reconstruct: Reconstruction of a (detrended) time series from output...
In WaveletComp: Computational Wavelet Analysis
Description
Usage
Arguments
Value
Author(s)
References
See Also
Examples
Description
This function reconstructs a (detrended) time series analyzed
by wavelet transformation using either function
analyze.wavelet or function analyze.coherency, subject to
optional criteria concerning: minimum wavelet power, significance of wavelet power at a
given significance level, specification of (Fourier) periods or
period bands, exclusive use of the power ridge and/or the cone of influence.
An option is provided to prevent the reconstructed series from final rescaling
(applying the original (detrended) series' mean and standard deviation).
(If the object provided as input is of class "analyze.coherency",
then the number or name of the time series must be specified.)
Optional: plot of wavelets used for reconstruction, plot of
reconstructed series against original (detrended)
series. An option is given to individualize the time axis
by specifying tick marks and labels.
Output includes the original (detrended) and the reconstructed
time series, along with reconstruction waves and parameters.
Usage
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reconstruct(WT, my.series = 1, lvl = 0,
only.coi = FALSE,
only.sig = TRUE, siglvl = 0.05,
only.ridge = FALSE,
sel.period = NULL, sel.lower = NULL, sel.upper = NULL,
rescale = TRUE,
plot.waves = FALSE, plot.rec = TRUE,
lty = 1, lwd = 1, col = 1:2, ylim = NULL,
show.legend = TRUE,
legend.coords = "topleft", legend.horiz = FALSE, legend.text = NULL,
label.time.axis = TRUE,
show.date = FALSE, date.format = NULL, date.tz = NULL,
timelab = NULL, timetck = 0.02, timetcl = 0.5,
spec.time.axis = list(at = NULL, labels = TRUE,
las = 1, hadj = NA, padj = NA),
main.waves = NULL, main.rec = NULL, main = NULL,
lwd.axis = 1,
verbose = TRUE)
Arguments
WT
an object of class "analyze.wavelet" or "analyze.coherency"
my.series
In case class(WT) = "analyze.coherency": number (1 or 2) or name of the series to be analyzed.
Default: 1.
lvl
minimum level of wavelet power to be applied for the inclusion of reconstruction waves.
Default: 0.
only.coi
Exclude borders influenced by edge effects in reconstruction, i.e. include the cone of influence only? Logical.
Default: FALSE.
only.sig
Use wavelet power significance in reconstruction? Logical.
Default: TRUE.
siglvl
level of wavelet power significance to be applied for the inclusion of reconstruction waves.
Default: 0.05.
only.ridge
Select only the wavelet power ridge? Logical.
Default: FALSE.
sel.period
a vector of numbers to select Fourier periods (or closest available periods)
and corresponding wavelets for the reconstruction.
Default: NULL.
sel.lower
a number to define a lower Fourier period (or the closest available) for the selection
of a band of wavelets for the reconstruction.
(Only effective if sel.period = NULL.)
Default: NULL.
sel.upper
a number to define an upper Fourier period (or the closest available) for the selection
of a band of wavelets for the reconstruction.
(Only effective if sel.period = NULL.)
Default: NULL.
rescale
Shall the reconstructed series finally be rescaled to attain the original (detrended) series' mean and standard deviation? Logical.
Default: TRUE.
plot.waves
Shall reconstruction waves be plotted? Logical.
Default: FALSE.
plot.rec
Shall the reconstructed series (together with the original (detrended) series) be plotted? Logical.
Default: TRUE.
lty
parameter for the plot of original vs. reconstructed series: line type, e.g. 1:2.
Default: 1.
lwd
parameter for the plot of original vs. reconstructed series: line width, e.g. 1:2.
Default: 1.
col
parameter for the plot of original vs. reconstructed series: color of lines.
Default: 1:2.
ylim
numeric vector of length 2, providing the range of vertical coordinates for the plot.
Default: NULL.
show.legend
Include legend into the plot of original vs. reconstructed series? Logical.
Default: TRUE.
legend.coords
coordinates to position the legend (as in function legend).
Default: "topleft".
legend.horiz
Set the legend horizontally rather than vertically? Logical.
Default: FALSE.
legend.text
legend text. Default: c("original (detrended)", "reconstructed").
label.time.axis
Label the time axis? Logical.
Default: TRUE.
show.date
Show calendar dates? (Effective only if dates are available as row names or by variable
date in the data frame which is analyzed.) Logical.
