| Title: | Robust Time Series Filters |
|---|---|
| Description: | Implementations for several robust procedures that allow for (online) extraction of the signal of univariate or multivariate time series by applying robust regression techniques to a moving time window are provided. Included are univariate filtering procedures based on repeated-median regression as well as hybrid and trimmed filters derived from it; see Schettlinger et al. (2006) <doi:10.1515/BMT.2006.010>. The adaptive online repeated median by Schettlinger et al. (2010) <doi:10.1002/acs.1105> and the slope comparing adaptive repeated median by Borowski and Fried (2013) <doi:10.1007/s11222-013-9391-7> choose the width of the moving time window adaptively. Multivariate versions are also provided; see Borowski et al. (2009) <doi:10.1080/03610910802514972> for a multivariate online adaptive repeated median and Borowski (2012) <doi:10.17877/DE290R-14393> for a multivariate slope comparing adaptive repeated median. Furthermore, a repeated-median based filter with automatic outlier replacement and shift detection is provided; see Fried (2004) <doi:10.1080/10485250410001656444>. |
| Authors: | Roland Fried [aut, cre], Karen Schettlinger [aut], Matthias Borowski [aut], Robin Nunkesser [ctb], Thorsten Bernholt [ctb] |
| Maintainer: | Roland Fried <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 4.1.5 |
| Built: | 2024-12-14 06:26:05 UTC |
| Source: | CRAN |
Implementations for several robust procedures that allow for (online) extraction of the signal of univariate or multivariate time series by applying robust regression techniques to a moving time window are provided. Included are univariate filtering procedures based on repeated-median regression as well as hybrid and trimmed filters derived from it; see Schettlinger et al. (2006) <doi:10.1515/BMT.2006.010>. The adaptive online repeated median by Schettlinger et al. (2010) <doi:10.1002/acs.1105> and the slope comparing adaptive repeated median by Borowski and Fried (2013) <doi:10.1007/s11222-013-9391-7> choose the width of the moving time window adaptively. Multivariate versions are also provided; see Borowski et al. (2009) <doi:10.1080/03610910802514972> for a multivariate online adaptive repeated median and Borowski (2012) <doi:10.17877/DE290R-14393> for a multivariate slope comparing adaptive repeated median. Furthermore, a repeated-median based filter with automatic outlier replacement and shift detection is provided; see Fried (2004) <doi:10.1080/10485250410001656444>.
The DESCRIPTION file:
| Package: | robfilter |
| Version: | 4.1.5 |
| Date: | 2024-07-14 |
| Title: | Robust Time Series Filters |
| Authors@R: | c(person("Roland", "Fried", email = "[email protected]", role = c("aut", "cre")), person("Karen", "Schettlinger", email = "[email protected]", role = "aut"), person("Matthias", "Borowski", email = "[email protected]", role = "aut"), person("Robin", "Nunkesser", role = "ctb"), person("Thorsten", "Bernholt", role = "ctb")) |
| Author: | Roland Fried [aut, cre], Karen Schettlinger [aut], Matthias Borowski [aut], Robin Nunkesser [ctb], Thorsten Bernholt [ctb] |
| Maintainer: | Roland Fried <[email protected]> |
| Imports: | stats, graphics, utils |
| Depends: | R (>= 3.6.0), robustbase, MASS, lattice |
| Description: | Implementations for several robust procedures that allow for (online) extraction of the signal of univariate or multivariate time series by applying robust regression techniques to a moving time window are provided. Included are univariate filtering procedures based on repeated-median regression as well as hybrid and trimmed filters derived from it; see Schettlinger et al. (2006) <doi:10.1515/BMT.2006.010>. The adaptive online repeated median by Schettlinger et al. (2010) <doi:10.1002/acs.1105> and the slope comparing adaptive repeated median by Borowski and Fried (2013) <doi:10.1007/s11222-013-9391-7> choose the width of the moving time window adaptively. Multivariate versions are also provided; see Borowski et al. (2009) <doi:10.1080/03610910802514972> for a multivariate online adaptive repeated median and Borowski (2012) <doi:10.17877/DE290R-14393> for a multivariate slope comparing adaptive repeated median. Furthermore, a repeated-median based filter with automatic outlier replacement and shift detection is provided; see Fried (2004) <doi:10.1080/10485250410001656444>. |
| License: | GPL (>= 2) |
| URL: | https://msnat.statistik.tu-dortmund.de/en/team/chair/ |
| LazyData: | yes |
| Repository: | CRAN |
| NeedsCompilation: | yes |
| Packaged: | 2024-07-14 14:44:17 UTC; abbas |
| Date/Publication: | 2024-07-16 09:20:05 UTC |
| RoxygenNote: | 7.2.1 |
Index of help topics:
adore.filter A Robust Adaptive Online Repeated Median Filter
for Univariate Time Series
const Correction factors to achieve unbiasedness of
the Qn scale estimator
const.Q Correction factors to achieve unbiasedness of
the regression-free Q scale estimator
critvals Critical Values for the RM Goodness of Fit Test
dfs Degrees of freedom for the SCARM test
statistic.
dr.filter Deepest Regression (DR) filter
dw.filter Robust Double Window Filtering Methods for
Univariate Time Series
hybrid.filter Robust Hybrid Filtering Methods for Univariate
Time Series
lms.filter Least Median of Squares (LMS) filter
lqd.filter Least Quartile Difference filter
lts.filter Least Trimmed Squares (LTS) filter
madore.filter A multivariate adaptive online repeated median
filter
med.filter Median (MED) filter
mscarm.filter MSCARM (Multivariate Slope Comparing Adaptive
Repeated Median)
multi.ts Generated Multivariate Time Series
rm.filter Repeated Median (RM) filter
robfilter-package Robust Time Series Filters
robreg.filter Robust Regression Filters for Univariate Time
Series
robust.filter Robust Filtering Methods for Univariate Time
Series
scarm.filter SCARM (Slope Comparing Adaptive Repeated
Median)
sizecorrection Bias correction factors for the robust scale
estimators MAD, Sn, Qn, and LSH
timecorrection Correction factors for the scale estimation of
the filtering procedure proposed by Fried
(2004).
var.n Variance of the Repeated Median slope
estimator.
wrm.filter Weighted Repeated Median Filters for Univariate
Time Series
wrm.smooth Weighted Repeated Median Smoothing
adore.filter A Robust Adaptive Online Repeated Median Filter
for Univariate Time Series
const.Q Correction factors to achieve unbiasedness of
the regression-free Q scale estimator
const Correction factors to achieve unbiasedness of
the Qn scale estimator
critvals Critical Values for the RM Goodness of Fit Test
dfs Degrees of freedom for the SCARM test statistic
dr.filter Deepest Regression (DR) filter
dw.filter Robust Double Window Filtering Methods for
Univariate Time Series
hybrid.filter Robust Hybrid Filtering Methods for Univariate
Time Series
lms.filter Least Median of Squares (LMS) filter
lqd.filter Least Quartile Difference (LQD) filter
lts.filter Least Trimmed Squares (LTS) filter
madore.filter A Robust Adaptive Online Filter for
Multivariate Time Series
med.filter Median (MED) filter
multi.ts Generated Multivariate Time Series
rm.filter Repeated Median (RM) filter
robreg.filter Robust Regression Filters for Univariate Time
Series
robust.filter Robust Filtering Methods for Univariate Time
Series
scarm.filter SCARM (Slope Comparing Adaptive Repeated Median)
var.n Variance of the Repeated Median slope estimator
wrm.filter Weighted Repeated Median Filters for Univariate
Time Series
wrm.smooth Weighted Repeated Median Smoothing
Roland Fried [aut, cre], Karen Schettlinger [aut], Matthias Borowski [aut], Robin Nunkesser [ctb], Thorsten Bernholt [ctb]
Maintainer: Roland Fried <[email protected]>
Procedure for robust online extraction of low frequency components (the signal) from a univariate time series by a moving window technique with adaptive window width selection (ADaptive Online REpeated median FILTER).
adore.filter(y, p.test=15, minNonNAs=5, min.width=10, max.width=200, width.search="geometric", rtr=2, extrapolate=FALSE, calc.qn=FALSE, sign.level=0.1)adore.filter(y, p.test=15, minNonNAs=5, min.width=10, max.width=200, width.search="geometric", rtr=2, extrapolate=FALSE, calc.qn=FALSE, sign.level=0.1)
y |
a numeric vector or (univariate) time series object. |
p.test |
defines the number of most recent Repeated Median residuals within each window used to test the goodness of fit of the online signal level. |
minNonNAs |
a positive integer |
min.width |
a positive integer |
max.width |
a positive integer |
width.search |
a character string defining the search algorithm used for finding an adequate window width at each point in time.
|
rtr |
a value in 0, 1, 2 specifying whether a 'restrict to range' rule should be applied.
|
extrapolate |
a logical indicating whether the level estimations should be extrapolated to the beginning of the time series. The extrapolation consists of all fitted values within the first time window. |
calc.qn |
a logical indicating whether the Qn scale (Rousseeuw, Croux, 1993) should also be calculated along with the signal level
as an estimate of the standard deviation in each window.
