robfilter (version 3.1)

scarm.filter: SCARM (Slope Comparing Adaptive Repeated Median)

Description

A procedure for robust online signal extraction from univariate time series by a moving window technique with adaptive window width selection based on the Repeated Median regression

Usage

scarm.filter(x, right.width=15, min.left.width=right.width, min.width=floor(right.width/3), max.width=200, sign.level=0.001, bound.slope.diff=0, bound.noise.sd=0, rtr=TRUE)

Value

scarm.filter returns an object of class scarm.filter. An object of class scarm.filter is a list containing the following components:signal.esta vector containing the signal estimationsslope.esta vector containing the slope estimationsadapted.widtha vector containing the adapted window widthstest.statistica vector containing the SCARM test statisticscritvalsa vector containing the critical values for test decisionnoise.sda vector containing the noise standard deviation estimated by a regression-free scale estimator (Gelper et al., 2009)slope.diffa vector containing the differences of the Repeated Median slopes estimated in the left-hand and right-hand windowIn addition, the original input data and 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.

Details

The scarm.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 test which is based on the comparison of 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 (2012).

References

Borowski, M., Fried, R. (2012) Robust moving window regression for online signal extraction from non-stationary time series: online window width adaption by testing for signal changes, submitted. 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.

See Also

robreg.filter, adore.filter, madore.filter.

Examples

# # # # # # # # # #
# Short and noisy time series
data(multi.ts)
x <- multi.ts[,1]

# SCARM Filter 
scarm.extr <- scarm.filter(x)
plot(scarm.extr)