Default: FALSE.
date.format
the format of calendar date given as a character string, e.g. "%Y-%m-%d", or equivalently "%F";
see strptime for a list of implemented date conversion specifications. Explicit information given here will overturn any specification
stored in WT. If unspecified, date formatting is attempted according to as.Date.
Default: NULL.
date.tz
a character string specifying the time zone of calendar date; see strptime. Explicit information given here will overturn
any specification stored in WT. If unspecified, "" (the local time zone) is used.
Default: NULL.
timelab
Time axis label.
Default: "index"; in case of a calendar axis: "calendar date".
timetck
length of tick marks on the time axis as a fraction of the smaller of the width or height of the plotting region; see par.
If timetck >= 0.5, timetck is interpreted as a fraction of the length of the time axis, so if timetck = 1
(and timetcl = NULL), vertical grid lines will be drawn.
Setting timetck = NA is to use timetcl = -0.5 (which is the R default setting of tck and tcl).
Default here: 0.02.
timetcl
length of tick marks on the time axis as a fraction of the height of a line of text; see par.
With timetcl = -0.5 (which is the R default setting of tcl), ticks will be drawn outward.
Default here: 0.5.
spec.time.axis
a list of tick mark and label specifications for individualized time axis labeling
(only effective if label.time.axis = TRUE):
[at:] locations of tick marks (when NULL, default plotting will be applied).
Valid tick marks can be provided as numerical values or as dates. Dates are used only in the case show.date = TRUE, however,
and date formats should conform to as.Date or the format given in date.format.
Default: NULL.
[labels:] either a logical value specifying whether annotations at the tick marks are the tick marks themselves,
or any vector of labels. If labels is non-logical, at should be of same length.
Default: TRUE.
[las:] the style of axis labels, see par.
Default: 1 (always horizontal).
[hadj:] adjustment of labels horizontal to the reading direction, see axis.
Default: NA (centering is used).
[padj:] adjustment of labels perpendicular to the reading direction (this can be a vector of adjustments for each label),
see axis.
Default: NA (centering is used).
Mismatches will result in a reset to default plotting.
main.waves
an overall title for the plot of reconstruction waves.
Default: NULL.
main.rec
an overall title for the plot of original vs. reconstructed series.
Default: NULL.
main
an overall title for both plots.
Default: NULL.
lwd.axis
line width of axes.
Default: 1.
verbose
Print verbose output on the screen? Logical.
Default: TRUE.
Value
A list of class reconstruct with the following elements:
series
a data frame building on WT$series with the following columns:
date : the calendar date (if available as column
in WT$series)
<x> : series <x>, with original name retained
: (detrended, if loess.span != 0)
<x>.trend : the trend series (if loess.span != 0)
<x>.r : the reconstructed (detrended) series
Row names are taken over from WT$series, and so are dates if given as row names.
If WT is of class analyze.coherency, the second series in the coherency analysis is retained;
if loess.span != 0, the second series is retained in the detrended version, and the trend is retained as well.
rec.waves
data frame of scaled waves used for reconstruction
loess.span
parameter alpha in loess controlling the degree of time series smoothing,
if the time series was detrended; no detrending if loess.span = 0.
lvl
minimum level of wavelet power for waves (wave segments) to be included
in the reconstruction
only.coi
Was the influence of edge effects excluded? I.e. was the cone of influence used only?
only.sig
Was wavelet power significance used in reconstruction?
siglvl
level of wavelet power significance
only.ridge
Was the wavelet power ridge used only?
rnum.used
the vector of Fourier period numbers used for reconstruction
rescale
Was the reconstructed series rescaled according to the mean and standard deviation
taken from the original (detrended) series?
dt
time resolution, i.e. sampling resolution in the time domain, 1/dt = number of observations per time unit
dj
frequency resolution, i.e. sampling resolution in the frequency domain, 1/dj = number of suboctaves (voices per octave)
Period
the Fourier periods
(measured in time units determined by dt, see the explanations concerning dt)
Scale
the scales (the Fourier periods divided by the Fourier factor)
nc
number of columns = number of observations = number of observation epochs; "epoch" meaning point in time
nr
number of rows = number of scales (Fourier periods)
axis.1
tick levels corresponding to the time steps used for (cross-)wavelet transformation: 1, 1+dt, 1+2dt, ....
The default time axis in plot functions provided by WaveletComp is determined by observation epochs, however; "epoch" meaning point in time.
axis.2
tick levels corresponding to the log of Fourier periods: log2(Period). This determines the period axis in plot functions provided by WaveletComp.
date.format
the format of calendar date (if available)
date.tz
the time zone of calendar date (if available)
Author(s)
Angi Roesch and Harald Schmidbauer
References
Carmona R., Hwang W.-L., and Torresani B., 1998.