Here, the |
sign.level |
significance level of the test procedure; must be a value in |
The adore.filter works by applying Repeated Median (RM)
regression (Siegel, 1982) to a moving time window with a length varying between
min.width and max.width.
For each point in time, the window width is adapted to the current data situation by a goodness of fit test for
the most recent signal level estimation.
The test uses the absolute value of the sum of the RM residuals in the subset specified by p.test.
The critical value for the test decision corresponds to a slightly modified 0.95-quantile of the
distribution of the test statistic and is stored in the data set critvals.
A more detailed description of the filter can be found in Schettlinger, Fried, Gather (2010).
adore.filter returns an object of class adore.filter.
An object of class adore.filter is a list containing the
following components:
level |
a numeric vector containing the signal level extracted by the RM filter with adaptive window width. |
slope |
a numeric vector containing the corresponding slope within each time window. |
width |
a numeric vector containing the corresponding window width used for the level and slope estimations. |
level.list |
a list which contains with as many elements as the length of the input time series.
If at time |
slope.list |
a list containing the slope estimations corresponding to the values in |
width.list |
a list containing the window widths used for the estimations in |
sigma |
a numeric vector containing the corresponding scale within each time window estimated by the robust Qn estimator
(only calculated if |
In addition, the original input time series is returned as list
member y, and the settings used for the analysis are
returned as the list members min.width, max.width, width.search,
p.test, minNonNAs, rtr, extrapolate, and calc.qn.
Application of the function plot to an object of class
aoRM returns a plot showing the original time series
with the filtered output.
Karen Schettlinger
Rousseeuw, P. J., Croux, C. (1993) Alternatives to the Median Absolute Deviation, Journal of the American Statistical Association 88, 1273-1283.
Schettlinger, K., Fried, R., Gather, U. (2010)
Real Time Signal Processing by Adaptive Repeated Median Filters,
International Journal of Adaptive Control and Signal Processing 24(5), 346-362.
Siegel, A.F. (1982)
Robust Regression Using Repeated Medians,
Biometrika 69 (1),
242-244.
robreg.filter, wrm.filter, madore.filter, scarm.filter.
# # # # # # # # # # # Short and noise-free time series series <- c(rep(0,30),rep(10,30),seq(10,5,length=20),seq(5,15,length=20)) # Adaptive online signal extraction without & with 'restrict to range' rule t.without.rtr <- adore.filter(series, rtr=0) plot(t.without.rtr) t.with.rtr1 <- adore.filter(series, rtr=1) lines(t.with.rtr1$level, col="blue") t.with.rtr2 <- adore.filter(series) lines(t.with.rtr2$level, col="green3",lty=2) legend("top",c("Signal with rtr=1","Signal with rtr=2"),col=c("blue","green3"),lty=c(1,2),bty="n") # # # # # # # # # # # Short and noise-free time series + 1 outlier ol.series <- series ol.series[63] <- 3 # Adaptive online signal extraction without & with 'restrict to range' rule t.without.rtr <- adore.filter(ol.series, rtr=0) plot(t.without.rtr) t.with.rtr1 <- adore.filter(ol.series, rtr=1) lines(t.with.rtr1$level, col="blue") t.with.rtr2 <- adore.filter(ol.series) lines(t.with.rtr2$level, col="green3",lty=2) legend("top",c("Signal with rtr=1","Signal with rtr=2"),col=c("blue","green3"),lty=c(1,2),bty="n") # # # # # # # # # # # Noisy time series with level shifts, trend changes and shifts in the scale of the error term true.signal <- c(rep(0,150),rep(10,150),seq(10,5,length=100),seq(5,15,length=100)) series2 <- true.signal + c(rnorm(250,sd=1), rnorm(200,sd=3), rnorm(50,sd=1)) # Adaptive online signal extraction with additional Qn scale estimation s2 <- adore.filter(series2, calc.qn=TRUE) par(mfrow=c(3,1)) plot(s2) plot(s2$sigma,type="l",main="Corresponding Qn Scale Estimation",ylab="sigma",xlab="time") lines(c(rep(1,250),rep(3,200),rep(1,150)),col="grey") legend("topleft",c("True scale","Qn"),lty=c(1,1),col=c("grey","black"),bty="n") plot(s2$width,type="l",main="Corresponding Window Width",ylab="width",xlab="time")# # # # # # # # # # # Short and noise-free time series series <- c(rep(0,30),rep(10,30),seq(10,5,length=20),seq(5,15,length=20)) # Adaptive online signal extraction without & with 'restrict to range' rule t.without.rtr <- adore.filter(series, rtr=0) plot(t.without.rtr) t.with.rtr1 <- adore.filter(series, rtr=1) lines(t.with.rtr1$level, col="blue") t.with.rtr2 <- adore.filter(series) lines(t.with.rtr2$level, col="green3",lty=2) legend("top",c("Signal with rtr=1","Signal with rtr=2"),col=c("blue","green3"),lty=c(1,2),bty="n") # # # # # # # # # # # Short and noise-free time series + 1 outlier ol.series <- series ol.series[63] <- 3 # Adaptive online signal extraction without & with 'restrict to range' rule t.without.rtr <- adore.filter(ol.series, rtr=0) plot(t.without.rtr) t.with.rtr1 <- adore.filter(ol.series, rtr=1) lines(t.with.rtr1$level, col="blue") t.with.rtr2 <- adore.filter(ol.series) lines(t.with.rtr2$level, col="green3",lty=2) legend("top",c("Signal with rtr=1","Signal with rtr=2"),col=c("blue","green3"),lty=c(1,2),bty="n") # # # # # # # # # # # Noisy time series with level shifts, trend changes and shifts in the scale of the error term true.signal <- c(rep(0,150),rep(10,150),seq(10,5,length=100),seq(5,15,length=100)) series2 <- true.signal + c(rnorm(250,sd=1), rnorm(200,sd=3), rnorm(50,sd=1)) # Adaptive online signal extraction with additional Qn scale estimation s2 <- adore.filter(series2, calc.qn=TRUE) par(mfrow=c(3,1)) plot(s2) plot(s2$sigma,type="l",main="Corresponding Qn Scale Estimation",ylab="sigma",xlab="time") lines(c(rep(1,250),rep(3,200),rep(1,150)),col="grey") legend("topleft",c("True scale","Qn"),lty=c(1,1),col=c("grey","black"),bty="n") plot(s2$width,type="l",main="Corresponding Window Width",ylab="width",xlab="time")
This matrix contains correction factors for the univariate Qn scale estimator (Rousseeuw, Croux, 1993) to achieve unbiasedness under Gaussian noise. The madore.filter estimates the local error covariance matrix by the orthogonalized Gnanadesikan-Kettenring estimator (Gnanadesikan, Kettenring, 1972, Maronna, Zamar, 2002) which is based on the Qn scale estimator.
constconst
A (96x2)-matrix containing the correction factors for the univariate Qn scale estimator for the samples sizes .
The correction factors have been obtained by simulations.
Gnanadesikan, R., Kettenring, J.R. (1972)
Robust Estimates, Residuals, and Outlier Detection with Multiresponse Data,
Biometrics 28, 81-124.
Maronna, R.A., Zamar, R.H. (2002)
Robust Estimates of Location and Dispersion for High-Dimensional Datasets,
Technometrics 44, 307-317.
Rousseeuw, P.J., Croux, C. (1993) Alternatives to the Median Absolute Deviation, Journal of the American Statistical Association 88, 1273-1283.
Correction factors for the regression-free Q scale estimator (Rousseeuw and Hubert, 1996, Gelper et al., 2009) to achieve unbiasedness under Gaussian noise; required by the function scarm.filter.
data(const.Q)data(const.Q)
The format is: num [1:151] NA NA NA NA 2.17 ...
The correction factors have been obtained by simulations.
Rousseeuw, P. and Hubert, M. (1996)
Regression-free and robust estimation of scale for bivariate data,
Computational Statistics and Data Analysis, 21(1), 67-85.
Gelper, S., Schettlinger, K., Croux, C., and Gather, U. (2009)
Robust online scale estimation in time series: A model-free approach,
Journal of Statistical Planning and Inference, 139(2), 335-349.
This matrix contains critical values for the goodness of fit test
for the last fitted value of a Repeated Median regression fit
to a sample of size n. The critical values are based on the 0.95-quantiles
of the distribution of a test statistic corresponding to the absolute value of
the sum of a subset of residual signs. The critical value for a test based on the
last nI out of n observations corresponds to critvals[n,nI].
critvalscritvals
A (600x61)-matrix containing 30550 observations.
Simulation.
Schettlinger, K., Fried, R., Gather, U. (2008)
Real Time Signal Processing by Adaptive Repeated Median Filters,
International Journal of Adaptive Control and Signal Processing, submitted.
Siegel, A.F. (1982)
Robust Regression Using Repeated Medians,
Biometrika 69 (1),
242-244.
