Description Details Slots Examples

`FreqRep`

is an S4 class that encapsulates, for a multivariate time
series *Y_0i,…,Y_{n-1,i}*,
*i=1,...,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_ti <= q})*, orthe weighted

*L1*-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_tni / n* where *R_tnj* denotes the rank of
*Y_ti* among *Y_0,…,Y_{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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ```
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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