Input Data Formats Used by SSA Routines

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Description

The inputs of SSA can be quite different depending on the kind of SSA used. However, there is a common of all the variants of SSA and all the routines. The package tries hard to preserve the specifics of input object as much as possible. This means, that all the attributes, etc. are copied back to the reconstructed objects. This way, the result of the SSA decomposition of a 'ts' object is a 'ts' object as well.

For forecasting, it is not possible in general to preserve the attributes of the input objects. However, Rssa knows about some common time series classes (e.g. 'ts') and tries to infer the time scales for forecasted objects as well.

The input formats are as follows:

1d SSA and Toeplitz SSA

Input is assumed to be a simple vector, or vector-like object (e.g. univariare 'ts' or 'zooreg' object). Everything else is coerced to vector.

2d SSA

Input assumed to be a matrix. If there are any NA's then the shaped variant of 2d SSA will be used. All non-NA elements will be used as a mask.

nd SSA

Input assumed to be an array of arbitrary dimension. If there are any NA's then the shaped variant will be used.

MSSA

While the representation of a one dimensional time series in R is pretty obvious, there are multiple possible ways of defining the multivariate time series. Let us outline some common choices.

  • Matrix with separate series in the columns. Optionally, additional time structure like in 'mts' objects, can be embedded.

  • Matrix-like (e.g. a 'data.frame') object with series in the columns. In particular, 'data.frame' would be a result of reading the series from the file via 'read.table' function.

  • List of separate time series objects (e.g. a 'list' of 'ts' or 'zoo' objects).

Also, the time scales of the individual time series can be normalized via head or tail padding with NA (for example, as a result of the ts.union call), or specified via time series attributes. Or, everything can be mixed all together.

The ssa routine with 'kind = mssa' allows one to provide any of the outlined multivariate series formats. As usual, all the attributes, names of the series, NA padding, etc. is carefully preserved.

CSSA

Complex vectors are assumed at the input.

See Also

ssa

Examples

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s <- ssa(co2) # Perform the decomposition using the default window length
r <- reconstruct(s, groups = list(Trend = c(1, 4),
                                  Seasonality = c(2, 3))) # Reconstruct into 2 series
class(r$Trend) # Result is 'ts' object

# Simultaneous trend extraction using MSSA
s <- ssa(EuStockMarkets, kind = "mssa")
r <- reconstruct(s, groups = list(Trend = c(1,2)))
class(r$Trend) # Result is 'mts' object

# Trend forecast
f <- rforecast(s, groups = list(Trend = c(1, 2)), len = 50, only.new = FALSE)
class(f) # For 'ts' objects the time scales are inferred automatically

# Artificial image for 2dSSA
mx <- outer(1:50, 1:50,
            function(i, j) sin(2*pi * i/17) * cos(2*pi * j/7) + exp(i/25 - j/20)) +
      rnorm(50^2, sd = 0.1)
# Decompose 'mx' with circular window
s <- ssa(mx, kind = "2d-ssa", wmask = circle(5), neig = 10)
# Reconstruct
r <- reconstruct(s, groups = list(1, 2:5))
# Plot components, original image and residuals
plot(r)

# 3D-SSA example (2D-MSSA)
data(Barbara)

ss <- ssa(Barbara, L = c(50, 50, 1))
plot(ss)

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