Perform vector SSA forecasting of the series

Description

Perform vector SSA forecasting of the series.

Usage

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## S3 method for class '1d.ssa'
vforecast(x, groups, len = 1, only.new = TRUE, ...,
          drop = TRUE, drop.attributes = FALSE)
## S3 method for class 'toeplitz.ssa'
vforecast(x, groups, len = 1, only.new = TRUE, ...,
          drop = TRUE, drop.attributes = FALSE)
## S3 method for class 'toeplitz.ssa'
vforecast(x, groups, len = 1, only.new = TRUE, ...,
          drop = TRUE, drop.attributes = FALSE)
## S3 method for class 'mssa'
vforecast(x, groups, len = 1,
          direction = c("row", "column"),
          only.new = TRUE, ...,
          drop = TRUE, drop.attributes = FALSE)
## S3 method for class 'cssa'
vforecast(x, groups, len = 1, only.new = TRUE, ...,
          drop = TRUE, drop.attributes = FALSE)
## S3 method for class 'pssa.1d.ssa'
vforecast(x, groups, len = 1, only.new = TRUE, ...,
          drop = TRUE, drop.attributes = FALSE)

Arguments

x

SSA object holding the decomposition

groups

list, the grouping of eigentriples to be used in the forecast

len

integer, the desired length of the forecasted series

direction

direction of forecast in multichannel SSA case, "column" stands for so-called L-forecast and "row" stands for K-forecast

only.new

logical, if 'TRUE' then only forecasted values are returned, whole series otherwise

...

additional arguments passed to decompose 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.

Details

The routines applies the vectors SSA forecasting algorithm to produce the new series which is expected to 'continue' the current series on the basis of the decomposition given. Vector forecast differs from recurrent forecast in such way that it continues the set of vectors in the subspace spanning the chosen eigenvectors (the same formula as described in lrr is used for constructing of the last components of the new vectors) and then derive the series out of this extended set of vectors.

For multichannel SSA, forecast uses the formulae from (Golyandina et al, 2015).

Value

List of forecasted objects. 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'.

References

Golyandina, N., Nekrutkin, V. and Zhigljavsky, A. (2001): Analysis of Time Series Structure: SSA and related techniques. Chapman and Hall/CRC. ISBN 1584881941

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. https://www.jstatsoft.org/article/view/v067i02

Golyandina, N. and Stepanov, D. (2005): SSA-based approaches to analysis and forecast of multidimensional time series. In Proceedings of the 5th St.Petersburg Workshop on Simulation, June 26-July 2, 2005, St. Petersburg State University, St. Petersburg, 293–298. http://www.gistatgroup.com/gus/mssa2.pdf

See Also

Rssa for an overview of the package, as well as, rforecast, bforecast, forecast.

Examples

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# Decompose 'co2' series with default parameters
s <- ssa(co2)
# Produce 24 forecasted values of the series using different sets of eigentriples
# as a base space for the forecast.
vfor <- vforecast(s, groups = list(c(1,4), 1:4), len = 24, only.new=FALSE)
matplot(data.frame(c(co2, rep(NA, 24)), vfor), type="l")

# Forecast `co2' trend by SSA with projections
s <- ssa(co2, column.projector = 2, row.projector = 2)
len <- 100
vfor <- vforecast(s, groups = list(trend = seq_len(nspecial(s))), len = len, only.new = FALSE)
matplot(data.frame(c(co2, rep(NA, len)), vfor), type = "l")

# Forecast finite rank series with polynomial component by SSA with projections
v <- 5000 * sin(2*pi / 13 * (1:100)) +  (1:100)^2 + 10000
s <- ssa(v, row.projector = 2, column.projector = 2)
plot(vforecast(s, groups = list(all = 1:6), len = 100, only.new = FALSE), type = "l")

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