This matrix contains degrees of freedom for the t-distributed SCARM test statistic; required by the function scarm.filter.
data(dfs)data(dfs)
A data frame with 20 observations on the following 20 variables.
X5a numeric vector
X10a numeric vector
X15a numeric vector
X20a numeric vector
X25a numeric vector
X30a numeric vector
X35a numeric vector
X40a numeric vector
X45a numeric vector
X50a numeric vector
X55a numeric vector
X60a numeric vector
X65a numeric vector
X70a numeric vector
X75a numeric vector
X80a numeric vector
X85a numeric vector
X90a numeric vector
X95a numeric vector
X100a numeric vector
The SCARM test from the function scarm.filter is based on the difference of Repeated Median slopes computed in a left-hand and right-hand window. The distribution of the SCARM test statistic is approximated by a t-distribution where the degrees of freedom depend on the width of the left- and right-hand window. This matrix delivers suitable degrees of freedom, obtained by simulations.
The degrees of freedom have been obtained by simulations.
Borowski, M. and Fried, R. (2011) Robust moving window regression for online signal extraction from non-stationary time series: online window width adaption by testing for signal changes, submitted.
This function extracts signals from time series by means of Deepest regression in a moving time window.
dr.filter(y, width, online = FALSE, extrapolate = TRUE)dr.filter(y, width, online = FALSE, extrapolate = TRUE)
y |
a numeric vector or (univariate) time series object. |
width |
a positive integer defining the window width used for fitting. |
online |
a logical indicating whether the current level estimate is
evaluated at the most recent time within each time window
( |
extrapolate |
a logical indicating whether the level
estimations should be extrapolated to the edges of the time series. |
dr.filter is suitable for extracting low
frequency components (the signal) from a time series which
may be contaminated with outliers and can contain level shifts.
For this, robust Deepest Regression is applied to a moving
window, and the signal level is estimated by the fitted value
either at the end of each time window for online signal
extraction without time delay (online=TRUE) or in the
centre of each time window (online=FALSE).
dr.filter returns an object of class robreg.filter.
An object of class robreg.filter is a list containing the
following components:
level |
a data frame containing the extracted signal level. |
slope |
a data frame containing the corresponding slope within each time window. |
In addition, the original input time series is returned as list
member y, and the settings used for the analysis are
returned as the list members width, online and extrapolate.
Application of the function plot to an object of class
robreg.filter returns a plot showing the original time series
with the filtered output.
Roland Fried, Karen Schettlinger and Matthias Borowski
Davies, P.L., Fried, R., Gather, U. (2004)
Robust Signal Extraction for On-Line Monitoring Data,
Journal of Statistical Planning and Inference 122,
65-78.
Gather, U., Schettlinger, K., Fried, R. (2006)
Online Signal Extraction by Robust Linear Regression,
Computational Statistics 21(1),
33-51.
Schettlinger, K., Fried, R., Gather, U. (2006) Robust Filters for Intensive Care Monitoring: Beyond the Running Median, Biomedizinische Technik 51(2), 49-56.
# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with DR filter: y.rr <- dr.filter(y,width=41,online=TRUE) plot(y.rr)# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with DR filter: y.rr <- dr.filter(y,width=41,online=TRUE) plot(y.rr)
Procedures for robust (online) extraction of low frequency components (the signal) from a univariate time series based on a moving window technique using two nested time windows in each step.
dw.filter(y, outer.width, inner.width, method = "all", scale = "MAD", d = 2, minNonNAs = 5, online = FALSE, extrapolate = TRUE)dw.filter(y, outer.width, inner.width, method = "all", scale = "MAD", d = 2, minNonNAs = 5, online = FALSE, extrapolate = TRUE)
y |
a numeric vector or (univariate) time series object. |
outer.width |
a positive integer specifying the window width
of the outer window used for determining the final estimate. |
inner.width |
a positive integer (not larger than |
method |
a (vector of) character string(s) containing the method(s) to be used for the estimation
of the signal level. |
scale |
a character string specifying the method to be used for robust estimation of the local variability (within one time window). Possible values are:
|
d |
a positive integer defining factor the current scale estimate is multiplied with for
determining the trimming boundaries for outlier detection. |
minNonNAs |
a positive integer defining the minimum number
of non-missing observations within each window which is required
for a ‘sensible’ estimation. Default: if windows contain
less than |
online |
a logical indicating whether the current level and
scale estimates are evaluated at the most recent time
within each (inner and outer) window ( |
extrapolate |
a logical indicating whether the level
estimations should be extrapolated to the edges of the time series. |
dw.filter is suitable for extracting low
frequency components (the signal) from a time series
which may be contaminated with outliers and can contain level
shifts. For this, moving window techniques are applied.
A short inner window of length inner.width is used in each
step for calculating an initial level estimate (by using either
the median or a robust regression fit) and a robust estimate of
the local standard deviation. Observations deviating strongly from this
initial fit are trimmed from an outer time window of length
outer.width, and the signal level is estimated from the
remaining observations (by using either a location or regression
estimator). Values specified in method determine which
combination of estimation methods should be applied to the inner
and outer window (see section ‘Methods’ below).
The applied method should be chosen based on an a-priori
guess of the underlying signal and the data quality: Location
based method (MED / MTM) are recommended in case
of a locally (piecewise) constant signal, regression based
approaches (RM / DWRM / TRM / MRM) in
case of locally linear, monotone trends.
Since no big differences have been reported between TRM
and MRM, the quicker and somewhat more efficient
TRM option might be preferred. DWRM is the quickest
of all regression based methods and performs better than the
ordinary RM at shifts, but it is the least robust and
least efficient method.
If location based methods are used, the inner.width should
be chosen at least twice the length of expected patches of
subsequent outliers in the time series; if regression based
methods are used, the inner.width should be at least three
times that length, otherwise outlier patches can influence the
estimations strongly. To increase the efficiency of the final
estimates, outer.width can then be chosen rather large -
provided that it is smaller than the time between subsequent
level shifts.
For robust scale estimation, MAD is the classical choice;
SN is a somewhat more efficient and almost equally robust
alternative, while QN is much more efficient if the
window widths are not too small, and it performs very well at the
occurrence of level shifts.
The factor d, specifying the trimming boundaries as a
multiple of the estimated scale, can be chosen similarly to
classical rules for detecting unusual observations in a Gaussian
sample. Choosing d=3 instead of d=2 increases
efficiency, but decreases robustness; d=2.5 might be seen
as a compromise.
dw.filter returns an object of class dw.filter.
An object of class dw.filter is a list containing the
following components:
level |
a data frame containing the corresponding signal level extracted by the filter(s) specified in |
slope |
a data frame containing the corresponding slope within each time window. |
sigma |
a data frame containing
|
In addition, the original input time series is returned as list
member y, and the settings used for the analysis are
returned as the list members outer.width,
inner.width, method, scale, d,
minNonNAs, online and extrapolate.
Application of the function plot to an object of class
dw.filter returns a plot showing the original time series
with the filtered output.
The following methods are available as method for signal extraction,
whereby the prefix DW denotes the fact that different
window widths are used in the first and second step of the
calculations within one window (i.e.
inner.width<outer.width) while for the
methods MED, RM, MTM, TRM and MRM
the first and second step take place in a window of fixed
length outer.width.
MEDordinary running median filter.
The simple median is applied to the observations within a moving
time window of length outer.width.
RMordinary repeated median filter.
Repeated median regression is applied to the observations within
a moving time window of length outer.width.
MTM, DWMTM
modified trimmed mean filters.
In a first step the median is applied to (MTM): the whole
window with outer.width or (DWMTM): the inner window
with inner.width; in a second step the mean is applied to
the (trimmed) observations in the whole window (with
outer.width).
TRM, DWTRM
trimmed repeated median filters.
In a first step repeated median regression is applied to
(TRM): the whole window with outer.width or
(DWTRM): the inner window with inner.width; in a
second step least squares regression is applied to the (trimmed)
observations in the whole window (with outer.width).
MRM, DWMRM
modified repeated median filters.
In a first step repeated median regression is applied to
(MRM): the whole window with outer.width or
(DWMRM): the inner window with inner.width; in a
second step another repeated median regression is applied to the
(trimmed) observations in the whole window (with
outer.width).
DWRMdouble window repeated median filter.
In a first step repeated median regression is applied to the
inner window with inner.width to determine the trend
(slope); in a second step the median is applied to the trend
corrected observations in the whole window with
outer.width (without trimming).
Missing values are treated by omitting them and thus by reducing
the corresponding window width. MED, RM, MTM, TRM and MRM
require at least minNonNAs non-missing observations in each
outer window; DWRM, DWMTM, DWTRM and
DWMRM require at least minNonNAs non-missing
observations in each inner window. Otherwise NAs are
returned for level, slope and sigma.
Roland Fried and Karen Schettlinger
Bernholt, T., Fried, R., Gather, U., Wegener, I. (2006)
Modified Repeated Median Filters,
Statistics and Computing 16,
177-192.
