reconstruct function

Perform a series reconstruction

Reconstruct the data given the SSA decomposition and the desired grouping of the elementary components.

## S3 method for class 'ssa'
reconstruct(x, groups, ..., drop.attributes = FALSE, cache = TRUE)

Arguments

• x: SSA object
• groups: list of numeric vectors, indices of elementary components used for reconstruction, the entries of the list can be named, see 'Value' for more information
• ...: further arguments passed to routines (e.g. to decompose routine if the continuation is desired).
• drop.attributes: logical, if 'TRUE' then the attributes of the input objects are not copied to the reconstructed ones.
• cache: logical, if 'TRUE' then intermediate results will be cached in the SSA object.

Details

Reconstruction is performed in a common form for different types of input objects. See Section 1.1.2.6 in Golyandina et al (2018) for the explanation. Formal algorithms are described in this book in Algorithm 2.2 for 1D-SSA, Algorithm 4.3 for MSSA, Algorithm 5.2 for 2D-SSA and Algorithm 5.6 for Shaped 2D-SSA.

Fast implementation of reconstruction with the help of FFT is described in Korobeynikov (2010) for the 1D case and in Section 6.2 (Rank-one quasi-hankelization) of Golyandina et al (2015) for the general case.

Returns

List of reconstructed objects. Elements of the list have the same names as elements of groups. If the group is unnamed, then corresponding component will obtain name Fn', where n' is its index in groups list.

Note

By default (argument drop.attributes) the routine tries to preserve all the attributes of the input object. This way, for example, the reconstruction result of 'ts' object is the 'ts' object with the same time scale.

References

Golyandina N., Korobeynikov A., Zhigljavsky A. (2018): Singular Spectrum Analysis with R. Use R!. Springer, Berlin, Heidelberg.

Korobeynikov, A. (2010): Computation- and space-efficient implementation of SSA. Statistics and Its Interface, Vol. 3, No. 3, Pp. 257-268

Golyandina, N., Korobeynikov, A., Shlemov, A. and Usevich, K. (2015): Multivariate and 2D Extensions of Singular Spectrum Analysis with the Rssa Package. Journal of Statistical Software, Vol. 67, Issue 2. tools:::Rd_expr_doi("10.18637/jss.v067.i02")

See Also

Rssa for an overview of the package, as well as, ssa-input, ssa, plot.reconstruction,

Examples

# Decompose 'co2' series with default parameters
s <- ssa(co2)
# Reconstruct the series, grouping elementary series.
r <- reconstruct(s, groups = list(Trend = c(1, 4), Season1 = c(2,3), Season2 = c(5, 6)))
plot(r)
# 'groups' argument might contain duplicate entries as well
r <- reconstruct(s, groups = list(1, 1:4, 1:6))
plot(r)

# Real example: Mars photo
data(Mars)
# Decompose only Mars image (without backgroud)
s <- ssa(Mars, mask = Mars != 0, wmask = circle(50), kind = "2d-ssa")
# Reconstruct and plot trend
plot(reconstruct(s, 1), fill.uncovered = "original")
# Reconstruct and plot texture pattern
plot(reconstruct(s, groups = list(c(13, 14, 17, 18))))

# Decompose 'EuStockMarkets' series with default parameters
s <- ssa(EuStockMarkets, kind = "mssa")
r <- reconstruct(s, groups = list(Trend = 1:2))
# Plot original series, trend and residuals superimposed
plot(r, plot.method = "xyplot", superpose = TRUE,
     auto.key = list(columns = 3),
     col = c("blue", "green", "red", "violet"),
     lty = c(rep(1, 4), rep(2, 4), rep(3, 4)))