Practical Time Frequency Analysis. Gabor and Wavelet Transforms with an Implementation in S.
Academic Press, San Diego.
Liu Y., Liang X.S., and Weisberg R.H., 2007.
Rectification of the Bias in the Wavelet Power Spectrum.
Journal of Atmospheric and Oceanic Technology 24, 2093–2102.
Torrence C., and Compo G.P., 1998.
A practical guide to wavelet analysis.
Bulletin of the American Meteorological Society 79 (1), 61–78.
See Also
analyze.wavelet, wt.image, wt.avg, wt.sel.phases, wt.phase.image, analyze.coherency,
wc.image, wc.avg, wc.sel.phases, wc.phasediff.image
Examples
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## Not run:
## The following example is adopted from Liu et al., 2007:
series.length = 6*128*24
x1 <- periodic.series(start.period = 1*24, length = series.length)
x2 <- periodic.series(start.period = 8*24, length = series.length)
x3 <- periodic.series(start.period = 32*24, length = series.length)
x4 <- periodic.series(start.period = 128*24, length = series.length)
x <- x1 + x2 + x3 + x4
plot(x, type = "l", xlab = "index", ylab = "", xaxs = "i",
main = "hourly series with periods of 1, 8, 32, 128 days")
my.data <- data.frame(x = x)
## Computation of wavelet power:
## a natural choice of 'dt' in the case of hourly data is 'dt = 1/24',
## resulting in one time unit equaling one day.
## This is also the time unit in which periods are measured.
my.w <- analyze.wavelet(my.data, "x",
loess.span = 0,
dt = 1/24, dj = 1/20,
lowerPeriod = 1/4,
make.pval = TRUE, n.sim = 10)
## Plot of wavelet power spectrum (with equidistant color breakpoints):
wt.image(my.w, color.key = "interval",
legend.params = list(lab = "wavelet power levels"),
periodlab = "period (days)")
## Reconstruction of the time series,
## including significant components only:
reconstruct(my.w)
## The same reconstruction, but showing wave components first:
reconstruct(my.w, plot.waves = TRUE)
## Reconstruction, including all components whether significant or not:
reconstruct(my.w, only.sig = FALSE)
## Reconstruction, including significant components,
## but selected periods only (e.g. ignoring period 8):
reconstruct(my.w, sel.period = c(1,32,128))
## Reconstruction, including significant components,
## but the ridge only:
reconstruct(my.w, only.ridge = TRUE)
## Alternate styles of the time axis:
## The plot with time elapsed in days, starting from 0 and proceeding
## in steps of 50 days (50*24 hours),
## instead of the (default) time index:
index.ticks <- seq(1, series.length, by = 50*24)
index.labels <- (index.ticks-1)/24
## Insert your specification of time axis:
reconstruct(my.w, only.ridge = TRUE,
timelab = "time elapsed (days)",
spec.time.axis = list(at = index.ticks, labels = index.labels))
## See the periods involved:
my.rec <- reconstruct(my.w, only.ridge = TRUE)
print(my.rec$Period[my.rec$rnum.used])
## The original and reconstructed time series can be retrieved:
plot(my.rec$series$x, type = "l", xlab = "index", ylab = "")
lines(my.rec$series$x.r, col="red")
legend("topleft", legend = c("original","reconstructed"),
lty = 1, col = c("black","red"))
## Please see also the examples in our guide booklet,
## URL http://www.hs-stat.com/projects/WaveletComp/WaveletComp_guided_tour.pdf.
## End(Not run)
WaveletComp documentation built on May 2, 2019, 6:33 a.m.
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Description Usage Arguments Value Author(s) References See Also Examples
Description
This function reconstructs a (detrended) time series analyzed
by wavelet transformation using either function
analyze.wavelet or function analyze.coherency, subject to
optional criteria concerning: minimum wavelet power, significance of wavelet power at a
given significance level, specification of (Fourier) periods or
period bands, exclusive use of the power ridge and/or the cone of influence.
An option is provided to prevent the reconstructed series from final rescaling
(applying the original (detrended) series' mean and standard deviation).
(If the object provided as input is of class "analyze.coherency",
then the number or name of the time series must be specified.)
Optional: plot of wavelets used for reconstruction, plot of reconstructed series against original (detrended) series. An option is given to individualize the time axis by specifying tick marks and labels.