(earlier version: http://hdl.handle.net/2003/5298)
Schettlinger, K., Fried, R., Gather, U. (2006) Robust Filters for Intensive Care Monitoring: Beyond the Running Median, Biomedizinische Technik 51(2), 49-56.
robreg.filter, robust.filter, hybrid.filter, wrm.filter.
## Not run: # Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Filtering with all methods: y.dw <- dw.filter(y, outer.width=31, inner.width=11, method="all") # Plot: plot(y.dw) # Filtering with trimmed RM and double window TRM only: y2.dw <- dw.filter(y, outer.width=31, inner.width=11, method=c("TRM","DWTRM")) plot(y2.dw) ## End(Not run)## Not run: # Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Filtering with all methods: y.dw <- dw.filter(y, outer.width=31, inner.width=11, method="all") # Plot: plot(y.dw) # Filtering with trimmed RM and double window TRM only: y2.dw <- dw.filter(y, outer.width=31, inner.width=11, method=c("TRM","DWTRM")) plot(y2.dw) ## End(Not run)
Procedures for robust extraction of low frequency components (the signal) from a univariate time series based on a moving window technique using the median of several one-sided half-window estimates (subfilters) in each step.
hybrid.filter(y, width, method = "all", minNonNAs=3, extrapolate = TRUE)hybrid.filter(y, width, method = "all", minNonNAs=3, extrapolate = TRUE)
y |
a numeric vector or (univariate) time series object. |
width |
an odd positive integer ( |
method |
a (vector of) character string(s) containing the method(s) to be used for the estimation
of the signal level. |
minNonNAs |
a positive integer defining the minimum number
of non-missing observations within each window (half) which is required
for a ‘sensible’ estimation. Default: if a window (half) contains
less than |
extrapolate |
a logical indicating whether the level
estimations should be extrapolated to the edges of the time series.
The extrapolation extends the first estimated value to the first
time in the first window and the last estimated value to
the last time in the last time window. Default is
|
hybrid.filter is suitable for extracting low frequency
components (the signal) from a time series which may be
contaminated with outliers and can contain level shifts or local
extremes. For this, moving window techniques are applied.
Within each time window several subfilters are applied to half-windows (left and right of the centre); the final signal level in the centre of the time window is then estimated by the median of the subfilter outputs.
For the subfilters, both, location-based and regression-based method are available, the former applying means or medians and the idea of a locally constant signal value, the latter using ordinary least squares (LS) regression or Siegel's (1982) repeated median (RM) and the idea of an underlying locally linear trend.
The methods should be chosen based on an a-priori guess of the
underlying signal and the data quality. Location based methods
(MED, MEAN, FMH, MH, MMH) are
recommended in case of a locally (piecewise) constant signal.
Regression based and predictive approaches (RM,
PFMH, PRMH, PRMMH) in case of locally linear
monotone trends. The combined filters (CFMH, CRMH,
CRMMH) can be seen as a compromise, but are
computationally somewhat more expensive and may be inferior to
the predictive filters during steep trends.
The approaches based on the median and RM are robust alternatives
to the (in Gaussian samples) more efficient mean and least
squares methods. The hybrid filters preserve shifts and local
extremes much better than MED, MEAN or RM
for the price of decreased robustness and / or Gaussian
efficiency.
hybrid.filter returns an object of class hybrid.filter.
An object of class hybrid.filter is a list containing the
following components:
level |
a data frame containing the signal level extracted
by the filter(s) specified in |
slope |
a data frame (possibly) containing |
In addition, the original input time series is returned as list
member y, and the settings used for the analysis are
returned as the list members width, method and
extrapolate.
Application of the function plot to an object of class
hybrid.filter returns a plot showing the original time series
with the filtered output.
The following methods are available as method for signal extraction.
Filters applying only one location or regression estimate
to the whole window of length width and taking the
location (in the centre of the time window) as final signal level
estimate:
MEDordinary running median filter.
MEANordinary moving average filter.
RMordinary repeated median filter.
Applies repeated median regression to each time window.
Filters applying several subfilters within one window, taking the median of the values listed below as the final signal level estimate:
FMHFIR median hybrid filter.
Uses half-window averages and the central observation.
PFMHpredictive FMH filter.
Uses half-window least squares regression and the central
observation.
CFMHcombined FMH filter.
Uses half-window averages, half-window least squares
regression, and the central observation.
MHmedian hybrid filter.
Uses half-window medians and the central observation.
PRMHpredictive repeated median hybrid filter.
Uses half-window repeated median regression and the
central observation.
CRMHcombined repeated median hybrid filter.
Uses half-window medians, half-window repeated median
regression, and the central observation.
MMHmedian/median hybrid filter.
Uses half-window medians and the median of all
observations in the window.
PRMMHpredictive repeated median/median filter.
Uses half-window repeated median regression and the
median of all observations in the window.
CRMMHcombined repeated median/median filter.
Uses half-window medians, half-window repeated median
regression, and the median of all observations in the window.
Missing values are treated by omitting them and thus by
reducing the corresponding window width.
The hybrid.filter function only offers filters for signal
extraction delayed by (width+1)/2 time units, in contrast
to other filters available from the robfilter package
which also offer online time series analysis without time delay.
Roland Fried and Karen Schettlinger
Fried, R., Bernholt, T., Gather, U. (2006)
Repeated Median and Hybrid Filters, Computational Statistics & Data Analysis 50,
2313-2338.
(earlier version: http://hdl.handle.net/2003/4866)
Schettlinger, K., Fried, R., Gather, U. (2006) Robust Filters for Intensive Care Monitoring: Beyond the Running Median, Biomedizinische Technik 51(2), 49-56.
robreg.filter, robust.filter, dw.filter, wrm.filter.
# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Filtering with all methods: y.hy <- hybrid.filter(y, width=31) # Plot: plot(y.hy) # Filtering with running median and PRMH only: y2.hy <- hybrid.filter(y, width=31, method=c("MED","PRMH")) plot(y2.hy)# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Filtering with all methods: y.hy <- hybrid.filter(y, width=31) # Plot: plot(y.hy) # Filtering with running median and PRMH only: y2.hy <- hybrid.filter(y, width=31, method=c("MED","PRMH")) plot(y2.hy)
This function extracts signals from time series by means of Least Median of Squares regression in a moving time window.
lms.filter(y, width, online = FALSE, extrapolate = TRUE)lms.filter(y, width, online = FALSE, extrapolate = TRUE)
y |
a numeric vector or (univariate) time series object. |
width |
a positive integer defining the window width used for fitting. |
online |
a logical indicating whether the current level estimate is
evaluated at the most recent time within each time window
( |
extrapolate |
a logical indicating whether the level
estimations should be extrapolated to the edges of the time series. |
lms.filter is suitable for extracting low
frequency components (the signal) from a time series which
may be contaminated with outliers and can contain level shifts.
For this, robust Least Median of Squares regression is applied to a moving
window, and the signal level is estimated by the fitted value
either at the end of each time window for online signal
extraction without time delay (online=TRUE) or in the
centre of each time window (online=FALSE).
lms.filter returns an object of class robreg.filter.
An object of class robreg.filter is a list containing the
following components:
level |
a data frame containing the extracted signal level. |
slope |
a data frame containing the corresponding slope within each time window. |
In addition, the original input time series is returned as list
member y, and the settings used for the analysis are
returned as the list members width, online and extrapolate.
Application of the function plot to an object of class
robreg.filter returns a plot showing the original time series
with the filtered output.
Roland Fried, Karen Schettlinger and Matthias Borowski
Davies, P.L., Fried, R., Gather, U. (2004)
Robust Signal Extraction for On-Line Monitoring Data,
Journal of Statistical Planning and Inference 122,
65-78.
Gather, U., Schettlinger, K., Fried, R. (2006)
Online Signal Extraction by Robust Linear Regression,
Computational Statistics 21(1),
33-51.
Schettlinger, K., Fried, R., Gather, U. (2006) Robust Filters for Intensive Care Monitoring: Beyond the Running Median, Biomedizinische Technik 51(2), 49-56.
# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with LMS filter: y.rr <- lms.filter(y,width=41,online=FALSE) plot(y.rr)# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with LMS filter: y.rr <- lms.filter(y,width=41,online=FALSE) plot(y.rr)
This function extracts signals from time series by means of Least Quartile Difference regression in a moving time window.
lqd.filter(y, width, online = FALSE, extrapolate = TRUE)lqd.filter(y, width, online = FALSE, extrapolate = TRUE)
y |
a numeric vector or (univariate) time series object. |
width |
a positive integer defining the window width used for fitting. |
online |
a logical indicating whether the current level estimate is
evaluated at the most recent time within each time window
( |
extrapolate |
a logical indicating whether the level
estimations should be extrapolated to the edges of the time series. |
lqd.filter is suitable for extracting low
frequency components (the signal) from a time series which
may be contaminated with outliers and can contain level shifts.
