Rfssa (version 2.0.0)

fssa: Functional Singular Spectrum Analysis

Description

This is a function which performs the decomposition (including embedding and functional SVD steps) stage for univariate functional singular spectrum analysis (ufssa) or multivariate functional singular spectrum analysis (mfssa). The algorithm (ufssa or mfssa) is chosen based on whether the supplied input is a univariate or multivariate functional time series (fts) object. The type parameter can also be set to "mfssa" if the user wishes to perform ufssa of a univariate fts object using the mfssa code. Also note that the variables of the fts maybe observed over different dimensional domains where the maximum dimension currently supported is two.

Usage

fssa(Y, L = NA, ntriples = 20, type = "ufssa")

Arguments

Y

An object of class fts.

L

A positive integer giving the window length.

ntriples

A positive integer specifying the number of eigentriples to calculate in the decomposition.

type

A string indicating which type of fssa to perform. Use type="ufssa" to perform univariate fssa (default for univariate fts). Use type="mfssa" to perform multivariate fssa (default for multivariate fts).

Value

An object of class fssa, which is a list of functional objects and the following components:

values

A numeric vector of eigenvalues.

L

The specified window length.

N

The length of the functional time series.

Y

The original functional time series.

Examples

# NOT RUN {
## Univariate FSSA Example on Callcenter data
require(Rfssa)
load_github_data("https://github.com/haghbinh/Rfssa/blob/master/data/Callcenter.RData")
## Define functional objects
D <- matrix(sqrt(Callcenter$calls), nrow = 240)
N <- ncol(D)
time <- seq(ISOdate(1999, 1, 1), ISOdate(1999, 12, 31), by = "day")
K <- nrow(D)
u <- seq(0, K, length.out = K)
d <- 22 # Optimal Number of basis elements
## Define functional time series
Y <- fts(list(D), list(list(d, "bspline")), list(u))
Y
plot(Y, mains = c("Sqrt of Call Center Data"))
## Univariate functional singular spectrum analysis
L <- 28
U <- fssa(Y, L)
plot(U, d = 13)
plot(U, d = 9, type = "lheats")
plot(U, d = 9, type = "lcurves")
plot(U, d = 9, type = "vectors")
plot(U, d = 10, type = "periodogram")
plot(U, d = 10, type = "paired")
plot(U, d = 10, type = "wcor")
gr <- list(1, 2:3, 4:5, 6:7, 8:20)
Q <- freconstruct(U, gr)
plot(Y, mains = "Sqrt of Call Center Data")
plot(Q[[1]], mains = "1st Component")
plot(Q[[2]], mains = "2nd Component")
plot(Q[[3]], mains = "3rd Component")
plot(Q[[4]], mains = "4th Component")
plot(Q[[5]], mains = "5th Component (Noise)")

## Other visualisation types for object of class "fts":

plot(Q[[1]], type = "3Dsurface", xlabels = "Intraday", tlabels = "Day", zlabels = "Output")
# Visualizing the first 60 observations in the reconstructed fts.
plot(Q[[2]][1:60], type = "heatmap", xlabels = "Intraday intervals")
plot(Q[[3]][1:60], type = "3Dline", xlabels = "Intraday", tlabels = "Day", zlabels = "Output")

## Multivariate FSSA Example on bivariate intraday
## temperature curves and smoothed images of vegetation
require(Rfssa)
load_github_data("https://github.com/haghbinh/Rfssa/blob/master/data/Montana.RData")
Temp <- Montana$Temp
NDVI <- Montana$NDVI
d_temp <- 11
d_NDVI <- 13
## Define functional time series
Y <- fts(
  list(Temp / sd(Temp), NDVI), list(
    list(d_temp, "bspline"),
    list(d_NDVI, d_NDVI, "bspline", "bspline")
  ),
  list(c(0, 23), list(c(1, 33), c(1, 33)))
)
# Plot the first 100 observations
plot(Y[1:100],
  xlabels = c("Time", "Lon."), ylabels = c("Temperature (\u00B0C)", "Lat."),
  zlabels = c("", "NDVI"), mains = c("Temperature Curves", "NDVI Images")
)
plot(Y, types = c("3Dline", "heatmap"), vars = c(1, 1))
plot(Y, types = "heatmap", vars = 2)
plot(Y, vars = c(2, 1))
L <- 45
## Multivariate functional singular spectrum analysis
U <- fssa(Y, L)
plot(U, type = "values", d = 10)
plot(U, type = "vectors", d = 4)
plot(U, type = "lheats", d = 4)
plot(U, type = "lcurves", d = 4, vars = c(1))
plot(U, type = "paired", d = 6)
plot(U, type = "wcor", d = 10)
plot(U, type = "periodogram", d = 4)
# Reconstruction of multivariate fts observed over different dimensional domains
Q <- freconstruct(U = U, groups = list(c(1), c(2:3), c(4)))
# Plotting reconstructions to show accuracy
plot(Q[[1]]) # mean
plot(Q[[2]]) # periodic
plot(Q[[3]]) # trend
# }