Output includes the original (detrended) and the reconstructed time series, along with reconstruction waves and parameters.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | reconstruct(WT, my.series = 1, lvl = 0,
only.coi = FALSE,
only.sig = TRUE, siglvl = 0.05,
only.ridge = FALSE,
sel.period = NULL, sel.lower = NULL, sel.upper = NULL,
rescale = TRUE,
plot.waves = FALSE, plot.rec = TRUE,
lty = 1, lwd = 1, col = 1:2, ylim = NULL,
show.legend = TRUE,
legend.coords = "topleft", legend.horiz = FALSE, legend.text = NULL,
label.time.axis = TRUE,
show.date = FALSE, date.format = NULL, date.tz = NULL,
timelab = NULL, timetck = 0.02, timetcl = 0.5,
spec.time.axis = list(at = NULL, labels = TRUE,
las = 1, hadj = NA, padj = NA),
main.waves = NULL, main.rec = NULL, main = NULL,
lwd.axis = 1,
verbose = TRUE)
|
Arguments
WT |
an object of class |
my.series |
In case Default: |
lvl |
minimum level of wavelet power to be applied for the inclusion of reconstruction waves. Default: |
only.coi |
Exclude borders influenced by edge effects in reconstruction, i.e. include the cone of influence only? Logical. Default: |
only.sig |
Use wavelet power significance in reconstruction? Logical. Default: |
siglvl |
level of wavelet power significance to be applied for the inclusion of reconstruction waves. Default: 0.05. |
only.ridge |
Select only the wavelet power ridge? Logical. Default: |
sel.period |
a vector of numbers to select Fourier periods (or closest available periods) and corresponding wavelets for the reconstruction. Default: |
sel.lower |
a number to define a lower Fourier period (or the closest available) for the selection
of a band of wavelets for the reconstruction. Default: |
sel.upper |
a number to define an upper Fourier period (or the closest available) for the selection
of a band of wavelets for the reconstruction. Default: |
rescale |
Shall the reconstructed series finally be rescaled to attain the original (detrended) series' mean and standard deviation? Logical. Default: |
plot.waves |
Shall reconstruction waves be plotted? Logical. Default: |
plot.rec |
Shall the reconstructed series (together with the original (detrended) series) be plotted? Logical. Default: |
lty |
parameter for the plot of original vs. reconstructed series: line type, e.g. Default: |
lwd |
parameter for the plot of original vs. reconstructed series: line width, e.g. Default: |
col |
parameter for the plot of original vs. reconstructed series: color of lines. Default: |
ylim |
numeric vector of length Default: |
show.legend |
Include legend into the plot of original vs. reconstructed series? Logical. Default: |
legend.coords |
coordinates to position the legend (as in function Default: |
legend.horiz |
Set the legend horizontally rather than vertically? Logical. Default: |
legend.text |
legend text. Default: |
label.time.axis |
Label the time axis? Logical. Default: |
show.date |
Show calendar dates? (Effective only if dates are available as row names or by variable
Default: |
date.format |
the format of calendar date given as a character string, e.g. Default: |
date.tz |
a character string specifying the time zone of calendar date; see Default: |
timelab |
Time axis label. Default: |
timetck |
length of tick marks on the time axis as a fraction of the smaller of the width or height of the plotting region; see Default here: |
timetcl |
length of tick marks on the time axis as a fraction of the height of a line of text; see Default here: |
spec.time.axis |
a list of tick mark and label specifications for individualized time axis labeling
(only effective if
Mismatches will result in a reset to default plotting. |
main.waves |
an overall title for the plot of reconstruction waves. Default: |
main.rec |
an overall title for the plot of original vs. reconstructed series. Default: |
main |
an overall title for both plots. Default: |
lwd.axis |
line width of axes. Default: |
verbose |
Print verbose output on the screen? Logical. Default: |
Value
A list of class reconstruct with the following elements:
series |
a data frame building on
Row names are taken over from WT$series, and so are dates if given as row names.
