# Perform recurrent SSA forecasting of the series

### Description

Perform recurrent SSA forecasting of the series.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
## S3 method for class '1d.ssa'
rforecast(x, groups, len = 1, base = c("reconstructed", "original"),
only.new = TRUE, reverse = FALSE, ...,
drop = TRUE, drop.attributes = FALSE, cache = TRUE)
## S3 method for class 'toeplitz.ssa'
rforecast(x, groups, len = 1, base = c("reconstructed", "original"),
only.new = TRUE, reverse = FALSE, ...,
drop = TRUE, drop.attributes = FALSE, cache = TRUE)
## S3 method for class 'mssa'
rforecast(x, groups, len = 1, base = c("reconstructed", "original"),
direction = c("row", "column"), only.new = TRUE, ..., drop = TRUE,
drop.attributes = FALSE, cache = TRUE)
## S3 method for class 'cssa'
rforecast(x, groups, len = 1, base = c("reconstructed", "original"),
only.new = TRUE, reverse = FALSE, ...,
drop = TRUE, drop.attributes = FALSE, cache = TRUE)
## S3 method for class 'pssa.1d.ssa'
rforecast(x, groups, len = 1, base = c("reconstructed", "original"),
only.new = TRUE, reverse = FALSE, ...,
drop = TRUE, drop.attributes = FALSE, cache = TRUE)
``` |

### 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 |

`base` |
series used as a 'seed' of forecast: original or
reconstructed according to the value of |

`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 |

`reverse` |
logical, direction of forecast in 1D SSA case, 'FALSE' (default) means that the forecast moves forward in the time and 'TRUE' means the opposite |

`...` |
additional arguments passed to |

`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 routines applies the recurrent SSA forecasting algorithm to produce the new series which is expected to 'continue' the current series on the basis of the decomposition given. The algorithm sequentialy projects the incomplete embedding vectors (either original or from reconstructed series) onto the subspace spanned by the selected eigentriples of the decomposition to derive the missed (ending) values of the such vectors.

In such a way the forecasted elements of the series are produced on one-by-one basis.

In particular, the *m*-th step of the forecast is calculated by
means of linear recurrence relation (see `lrr`

) as
*y_{n+m}=∑_{k=1}^{L-1} a_k y_{n+m-k}* where the starting points
*y_{n-(L-2)}*, ..., *y_{n}* are taken from the reconstructed
time series (`base="reconstructed"`

) or from the initial
(`base="initial"`

) time series.

For multichannel SSA the column forecast is obtained via applying the LRR to each series separately. Forecast uses the formulae from (Golyandina and Stepanov, 2005, and 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,
`forecast`

,
`vforecast`

,
`bforecast`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
# 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.
rfor <- rforecast(s, groups = list(c(1,4), 1:4), len = 24, only.new=FALSE)
matplot(data.frame(c(co2, rep(NA, 24)), rfor), type = "l")
# Forecast `co2' trend by SSA with projections
s <- ssa(co2, column.projector = 2, row.projector = 2)
len <- 100
rfor <- rforecast(s, groups = list(trend = seq_len(nspecial(s))), len = len, only.new = FALSE)
matplot(data.frame(c(co2, rep(NA, len)), rfor), 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(rforecast(s, groups = list(all = 1:6), len = 100, only.new = FALSE), type = "l")
``` |