Core data of periodic time series
Vec.RdCore data of periodic time series.
Usage
Vec(x, ...)
tsMatrix(x, ...)
tsVector(x, ...)
tsVec(x, ...)
pcMatrix(x, ...)
pcArray(x, ndim = 3, ...)
pctsArray(x, ndim = 3, ...)Details
These functions give the core data in various common forms.
The data values can be extracted as a vector from a periodic time
series object, say x, with as.vector(x) or as(x,
"vector"). Similarly, as.matrix() and as(x, "matrix")
extract the data as a matrix containing one column per variable. For
multivariate time series the vector returned by as.vector(x)
(or as(x, "vector")) is equivalent to
as.vector(as.matrix(x)).
Vec() is like as.vector() but returns the result as a
matrix with one column (column vector), as is usual in matrix
calculus. The default does literally this.
The most common representation of data in statistics is matrix-like with one column per variable. The descriptions of algorithms for multivariate time series however usually define the vector of observations at a given time to be a column vector. In particular, implementations of the Kalman filter often require precisely this arrangement. In that case the data matrix is the transposed of the more common one and the vectorising operation stacks the observations, not the variables.
The functions tsMatrix(), tsVector() and tsVec()
provide the analogues of as.vector(), as.matrix() and
Vec() for the ``transposed'' arrangement.
These functions may look redundant since they are simple combinations of the above and traspose operations. Having functions makes for more readable programming. They may be more efficient, as well, for example if the underlying time series class stores the data in the transposed format.
pcMatrix() and pcArray() also give the core
data. Effectively, they give an additional dimension to the
seasons. The season becomes the first dimension since for column
oriented data the season changes fastest. pcMatrix is most
suitable for univariate time series, pcArray() for
multivariate. Note that pcArray() easily extends to multiple
periodicities although currently (2019-04-19) there are no methods
that exploit this.
For univariate time series, in the matrix returned by
pcMatrix() each row represents the data for one season and each
column for one cycle. For multivariate time series, the matrices for
each variable are put next to each other.
pcArray() returns the data as an array, whose last dimension
corresponds to variables. In the default case the array is
3-dimensonal with dimensions (season, year, variable).
pctsArray() is a variant of pcArray() corresponding to
the arrangement of tsMatrix(). The ordering of the dimensions
here is (variable, season, cycle).
Examples
## window to make number of years different from number of months
ap <- pcts(window(AirPassengers, start = c(1956, 1)))
class( as.vector(ap) )
#> [1] "numeric"
class( as(ap, "vector") )
#> [1] "numeric"
dim( as.matrix(ap) )
#> [1] 60 1
dim( as(ap, "matrix") )
#> [1] 60 1
dim( tsMatrix(ap) )
#> [1] 1 60
class( tsVector(ap) )
#> [1] "numeric"
dim( tsVec(ap) )
#> [1] 60 1
dim( pcMatrix(ap) )
#> [1] 12 5
dim( pcArray(ap) )
#> [1] 12 5 1
dim( pctsArray(ap) )
#> [1] 1 12 5
dfr <- pcts(dataFranses1996)
dim(dfr) # c(148, 19)
#> [1] 148 19
nSeasons(dfr) # 4
#> [1] 4
length(as.vector(dfr))
#> [1] 2812
all.equal(as.vector(dfr)[1:148], as.matrix(dfr)[ , 1]) # TRUE
#> [1] TRUE
all.equal(tsVector(dfr)[1:19], unname(as.matrix(dfr)[1, ])) # TRUE
#> [1] TRUE
dim( as.matrix(dfr) ) # c(148, 19)
#> [1] 148 19
dim( tsMatrix(dfr) ) # c(19, 148)
#> [1] 19 148
all.equal(tsMatrix(dfr)[ , 1], as.matrix(dfr)[1, ]) # TRUE
#> [1] TRUE
dim( Vec(dfr) )
#> [1] 2812 1
dim( tsVec(dfr) )
#> [1] 2812 1
all.equal(tsVec(dfr)[1:19], unname(as.matrix(dfr)[1, ])) # TRUE
#> [1] TRUE
dim( pcMatrix(dfr) ) # c(4, 703), one row for each season
#> [1] 4 703
dim( pcArray(dfr) ) # c(4, 37, 19), note: 703 == 37*19
#> [1] 4 37 19
dim( pctsArray(dfr) ) # c(19, 4, 37), note: 703 == 37*19
#> [1] 19 4 37