If |
rec.waves |
data frame of scaled waves used for reconstruction |
loess.span |
parameter |
lvl |
minimum level of wavelet power for waves (wave segments) to be included in the reconstruction |
only.coi |
Was the influence of edge effects excluded? I.e. was the cone of influence used only? |
only.sig |
Was wavelet power significance used in reconstruction? |
siglvl |
level of wavelet power significance |
only.ridge |
Was the wavelet power ridge used only? |
rnum.used |
the vector of Fourier period numbers used for reconstruction |
rescale |
Was the reconstructed series rescaled according to the mean and standard deviation taken from the original (detrended) series? |
dt |
time resolution, i.e. sampling resolution in the time domain, |
dj |
frequency resolution, i.e. sampling resolution in the frequency domain, |
Period |
the Fourier periods
(measured in time units determined by |
Scale |
the scales (the Fourier periods divided by the Fourier factor) |
nc |
number of columns = number of observations = number of observation epochs; "epoch" meaning point in time |
nr |
number of rows = number of scales (Fourier periods) |
axis.1 |
tick levels corresponding to the time steps used for (cross-)wavelet transformation: |
axis.2 |
tick levels corresponding to the log of Fourier periods: |
date.format |
the format of calendar date (if available) |
date.tz |
the time zone of calendar date (if available) |
Author(s)
Angi Roesch and Harald Schmidbauer
References
Carmona R., Hwang W.-L., and Torresani B., 1998. Practical Time Frequency Analysis. Gabor and Wavelet Transforms with an Implementation in S. Academic Press, San Diego.
Liu Y., Liang X.S., and Weisberg R.H., 2007. Rectification of the Bias in the Wavelet Power Spectrum. Journal of Atmospheric and Oceanic Technology 24, 2093–2102.
Torrence C., and Compo G.P., 1998. A practical guide to wavelet analysis. Bulletin of the American Meteorological Society 79 (1), 61–78.
See Also
analyze.wavelet, wt.image, wt.avg, wt.sel.phases, wt.phase.image, analyze.coherency,
wc.image, wc.avg, wc.sel.phases, wc.phasediff.image
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 | ## Not run:
## The following example is adopted from Liu et al., 2007:
series.length = 6*128*24
x1 <- periodic.series(start.period = 1*24, length = series.length)
x2 <- periodic.series(start.period = 8*24, length = series.length)
x3 <- periodic.series(start.period = 32*24, length = series.length)
x4 <- periodic.series(start.period = 128*24, length = series.length)
x <- x1 + x2 + x3 + x4
plot(x, type = "l", xlab = "index", ylab = "", xaxs = "i",
main = "hourly series with periods of 1, 8, 32, 128 days")
my.data <- data.frame(x = x)
## Computation of wavelet power:
## a natural choice of 'dt' in the case of hourly data is 'dt = 1/24',
## resulting in one time unit equaling one day.
## This is also the time unit in which periods are measured.
my.w <- analyze.wavelet(my.data, "x",
loess.span = 0,
dt = 1/24, dj = 1/20,
lowerPeriod = 1/4,
make.pval = TRUE, n.sim = 10)
## Plot of wavelet power spectrum (with equidistant color breakpoints):
wt.image(my.w, color.key = "interval",
legend.params = list(lab = "wavelet power levels"),
periodlab = "period (days)")
## Reconstruction of the time series,
## including significant components only:
reconstruct(my.w)
## The same reconstruction, but showing wave components first:
reconstruct(my.w, plot.waves = TRUE)
## Reconstruction, including all components whether significant or not:
reconstruct(my.w, only.sig = FALSE)
## Reconstruction, including significant components,
## but selected periods only (e.g. ignoring period 8):
reconstruct(my.w, sel.period = c(1,32,128))
## Reconstruction, including significant components,
## but the ridge only:
reconstruct(my.w, only.ridge = TRUE)
## Alternate styles of the time axis:
## The plot with time elapsed in days, starting from 0 and proceeding
## in steps of 50 days (50*24 hours),
## instead of the (default) time index:
index.ticks <- seq(1, series.length, by = 50*24)
index.labels <- (index.ticks-1)/24
## Insert your specification of time axis:
reconstruct(my.w, only.ridge = TRUE,
timelab = "time elapsed (days)",
spec.time.axis = list(at = index.ticks, labels = index.labels))
## See the periods involved:
my.rec <- reconstruct(my.w, only.ridge = TRUE)
print(my.rec$Period[my.rec$rnum.used])
## The original and reconstructed time series can be retrieved:
plot(my.rec$series$x, type = "l", xlab = "index", ylab = "")
lines(my.rec$series$x.r, col="red")
legend("topleft", legend = c("original","reconstructed"),
lty = 1, col = c("black","red"))
## Please see also the examples in our guide booklet,
## URL http://www.hs-stat.com/projects/WaveletComp/WaveletComp_guided_tour.pdf.
## End(Not run)
|
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