For this, robust Least Quartile Difference regression is applied to a moving
window, and the signal level is estimated by the fitted value
either at the end of each time window for online signal
extraction without time delay (online=TRUE) or in the
centre of each time window (online=FALSE).
lqd.filter returns an object of class robreg.filter.
An object of class robreg.filter is a list containing the
following components:
level |
a data frame containing the extracted signal level. |
slope |
a data frame containing the corresponding slope within each time window. |
In addition, the original input time series is returned as list
member y, and the settings used for the analysis are
returned as the list members width, online and extrapolate.
Application of the function plot to an object of class
robreg.filter returns a plot showing the original time series
with the filtered output.
Roland Fried, Karen Schettlinger and Matthias Borowski
Davies, P.L., Fried, R., Gather, U. (2004)
Robust Signal Extraction for On-Line Monitoring Data,
Journal of Statistical Planning and Inference 122,
65-78.
Gather, U., Schettlinger, K., Fried, R. (2006)
Online Signal Extraction by Robust Linear Regression,
Computational Statistics 21(1),
33-51.
Schettlinger, K., Fried, R., Gather, U. (2006) Robust Filters for Intensive Care Monitoring: Beyond the Running Median, Biomedizinische Technik 51(2), 49-56.
# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with LQD filter: y.rr <- lqd.filter(y,width=41,online=FALSE) plot(y.rr)# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with LQD filter: y.rr <- lqd.filter(y,width=41,online=FALSE) plot(y.rr)
This function extracts signals from time series by means of Least Trimmed Squares regression in a moving time window.
lts.filter(y, width, h = floor(width/2) + 1, online = FALSE, extrapolate = TRUE)lts.filter(y, width, h = floor(width/2) + 1, online = FALSE, extrapolate = TRUE)
y |
a numeric vector or (univariate) time series object. |
width |
a positive integer defining the window width used for fitting. |
h |
a positive integer defining the trimming quantile. |
online |
a logical indicating whether the current level estimate is
evaluated at the most recent time within each time window
( |
extrapolate |
a logical indicating whether the level
estimations should be extrapolated to the edges of the time series. |
lts.filter is suitable for extracting low
frequency components (the signal) from a time series which
may be contaminated with outliers and can contain level shifts.
For this, robust Least Trimmed Squares regression is applied to a moving
window, and the signal level is estimated by the fitted value
either at the end of each time window for online signal
extraction without time delay (online=TRUE) or in the
centre of each time window (online=FALSE).
lts.filter returns an object of class robreg.filter.
An object of class robreg.filter is a list containing the
following components:
level |
a data frame containing the extracted signal level. |
slope |
a data frame containing the corresponding slope within each time window. |
In addition, the original input time series is returned as list
member y, and the settings used for the analysis are
returned as the list members width, online and extrapolate.
Application of the function plot to an object of class
robreg.filter returns a plot showing the original time series
with the filtered output.
Roland Fried, Karen Schettlinger and Matthias Borowski
Davies, P.L., Fried, R., Gather, U. (2004)
Robust Signal Extraction for On-Line Monitoring Data,
Journal of Statistical Planning and Inference 122,
65-78.
Gather, U., Schettlinger, K., Fried, R. (2006)
Online Signal Extraction by Robust Linear Regression,
Computational Statistics 21(1),
33-51.
Schettlinger, K., Fried, R., Gather, U. (2006) Robust Filters for Intensive Care Monitoring: Beyond the Running Median, Biomedizinische Technik 51(2), 49-56.
# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with LTS filter: y.rr <- lts.filter(y,width=41,online=FALSE) plot(y.rr)# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with LTS filter: y.rr <- lts.filter(y,width=41,online=FALSE) plot(y.rr)
Procedure for robust signal extraction from a multivariate time series by a moving window technique with adaptive window width selection (multivariate adaptive online repeated median filter). The window width adaption is based on the univariate adore.filter.
madore.filter(Y, byrow=FALSE, min.width=10, max.width=200, test.sample.size=min.width/2, width.search="geometric", rtr.size=min.width, sign.level=0.1, NA.sample.size=min.width, minNonNAs=min.width/2)madore.filter(Y, byrow=FALSE, min.width=10, max.width=200, test.sample.size=min.width/2, width.search="geometric", rtr.size=min.width, sign.level=0.1, NA.sample.size=min.width, minNonNAs=min.width/2)
Y |
a numeric matrix or (multivariate) time series object. |
byrow |
logical. If |
min.width |
a positive integer |
max.width |
a positive integer |
test.sample.size |
a positive integer in [5, |
width.search |
a character string defining the search algorithm used for finding an adequate window width at each point in time.
|
rtr.size |
a non-negative integer specifying the size of a subset of the most recent observations within each window. The signal estimation is restricted to the range of the observations within this subset. |
sign.level |
the level of significance for the goodness of fit test (see |
NA.sample.size |
a positive integer in [10, |
minNonNAs |
a positive integer in [5, |
The madore.filter is based on Repeated Median regression (Siegel, 1982) in moving time windows and serves for separating signals from noise and outliers in multivariate time series. At each time point the test procedure of the adaptive online Repeated Median filter (Schettlinger, Fried, Gather, 2010) is used to determine an appropriate window width in [min.width, max.width]. Then the signal vector at time is estimated within the time window by a slight modification of the multivariate Trimmed Repeated Median-Least Squares regression (Lanius, Gather, 2010). A more detailed description of the madore.filter can be found in Borowski, Schettlinger, Gather (2009).
madore.filter returns an object of class madore.filter. An object of class madore.filter is a list containing the following components:
signals |
a matrix containing the estimated signal vectors at each time point |
widths |
a matrix containing the individual window widths of each variable at each time point |
overall.width |
a vector containing the overall window widths at each time point |
In addition, the original input data is returned as list member Y, and the settings used for the analysis are returned as the list members byrow, min.width, max.width, start.width, test.sample.size, width.search, rtr.size, extr.delay, NA.sample.size, and minNonNAs. Application of the function plot to an object of class madore.filter returns a plot showing the original multivariate time series with the filtered output.
Matthias Borowski
Borowski, M., Schettlinger, K., Gather, U. (2009)
Multivariate Real Time Signal Extraction by a Robust Adaptive Regression Filter, Communications in Statistics - Simulation and Computation 38, 426-440.
Lanius, V., Gather, U. (2010)
Robust Online Signal Extraction from Multivariate Time Series,
Computational Statistics and Data Analysis 54(4), 966-975.
Schettlinger, K., Fried, R., Gather, U. (2010)
Real Time Signal Processing by Adaptive Repeated Median Filters,
International Journal of Adaptive Control and Signal Processing 24(5), 346-362.
Siegel, A.F. (1982)
Robust Regression Using Repeated Medians,
Biometrika 69(1), 242-244.
robreg.filter, adore.filter, scarm.filter, mscarm.filter.
## Not run: data(multi.ts) extr <- madore.filter(multi.ts) plot(extr) ## End(Not run)## Not run: data(multi.ts) extr <- madore.filter(multi.ts) plot(extr) ## End(Not run)
This function extracts signals from time series by means of a running median.
med.filter(y, width, minNonNAs = 5, online = FALSE, extrapolate = TRUE)med.filter(y, width, minNonNAs = 5, online = FALSE, extrapolate = TRUE)
y |
a numeric vector or (univariate) time series object. |
width |
a positive integer defining the window width used for fitting. |
minNonNAs |
a positive integer defining the minimum number of non-missing observations within one window which is required for a ‘sensible’ estimation. |
online |
a logical indicating whether the current level estimate is
evaluated at the most recent time within each time window
( |
extrapolate |
a logical indicating whether the level
estimations should be extrapolated to the edges of the time series. |
med.filter is suitable for extracting low
frequency components (the signal) from a time series which
may be contaminated with outliers and can contain level shifts.
For this, the median is computed in a moving
window, and the signal level is estimated either at the end of each time window for online signal
extraction without time delay (online=TRUE) or in the
centre of each time window (online=FALSE).
med.filter returns an object of class robreg.filter.
An object of class robreg.filter is a list containing the
following components:
level |
a data frame containing the extracted signal level. |
slope |
a data frame containing the corresponding slope within each time window. |
In addition, the original input time series is returned as list
member y, and the settings used for the analysis are
returned as the list members width, minNonNAs,
online and extrapolate.
Application of the function plot to an object of class
robreg.filter returns a plot showing the original time series
with the filtered output.
Missing values are treated by omitting them and thus by reducing
the corresponding window width. The signal estimation is
only returned as NA if the window the estimation is based
on contains less than minNonNAs non-missing values.
Roland Fried, Karen Schettlinger and Matthias Borowski
Davies, P.L., Fried, R., Gather, U. (2004)
Robust Signal Extraction for On-Line Monitoring Data,
Journal of Statistical Planning and Inference 122,
65-78.
Gather, U., Schettlinger, K., Fried, R. (2006)
Online Signal Extraction by Robust Linear Regression,
Computational Statistics 21(1),
33-51.
