University]. ProQuest Dissertations Publishing.
Trinka, J., Haghbin, H., and Maadooliat, M. (2021). Functional time series forecasting: Functional singular spectrum analysis approaches. Version 4 retrieved from https://arxiv.org/abs/2011. 13077.
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