FreqRep-class | R Documentation |
FreqRep
is an S4 class that encapsulates, for a multivariate time
series (Y_{t,i})_{t=0,\ldots,n-1}
,
i=1,\ldots,d
the data structures for the storage of a frequency representation. Examples
of such frequency representations include
the Fourier transformation of the clipped time series
(\{I\{Y_{t,i} \leq q\})
, or
the weighted L_1
-projection of (Y_{t,i})
onto an harmonic
basis.
Examples are realized by implementing a sub-class to
FreqRep
.
Currently, implementations for the two examples mentioned above are available:
ClippedFT
and
QRegEstimator
.
It is always an option to base the calculations on the pseudo data
R_{t,n,i} / n
where R_{t,n,i}
denotes the rank of
Y_{t,i}
among (Y_{t,i})_{t=0,\ldots,n-1}
.
To allow for a block bootstrapping procedure a number of B
estimates
determined from bootstrap replications of the time series which are yield by
use of a BootPos
-object can be stored on initialization.
The data in the frequency domain is stored in the array values
, which
has dimensions (J,P,K,B+1)
, where J
is the number of
frequencies
, P
is the dimension of the time series,
K
is the number of levels
and B
is
the number of bootstrap replications requested on intialization.
In particular, values[j,i,k,1]
corresponds to the time series' frequency
representation with frequencies[j]
, dimension i
and levels[k]
, while
values[j,i,k,b+1]
is the for the same, but determined from the
b
th block bootstrapped replicate of the time series.
Y
The time series of which the frequency representation is to be determined.
frequencies
The frequencies for which the frequency representation will
be determined. On initalization
frequenciesValidator
is called, so that it
will always be a vector of reals from [0,\pi]
.
Also, only Fourier frequencies of the form
2\pi j / n
with integers j
and n
the length(Y)
are allowed.
levels
The levels for which the frequency representation will be
determined. If the flag isRankBased
is set to FALSE
,
then it can be any vector of reals. If isRankBased
is set
to TRUE
, then it has to be from [0,1]
.
values
The array holding the determined frequency representation. Use a
getValues
method of the relevant subclass to access it.
isRankBased
A flag that is FALSE
if the determined values
are based on the original time series and TRUE
if it
is based on the pseudo data as described in the Details
section of this topic.
positions.boot
An object of type BootPos
,
that is used to determine the block bootstrapped
replicates of the time series.
B
Number of bootstrap replications to perform.
Y <- rnorm(32)
freq <- 2*pi*c(0:31)/32
levels <- c(0.25,0.5,0.75)
cFT <- clippedFT(Y, freq, levels)
plot(cFT)
# Get values for all Fourier frequencies and all levels available.
V.all <- getValues(cFT)
# Get values for every second frequency available
V.coarse <- getValues(cFT, frequencies = 2*pi*c(0:15)/16, levels = levels)
# Trying to get values on a finer grid of frequencies than available will
# yield a warning and then all values with frequencies closest to that finer
# grid.
V.fine <- getValues(cFT, frequencies = 2*pi*c(0:63)/64, levels = levels)
# Finally, get values for the available Fourier frequencies from [0,pi] and
# only for tau=0.25
V.part <- getValues(cFT, frequencies = 2*pi*c(0:16)/32, levels = c(0.25))
# Alternatively this can be phrased like this:
V.part.alt <- getValues(cFT, frequencies = freq[freq <= pi], levels = c(0.25))
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