Schettlinger, K., Fried, R., Gather, U. (2006) Robust Filters for Intensive Care Monitoring: Beyond the Running Median, Biomedizinische Technik 51(2), 49-56.
# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with MED filter: y.rr <- med.filter(y,width=41,online=FALSE) plot(y.rr)# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with MED filter: y.rr <- med.filter(y,width=41,online=FALSE) plot(y.rr)
A multivariate version of the scarm.filter which also gives information about parallel running components of the multivariate time series
mscarm.filter(time.series, right.width=30, min.left.width=right.width, min.width=floor(right.width/3), max.width=200, sign.level=0.001, bound.noise.sd=0.01, rtr=TRUE, autocorrelations="automatic", c.bound=3, r.bound=0)mscarm.filter(time.series, right.width=30, min.left.width=right.width, min.width=floor(right.width/3), max.width=200, sign.level=0.001, bound.noise.sd=0.01, rtr=TRUE, autocorrelations="automatic", c.bound=3, r.bound=0)
time.series |
a numeric matrix or multivariate time series object. |
right.width |
a positive integer |
min.left.width |
a positive integer |
min.width |
a positive integer |
max.width |
a positive integer |
sign.level |
significance level of the SCARM test procedure; must be a value in |
bound.noise.sd |
a lower bound for the estimate of the noise standard deviation; this bound ensures that the noise scale estimate cannot be zero due to ties in the data; must be a value |
rtr |
if |
autocorrelations |
the |
c.bound |
the bound for the SSM (Similar Slope Monitoring) statistic which is the absolute difference of RM (Repeated Median) trend estimates (of two univariate time series) relative to the estimated standard deviation of this difference; if the SSM statistic is not larger than |
r.bound |
the bound for the ratio of adapted window widths (of two univariate time series); a relationship between the two time series is only possible, if this ratio (smaller window width divided by larger window width) is smaller than |
The mscarm.filter is a procedure for real-time signal extraction from noisy and outlier-contaminated instationary multivariate time series. It is based on Repeated Median regression (Siegel, 1982) in moving time windows. At each time point the test procedure of the SCARM filter (Borowski and Fried, 2011) is used to determine an appropriate window width in [min.width, max.width]. Then the signal vector at time is estimated within the time window by a slight modification of the multivariate Trimmed Repeated Median-Least Squares regression (Lanius, Gather, 2010). At each time point , the mscarm.filter uses the Similar Slope Monitoring (SSM) method to build blocks of currently interrelated univariate time series. This information is given to the user and is used to improve the signal estimations. A detailed description of the mscarm.filter can be found in Borowski (2012).
mscarm.filter returns an object of class mscarm.filter.
An object of class mscarm.filter is a list containing the
following components:
signal.est |
a matrix containing the signal estimations |
slope.est |
a matrix containing the slope (or trend) estimations |
adapted.width |
a matrix containing the adapted window widths |
noise.sd.est |
a matrix containing the estimated noise standard deviations |
scarm.signal.est |
a matrix containing the signal estimates of the univariate SCARM |
scarm.width |
a matrix containing the adapted window widths of the univariate SCARM |
scarm.statistic |
a matrix containing the SCARM test statistics |
scarm.critval |
a matrix containing the critical values of the SCARM test |
ssm.statistic |
a matrix containing the SSM statistics |
blocks |
a matrix of the blocks built by the SSM procedure |
acf.lag.one |
a matrix containing the estimated autocorrelations at lag one for each time point; estimation is done on the recent |
time.series |
the original input data |
In addition, the input arguments used for the analysis are returned as list members.
Application of the function plot to an object of class
mscarm.filter returns a plot showing the original time series
with the filtered output. If info==TRUE (default), a plot showing the results of the SSM procedure is given.
Matthias Borowski
Borowski, M. (2012)
Echtzeit-Extraktion relevanter Information aus multivariaten Zeitreihen basierend auf robuster Regression, PhD thesis, TU Dortmund University (in German).
Borowski, M. and Fried, R. (2011)
Robust repeated median regression in moving windows with data-adaptive width selection, Discussion Paper 28/2011, SFB 823, TU Dortmund University.
Lanius, V., Gather, U. (2010)
Robust Online Signal Extraction from Multivariate Time Series,
Computational Statistics and Data Analysis 54(4), 966-975.
Siegel, A.F. (1982)
Robust Regression Using Repeated Medians,
Biometrika 69(1), 242-244.
robreg.filter, adore.filter, madore.filter, scarm.filter.
## Not run: # Multivariate time series data(multi.ts) # apply MSCARM Filter mscarm.extr <- mscarm.filter(multi.ts) plot(mscarm.extr) ## End(Not run)## Not run: # Multivariate time series data(multi.ts) # apply MSCARM Filter mscarm.extr <- mscarm.filter(multi.ts) plot(mscarm.extr) ## End(Not run)
This data matrix contains a 4-variate time series of length 500. It consists of two Blocks and two Doppler signals each overlaid by highly correlated bivariate Gaussian noise.
multi.tsmulti.ts
A (500x4)-matrix containing a 4-variate time series of length 500.
Data generated by means of the packages wmtsa and MASS.
This function extracts signals from time series by means of Repeated Median regression in a moving time window.
rm.filter(y, width, minNonNAs = 5, online = FALSE, extrapolate = TRUE)rm.filter(y, width, minNonNAs = 5, online = FALSE, extrapolate = TRUE)
y |
a numeric vector or (univariate) time series object. |
width |
a positive integer defining the window width used for fitting. |
minNonNAs |
a positive integer defining the minimum number of non-missing observations within one window which is required for a ‘sensible’ estimation. |
online |
a logical indicating whether the current level estimate is
evaluated at the most recent time within each time window
( |
extrapolate |
a logical indicating whether the level
estimations should be extrapolated to the edges of the time series. |
rm.filter is suitable for extracting low
frequency components (the signal) from a time series which
may be contaminated with outliers and can contain level shifts.
For this, robust Repeated Median regression is applied to a moving
window, and the signal level is estimated by the fitted value
either at the end of each time window for online signal
extraction without time delay (online=TRUE) or in the
centre of each time window (online=FALSE).
rm.filter returns an object of class robreg.filter.
An object of class robreg.filter is a list containing the
following components:
level |
a data frame containing the extracted signal level. |
slope |
a data frame containing the corresponding slope within each time window. |
In addition, the original input time series is returned as list
member y, and the settings used for the analysis are
returned as the list members width, minNonNAs,
online and extrapolate.
Application of the function plot to an object of class
robreg.filter returns a plot showing the original time series
with the filtered output.
Missing values are treated by omitting them and thus by reducing
the corresponding window width. The estimated signal level is
only returned as NA if the window the estimation is based
on contains less than minNonNAs non-missing values.
Roland Fried, Karen Schettlinger and Matthias Borowski
Davies, P.L., Fried, R., Gather, U. (2004)
Robust Signal Extraction for On-Line Monitoring Data,
Journal of Statistical Planning and Inference 122,
65-78.
Gather, U., Schettlinger, K., Fried, R. (2006)
Online Signal Extraction by Robust Linear Regression,
Computational Statistics 21(1),
33-51.
Schettlinger, K., Fried, R., Gather, U. (2006) Robust Filters for Intensive Care Monitoring: Beyond the Running Median, Biomedizinische Technik 51(2), 49-56.
robreg.filter,scarm.filter,adore.filter,madore.filter
# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with RM filter: y.rr <- rm.filter(y,width=41,online=TRUE) plot(y.rr)# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Online filtering with RM filter: y.rr <- rm.filter(y,width=41,online=TRUE) plot(y.rr)
Procedures for robust (online) extraction of low frequency components (the signal) from a univariate time series by applying robust regression techniques to moving time windows.
robreg.filter(y, width, method = "all", h = floor(width/2)+1, minNonNAs = 5, online = FALSE, extrapolate = TRUE)robreg.filter(y, width, method = "all", h = floor(width/2)+1, minNonNAs = 5, online = FALSE, extrapolate = TRUE)
y |
a numeric vector or (univariate) time series object. |
width |
a positive integer defining the window width used for fitting. |
method |
a (vector of) character string(s) containing the method(s) to be used for robust approximation of the signal within one time window. It is possible to specify any combination of the values:
Using |
h |
a positive integer defining the trimming quantile for LTS regression. |
minNonNAs |
a positive integer defining the minimum number of
non-missing observations within one window which is required
for a ‘sensible’ estimation.
Currently, this option only has an effect for the two methods |
online |
a logical indicating whether the current level estimate is
evaluated at the most recent time within each time window
( |
extrapolate |
a logical indicating whether the level
estimations should be extrapolated to the edges of the time series. |
robreg.filter is suitable for extracting low
frequency components (the signal) from a time series which
may be contaminated with outliers and can contain level shifts.
For this, robust regression methods are applied to a moving
window, and the signal level is estimated by the fitted value
either at the end of each time window for online signal
extraction without time delay (online=TRUE) or in the
centre of each time window (online=FALSE).
robreg.filter returns an object of class robreg.filter.
