rforecast function

Perform recurrent SSA forecasting of the series

Perform recurrent SSA forecasting of the series.

## 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 groups argument

• 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 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 routines applies the recurrent SSA forecasting algorithm to produce the new series which is expected to 'continue' the current series on the basis of a given decomposition. The algorithm sequentialy projects the incomplete embedding vectors (from either the original or the reconstructed series) onto the subspace spanned by the selected eigentriples of the decomposition to derive the missed (last) values of the such vectors. Then the filled value In such a way the forecasting elements are produced on one-by-one basis.

It is shown in Golyandina et al (2001) that this approach corresponds to application of a linear recurrence formula (the same formula as described in lrr) to initial data taken from either the original or the reconstructed series.

In particular, the $m$-th step of the forecast is calculated by means of linear recurrence relation (see lrr) as $y_{n+m}=\sum_{k=1}^{L-1} a_k y_{n+m-k}$ 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. The row forecast is more complicated and is based on a multivariate LRR. Forecast uses the formulae from Golyandina and Stepanov (2005) and Golyandina et.al (2015).

For details of 1D-SSA recurrent forecasting, see Section 3.2.1.2 and Algorithm 3.5 in Golyandina et al (2018). For details of MSSA recurrent forecasting, see Section 4.3.1.2 and Algorithm 4.4 (column forecasting).

Returns

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. tools:::Rd_expr_doi("10.18637/jss.v067.i02")

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. https://www.gistatgroup.com/gus/mssa2.pdf

See Also

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

Examples

# 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")