Description Usage Arguments Details Value Examples
Returns a list of two arrays lowerCIs
and upperCIs
that contain
the upper and lower limits for a level 1alpha
confidence interval of
the quantity of interest. Each array is of dimension [J,K1,K2]
if a
univariate time series is being analysed or of dimension [J,D1,K1,D2,K2]
,
where J=length(frequencies)
, D1=length(d1)
, D2=length(d2)
,
K1=length(levels.1)
, and K2=length(levels.2))
.
At position (j,k1,k2)
or (j,i1,k1,i2,k2)
the real (imaginary)
part of the returned values are the bounds of the confidence interval for the
the real (imaginary) part of the quantity under anlysis, which corresponds to
frequencies[j]
, d1[i1]
, d2[i2]
, levels.1[k1]
and
levels.2[k2]
closest to the Fourier frequencies, levels.1
and
levels.2
available in object
; closest.pos
is used
to determine what closest to means.
1 2 3 4 5 6 7 8 9 10 11 12 13  ## S4 method for signature 'SmoothedPG'
getPointwiseCIs(
object,
quantity = c("spectral density", "coherency", "coherence"),
frequencies = 2 * pi * (0:(lenTS(object@qPG@freqRep@Y) 
1))/lenTS(object@qPG@freqRep@Y),
levels.1 = getLevels(object, 1),
levels.2 = getLevels(object, 2),
d1 = 1:(dim(object@values)[2]),
d2 = 1:(dim(object@values)[4]),
alpha = 0.1,
type = c("naive.sd", "boot.sd", "boot.full")
)

object 

quantity 
a flag indicating for which the pointwise confidence bands will be determined. Can take one of the possible values discussed above. 
frequencies 
a vector of frequencies for which to get the result 
levels.1 
the first vector of levels for which to get the result 
levels.2 
the second vector of levels for which to get the result 
d1 
optional parameter that determine for which j1 to return the data; may be a vector of elements 1, ..., D 
d2 
same as d1, but for j2 
alpha 
the level of the confidence interval; must be from (0,1) 
type 
a flag indicating which type of confidence interval should be returned; can take one of the three values discussed above. 
Currently, pointwise confidence bands for two different quantity
are implemented:
"spectral density"
: confidence intervals for the quantile spectral
density as described in Kley et. al (2016) for the univariate case and
in Barunik and Kley (2015) for the multivariate case.
"coherency"
: confidence intervals for the quantile coherency as
described in Barunik and Kley (2015).
Currently, three different type
s of confidence intervals are
available:
"naive.sd"
: confidence intervals based on the asymptotic
normality of the smoothed quantile periodogram; standard deviations
are estimated using getSdNaive
.
"boot.sd"
: confidence intervals based on the asymptotic
normality of the smoothed quantile periodogram; standard deviations
are estimated using getSdBoot
.
"boot.full"
: confidence intervals determined by estimating the
quantiles of he distribution of the smoothed quantile periodogram,
by the empirical quantiles of the sample of bootstrapped
replications.
Returns a named list of two arrays lowerCIS
and upperCIs
containing the lower and upper bounds for the confidence intervals.
1 2 3 4 5 6 7 8 9  sPG < smoothedPG(rnorm(2^10), levels.1=0.5)
CI.upper < Re(getPointwiseCIs(sPG)$upperCIs[,1,1])
CI.lower < Re(getPointwiseCIs(sPG)$lowerCIs[,1,1])
freq = 2*pi*(0:1023)/1024
plot(x = freq, y = rep(0.25/(2*pi),1024),
ylim=c(min(CI.lower), max(CI.upper)),
type="l", col="red") # true spectrum
lines(x = freq, y = CI.upper)
lines(x = freq, y = CI.lower)

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