gapfill: Perform SSA gapfilling via forecast

Description

Perform SSA gapfilling of the series.

Usage

# S3 method for 1d.ssa
gapfill(x, groups, base = c("original", "reconstructed"),
        method = c("sequential", "simultaneous"),
        alpha = function(len) seq.int(0, 1, length.out = len), ...,
        drop = TRUE, drop.attributes = FALSE, cache = TRUE)
# S3 method for mssa
gapfill(x, groups, base = c("original", "reconstructed"),
        alpha = function(len) seq.int(0, 1, length.out = len), ...,
        drop = TRUE, drop.attributes = FALSE, cache = TRUE)
# S3 method for cssa
gapfill(x, groups, base = c("original", "reconstructed"),
        method = c("sequential", "simultaneous"),
        alpha = function(len) seq.int(0, 1, length.out = len), ...,
        drop = TRUE, drop.attributes = FALSE, cache = TRUE)
# S3 method for toeplitz.ssa
gapfill(x, groups, base = c("original", "reconstructed"),
        method = c("sequential", "simultaneous"),
        alpha = function(len) seq.int(0, 1, length.out = len), ...,
        drop = TRUE, drop.attributes = FALSE, cache = TRUE)

Value

List of objects with gaps filled in. Elements of the list have the same names as elements of groups. If group is unnamed, corresponding component gets name `Fn', where `n' is its index in

groups list.

Or, the forecasted object itself, if length of groups is one and 'drop = TRUE'.

Arguments

x: Shaped SSA object holding the decomposition
groups: list, the grouping of eigentriples to be used in the forecast
base: series used as a 'seed' for gapfilling: original or reconstructed according to the value of groups argument
method: method used for gapfilling, "sequential" means to filling by a recurrent forecast from complete parts; "simultaneous" tries to build a projections onto the signal subspace. See 'References' for more info.
alpha: weight used for combining forecasts from left and right when method = "sequential"; 0.5 means that the forecasts are averaged, 0 (1) means that only forecast from the left (right correspondingly) is used, arbitrary function could be specified; by default linear weights are used.
...: additional arguments passed to reconstruct routines
drop: logical, if 'TRUE' then the result is coerced to series itself, when possible (length of 'groups' is one)
drop.attributes: logical, if 'TRUE' then the attributes of the input series are not copied to the reconstructed ones.
cache: logical, if 'TRUE' then intermediate results will be cached in the SSA object.

Details

The function fills in the missed entries in the series. Both methods described in Golyandina and Osipov (2007) are implemented:

method = "sequential" performs forecast from complete chunks onto incomplete. For internal gaps forecast is performed from both sides of the gap and average is taken in order to reduce the forecast error. For gaps in the beginning or end of the series the method coincides with ordinary recurrent forecast;
method = "simultaneous" performs gap filling via projections onto signal subspace. The method may fail if insufficient complete observations are provided.

Details of the used algorithms see in Golyandina et al (2018), Algorithms 3.8 and 3.9 respectively.

References

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

N. Golyandina, E. Osipov (2007): The "Caterpillar"-SSA method for analysis of time series with missing values. Journal of Statistical Planning and Inference, Vol. 137, No. 8, Pp 2642--2653 https://www.gistatgroup.com/cat/mvssa1en.pdf

Examples

Run this code

# Produce series with gaps
F <- co2; F[100:200] <- NA
# Perform shaped SSA
s <- ssa(F, L = 72)
# Fill in gaps using the trend and 2 periodicty components
g <- gapfill(s, groups = list(1:6))
# Compare the result
plot(g)
lines(co2, col = "red")

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