An object of class robreg.filter is a list containing the
following components:
level |
a data frame containing the signal level extracted by the filter(s) specified in |
slope |
a data frame containing the corresponding slope within each time window. |
In addition, the original input time series is returned as list
member y, and the settings used for the analysis are
returned as the list members width, method,
h, minNonNAs, online and extrapolate.
Application of the function plot to an object of class
robreg.filter returns a plot showing the original time series
with the filtered output.
Missing values are treated by omitting them and thus by reducing
the corresponding window width. The estimated signal level is
only returned as NA if the window the estimation is based
on contains less than minNonNAs non-missing values.
C++ code: Thorsten Bernholt and Robin Nunkesser
Port to R: Roland Fried and Karen Schettlinger
Davies, P.L., Fried, R., Gather, U. (2004)
Robust Signal Extraction for On-Line Monitoring Data,
Journal of Statistical Planning and Inference 122,
65-78.
(earlier version: http://hdl.handle.net/2003/5043)
Gather, U., Schettlinger, K., Fried, R. (2006)
Online Signal Extraction by Robust Linear Regression,
Computational Statistics 21(1),
33-51.
(earlier version: http://hdl.handle.net/2003/5305)
Schettlinger, K., Fried, R., Gather, U. (2006) Robust Filters for Intensive Care Monitoring: Beyond the Running Median, Biomedizinische Technik 51(2), 49-56.
wrm.filter, robust.filter, dw.filter, hybrid.filter.
# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Filtering with all methods: y.rr <- robreg.filter(y, width=31, method=c("RM", "LMS", "LTS", "DR", "LQD")) # Plot: plot(y.rr) # Delayed filtering with RM and LMS filter: y2.rr <- robreg.filter(y,width=31,method=c("RM","LMS")) plot(y2.rr) # Online filtering with RM filter: y3.rr <- rm.filter(y,width=41,online=TRUE) plot(y3.rr)# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Filtering with all methods: y.rr <- robreg.filter(y, width=31, method=c("RM", "LMS", "LTS", "DR", "LQD")) # Plot: plot(y.rr) # Delayed filtering with RM and LMS filter: y2.rr <- robreg.filter(y,width=31,method=c("RM","LMS")) plot(y2.rr) # Online filtering with RM filter: y3.rr <- rm.filter(y,width=41,online=TRUE) plot(y3.rr)
Procedure for robust (online) extraction of low frequency components (the signal) from a univariate time series with optional rules for outlier replacement and shift detection.
robust.filter(y, width, trend = "RM", scale = "QN", outlier = "T", shiftd = 2, wshift = floor(width/2), lbound = 0.1, p = 0.9, adapt = 0, max.width = width, online = FALSE, extrapolate = TRUE)robust.filter(y, width, trend = "RM", scale = "QN", outlier = "T", shiftd = 2, wshift = floor(width/2), lbound = 0.1, p = 0.9, adapt = 0, max.width = width, online = FALSE, extrapolate = TRUE)
y |
a numeric vector or (univariate) time series object. |
width |
a positive integer defining the window width used for fitting.
If |
trend |
a character string defining the method to be used for robust approximation of the signal
within one time window. Possible values are:
|
scale |
a character string defining the method to be used for robust estimation of the local
variability (within one time window).
Possible values are:
|
outlier |
a single character defining the rule to be used for outlier detection and outlier treatment.
Observations deviating more than
|
shiftd |
a positive numeric value defining the factor the current scale estimate is multiplied
with for shift detection. Default is |
wshift |
a positive integer specifying the number of the most recent observations used for shift detection
(regulates therefore also the delay of shift detection). Only used
in the |
lbound |
a positive real value specifying an optional lower bound for the scale to prevent the scale estimate from reaching zero (implosion). |
p |
a fraction |
adapt |
a numeric value defining the fraction which regulates the adaption of the
moving window width. |
max.width |
a positive integer ( |
online |
a logical indicating whether the current level and
scale estimates are evaluated at the most recent time
within each window ( |
extrapolate |
a logical indicating whether the level
estimations should be extrapolated to the edges of the time series. |
robust.filter works by applying the methods
specified by trend and scale to a moving time
window of length width.
Before moving the time window, it is checked whether the next
(incoming) observation is considered an 'outlier' by applying the
rule specified by outlier. Therefore, the trend in the
current time window is extrapolated to the next point in time and
the residual of the incoming observation is standardised by the
current scale estimate.
After moving the time window, it can be tested whether a level
shift has occurred within the window: If more than half of the
residuals in the right part of the window are larger than
shiftd, a shift is detected and
appropriate actions are taken. In
the online mode, the number of the rightmost residuals can be
chosen by wshift to regulate the resistance of the detection
rule against outliers, its power and the time delay of detection.
A more detailed description of the filter can be found in Fried (2004). The adaption of the window width is described by Gather and Fried (2004). For more explanations on shift detection, see Fried and Gather (2007).
robust.filter returns an object of class robust.filter.
An object of class robust.filter is a list containing the
following components:
level |
a numeric vector containing the signal level extracted by the (regression) filter specified by |
slope |
a numeric vector containing the corresponding slope within each time window. |
sigma |
a numeric vector containing the corresponding scale within each time window. |
ol |
an outlier indicator. 0: no outlier, +1: positive outlier, -1: negative outlier |
level.shift |
a level shift indicator. 0: no level shift, t: positive level shift detected at processing time t, -t: negative level shift detected at processing time t (the position in the vector gives an estimate of the point in time before which the shift has occurred). |
In addition, the original input time series is returned as list
member y, and the settings used for the analysis are
returned as the list members width, trend,
scale, outlier, shiftd,
wshift, lbound,
p, adapt, max.width, online and extrapolate.
Application of the function plot to an object of class
robust.filter returns a plot showing the original time series
with the filtered output.
Missing values have to be replaced or removed from the time series
before applying robust.filter.
Roland Fried and Karen Schettlinger
Fried, R. (2004), Robust Filtering of Time Series with
Trends, Journal of Nonparametric Statistics 16,
313-328.
(earlier version: http://hdl.handle.net/2003/4992)
Fried, R., Gather, U. (2007), On Rank Tests for Shift Detection in Time Series,
Computational Statistics and Data Analysis, Special Issue on Machine Learning and Robust Data Mining 52, 221-233.
(earlier version: http://hdl.handle.net/2003/23301)
Gather, U., Fried, R. (2004), Methods and Algorithms for Robust Filtering,
COMPSTAT 2004: Proceedings in Computational Statistics, J. Antoch (eds.), Physika-Verlag, Heidelberg, 159-170.
Schettlinger, K., Fried, R., Gather, U. (2006) Robust Filters for Intensive Care Monitoring: Beyond the Running Median, Biomedizinische Technik 51(2), 49-56.
robreg.filter, hybrid.filter, dw.filter, wrm.filter.
# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Delayed Filtering of the time series with window width 23: y.rf <- robust.filter(y, width=23) # Plot: plot(y.rf) # Delayed Filtering with different settings and fixed window width 31: y.rf2 <- robust.filter(y, width=31, trend="LMS", scale="QN", outlier="W") plot(y.rf2) # Online Filtering with fixed window width 24: y.rf3 <- robust.filter(y, width=24, online=TRUE) plot(y.rf3) # Delayed Filtering with adaptive window width (minimal width 11, maximal width 51): y.rf4 <- robust.filter(y, width=11, adapt=0.7, max.width=51) plot(y.rf4)# Generate random time series: y <- cumsum(runif(500)) - .5*(1:500) # Add jumps: y[200:500] <- y[200:500] + 5 y[400:500] <- y[400:500] - 7 # Add noise: n <- sample(1:500, 30) y[n] <- y[n] + rnorm(30) # Delayed Filtering of the time series with window width 23: y.rf <- robust.filter(y, width=23) # Plot: plot(y.rf) # Delayed Filtering with different settings and fixed window width 31: y.rf2 <- robust.filter(y, width=31, trend="LMS", scale="QN", outlier="W") plot(y.rf2) # Online Filtering with fixed window width 24: y.rf3 <- robust.filter(y, width=24, online=TRUE) plot(y.rf3) # Delayed Filtering with adaptive window width (minimal width 11, maximal width 51): y.rf4 <- robust.filter(y, width=11, adapt=0.7, max.width=51) plot(y.rf4)
A procedure for robust online signal extraction from univariate time series ("smoothing") by a moving window technique with adaptive window width selection based on Repeated Median regression
scarm.filter(time.series, right.width=30, min.left.width=right.width, min.width=floor(right.width/3), max.width=200, sign.level=0.001, bound.noise.sd=0.01, rtr=TRUE, autocorrelations="automatic")scarm.filter(time.series, right.width=30, min.left.width=right.width, min.width=floor(right.width/3), max.width=200, sign.level=0.001, bound.noise.sd=0.01, rtr=TRUE, autocorrelations="automatic")
time.series |
a numeric vector or (univariate) time series object. |
right.width |
a positive integer >=5 defining the fixed width of the right-hand window used for testing; the choice of |
min.left.width |
a positive integer |
min.width |
a positive integer |
max.width |
a positive integer |
sign.level |
significance level of the test procedure; must be a value in |
bound.noise.sd |
a lower bound for the estimate of the noise standard deviation; this bound ensures that the noise scale estimate cannot be zero due to ties in the data; must be a value |
rtr |
if |
autocorrelations |
the |
The scarm.filter fits a Repeated Median (RM, Siegel, 1982) regression line to a moving window sample with length varying between min.width and max.width.
