FSSA"
In Rfssa: Functional Singular Spectrum Analysis

Options and Parameters defined in the Side Bar Panel

Contains the inputs that will be used in different sub-panels. The following inputs will be used in sub-panels Basis Functions (to generate the basis functions), Data Description (for Smoothing, FPCA, SSA and FSSA), and Forecasting:

Degree of B-spline Basis
Deg. of freedom of B-spline or Fourier Basis
Groups: 3rd step of the SSA(FSSA) algorithm:
- Each group is specified via a vector (e.g. 'c(1,2,4)' or '1:3') and seperated from other groups via comma (',')
d is the dimensions used in FPCA, SSA and FSSA (Scree, W.Correlation, Paired, Singular Vectors & Functions, and Periodogram Plots)
Functions
- Demean: Subtract the mean to obtain mean-zero functions
- Dbl Range: extending the y-axis to cover all potential mirrord functions (e.g. sometime FPCs may get multiply by a '-' sign)
Win.L.: Window length parameter used in SSA and FSSA
run (F)SSA button is used to run SSA and FSSA using the specified parameters for the given dataset. The top inputs (above red line) are mostly to describe the basis functions. The bottom inputs (below red line) are used to specify SSA and FSSA parameters.

For more details on the option and parameters we refer the readers to the References given in the end of the page.

Options in the Main Panel

1. Input Data

One can either use the files posted in Server

Callcenter: used in the FSSA paper (package)
NDVI and EVI: Jambi Sattelite data used in the FSSA paper (package)

or simulate FTS (see FSSA paper for more details),

or upload any FTS to be analyzed.

2. Basis Functions

Using a visualization technique, we illustrate the B-spline (or Fourier) basis that is used in the algorithm.

3. Data Analysis

Summary of the data:

Functional Time Series: Provide a variety of visualizations to describe the data.
Plot Choices:
- All: Cobmines all FTS
- Multiple: Combine FTS at different Period(frequency) together and the combined clusters can be tracked by the end user
- Single: Track FTS individually
Plots:
- Time Series (Raw Data): provides the observed FTS
- True Functions: provides the TRUE FTS (in the case of simulation)
- Functional SSA: provides FSSA results from the Rfssa package
- Multivariate SSA: provides MSSA results from the Rssa package
- Functional PCA: provides FPCA results from the fda package
- Basis Functions: embeds the basis functions on top of FTS
- Smoothing: provides the results of smoothing via basis functions
How many basis? (GCV): provides the optimal number of basis based on GCV criteria.

In this panel we can also select plots (outputs) under SSA and FSSA:

Scree plot: based on the trajectory matrix
W.Correlation plot: w-correlation plot
Paired plots
Singular Vectors plots
Periodogram plots
Singular Functions (Heat or Regular plots)
Reconstruction of FTS using different Type of plots (Heat, Regular, 3D(line) and 3D(surface))

4. Forecasting

This sub-panel would be accessible after user runs the FSSA procedure, and it includes the functionalities of R-forecasting and V-forecasting algorithms.

5. Manual

The sub-panel that contains this instruction manual.

References

Haghbin, H., Najibi, S. M., Mahmoudvand, R., Trinka, J., Maadooliat, M. (2021). Functional singular spectrum analysis. Stat, 10(1), e330.
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., Maadooliat, M. (2022). Multivariate Functional Singular Spectrum Analysis: A Nonparametric Approach for Analyzing Multivariate Functional Time Series. In Innovations in Multivariate Statistical Modeling: Navigating Theoretical and Multidisciplinary Domains (pp. 187-221). Cham: Springer International Publishing.
Trinka, J., Haghbin, H., Shang, H., Maadooliat, M. (2023). Functional Time Series Forecasting: Functional Singular Spectrum Analysis Approaches. Stat, e621.