For each time point, the window width is adapted to the current data situation by a test comparing two RM slopes estimated in separated sub-windows, a right-hand and a left-hand window.
A more detailed description of the filter can be found in Borowski and Fried (2011).
scarm.filter returns an object of class scarm.filter.
An object of class scarm.filter is a list containing the
following components:
signal.est |
a vector containing the signal estimations |
slope.est |
a vector containing the slope (or trend) estimations |
adapted.width |
a vector containing the adapted window widths |
test.statistic |
a vector containing the SCARM test statistics |
critvals |
a vector containing the critical values for test decision |
noise.sd |
a vector containing the estimates of the noise standard deviation |
slope.diff |
a vector containing the differences of the Repeated Median slopes estimated in the left-hand and right-hand window |
acf.lag.one |
a vector containing the estimated autocorrelations at lag one for each time point; estimation is done on the recent |
time.series |
the original input data |
In addition, the input arguments used for the analysis are returned as list members.
Application of the function plot to an object of class
scarm.filter returns a plot showing the original time series
with the filtered output. If info==TRUE (default), a plot of the adapted window widths is also given.
Matthias Borowski
Borowski, M. and Fried, R. (2011)
Robust repeated median regression in moving windows with data-adaptive width selection, Discussion Paper 28/2011, SFB 823, TU Dortmund University.
Gelper, S., Schettlinger, K., Croux, C., and Gather, U. (2009)
Robust online scale estimation in time series: A model-free approach,
Journal of Statistical Planning and Inference, 139(2), 335-349.
Siegel, A.F. (1982)
Robust Regression Using Repeated Medians,
Biometrika 69(1), 242-244.
robreg.filter, adore.filter, madore.filter, mscarm.filter.
# Time series data(multi.ts) x <- multi.ts[,1] # apply SCARM Filter scarm.extr <- scarm.filter(x) plot(scarm.extr)# Time series data(multi.ts) x <- multi.ts[,1] # apply SCARM Filter scarm.extr <- scarm.filter(x) plot(scarm.extr)
This matrix contains correction factors for the MAD, Sn, Qn, and LSH scale estimators to achieve unbiasedness under Gaussian noise.
sizecorrectionsizecorrection
A (31x4)-matrix containing correction factors for the MAD, Sn, Qn, and LSH scale estimators.
The correction factors have been obtained by simulations.
Fried's (2004) signal extraction procedure includes optional rules for outlier replacement based on local scale estimation. Since detected outliers are treated as missing values, the finite sample correction for the scale estimation is adjusted for the reduced sample size, using the correction factors in the dataset 'timecorrection'.
timecorrectiontimecorrection
A (250x16)-matrix containing the correction factors for the scale estimators MAD, Qn, Sn, and LSH and for the outlier treatments 'trimming', 'downsizing large values', 'downsizing moderate values', and 'winsorization'.
The correction factors have been obtained by simulations.
Fried, R. (2004), Robust Filtering of Time Series with
Trends, Journal of Nonparametric Statistics 16,
313-328.
Empirical variance of the Repeated Median slope estimator, computed on standard normal noise in moving windows of width n; required by the function scarm.filter.
data(var.n)data(var.n)
The format is: num [1:300] NA NA NA NA 0.138 ...
The variance of the Repeated Median slope estimator depends on the size of the window sample, i.e. the window width n. These are results from simulations, where the Repeated Median slope has been computed on standard normal noise in moving windows of width n. The value var.n[n] is the variance for the window width n.
The empirical variances have been obtained by simulations.
Borowski, M. and Fried, R. (2011) Robust moving window regression for online signal extraction from non-stationary time series: online window width adaption by testing for signal changes, submitted.
Filtering procedure based on a weighted version of Siegel's (1982) repeated median (RM) and a moving time window for robust extraction of low frequency components (the signal) in the presence of outliers and shifts. One of several weight functions can be chosen to weight the observations in each time window.
wrm.filter(y, width, weight.type = 1, del = floor(width/2), extrapolate = TRUE)wrm.filter(y, width, weight.type = 1, del = floor(width/2), extrapolate = TRUE)
y |
a numeric vector or (univariate) time series object. |
width |
a positive integer defining the window width used for fitting. |
weight.type |
Indicates the weight function used.
|
del |
a positve integer (smaller than width) specifying the delay of the signal extraction. |
.
extrapolate |
a logical indicating whether the level
estimations should be extrapolated to the edges of the time series. |
For online signal extraction without time delay, weighted repeated median filtering with triangular weights is recommendable in the presence of isolated outliers and abrupt level shifts since it reacts more quickly to shifts than unweighted repeated median filtering and provides higher efficiencies. The window width should be chosen based on a guess of the minimal time period in which the signal can be approximated by a straight line without abrupt shifts. Better results can be obtained by increasing the delay, but often minimization of the time delay itself is one of the objectives so that one prefers del=0. The procedure replaces missing values by simple extrapolations if these are not within the first time window used for initialization.
For "offline" situations, it is intuitive to set del roughly
equal to width/2. If the focus is rather on smoothing than on
signal extraction, the Epanechnikov kernel should be used rather than
the triangular kernel. In this case one can also use directly function wrm.smooth.
wrm.filter returns an object of class
wrm.filter. An
object of class wrm.filter is a list containing the
following components:
y |
the original input time series. |
level |
the corresponding signal level extracted by the filter. |
slope |
the corresponding slope within each time window. |
del |
the parameter specifying the delay of the signal extraction. |
width |
width of the time window. |
weight.type |
name of the weight function used for the fit. |
The function plot returns a plot
showing the original time series with the filtered output.
Roland Fried and Jochen Einbeck
These filtering procedures are described and investigated in
Fried, R., Einbeck, J., Gather, U. (2007), Weighted Repeated Median Smoothing and Filtering,
Journal of the American Statistical Association 102, 1300-1308.
Preliminary version available as technical report from https://eldorado.tu-dortmund.de/handle/2003/21637
dw.filter, hybrid.filter, wrm.smooth
data(Nile) nile <- as.numeric(Nile) obj <- wrm.filter(nile, width=11) plot(obj)data(Nile) nile <- as.numeric(Nile) obj <- wrm.filter(nile, width=11) plot(obj)
A robust smoothing tool using a kernel weighted version of Siegel's (1982) repeated median. It can be seen as an alternative to local linear L1 regression.
wrm.smooth(x, y, h, xgrid, weight = 2)wrm.smooth(x, y, h, xgrid, weight = 2)
x |
Vector of predictors. |
y |
Vector of responses, needs to have the same length as |
h |
Bandwidth, measured in the same units as the explanatory (independent) variable x:
(x[0]- |
xgrid |
Grid on which fitted values are to be evaluated. The default is here to take the input
values |
weight |
Indicates the weight function used.
|
Weighted repeated median (WRM) smoothing was suggested in a signal extraction framework by Fried, Einbeck & Gather (2007). It combines the advantages of weighted and repeated medians, i.e. the WRM smoother is robust to outliers and adapts to linear trends (through the slope parameter of the repeated median, which is calculated by applying two consecutive weighted medians onto the pairwise slopes). The theory and simulations provided by Fried, Einbeck & Gather focus on online signal extraction from time series. Warning: The case of a kernel weighted repeated median smoother for arbitraty non-equidistant design (as implemented here) is not fully investigated yet.
The procedure copes with missing values by omitting them.
wrm.smooth returns an object of class
wrm.smooth. An
object of class wrm.smooth is a list containing the
following components:
y |
the original input time series. |
level |
the corresponding signal level extraceted by the weighted Repeated Median filter. |
slope |
the corresponding WRM slope within each time window. |
h |
bandwidth. |
xgrid |
vector with grid values. |
weight |
name of the weight function used for the fit. |
The function plot returns a plot
showing the original data with the smoothed output.
Jochen Einbeck and Roland Fried
Fried, R., Einbeck, J., Gather, U. (2007), Weighted Repeated Median Smoothing and Filtering,
Journal of the American Statistical Association 102, 1300-1308.
Preliminary version available as technical report from https://eldorado.tu-dortmund.de/handle/2003/21637
Siegel, A.F. (1982). Robust regression using repeated medians. Biometrika 68, 242-244.
data(faithful) # Old Faithful Geyser data faith.WRM <- wrm.smooth(faithful$w, faithful$e,h=4) plot(faith.WRM)data(faithful) # Old Faithful Geyser data faith.WRM <- wrm.smooth(faithful$w, faithful$e,h=4) plot(faith.WRM)