robfilter (version 3.0)

madore.filter: A Robust Adaptive Online Filter for Multivariate Time Series

Description

Procedure for robust online extraction of a signal 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.

Usage

madore.filter(Y, byrow=FALSE, 
                 min.width=20, max.width=200, start.width=min.width, 
                 test.sample.size=min.width/2, width.search="geometric", 
                 rtr.size=10, extr.delay=0, 
                 NA.sample.size=10, minNonNAs=5)

Value

madore.filter returns an object of class madore.filter. An object of class madore.filter is a list containing the following components:signalsa matrix containing the estimated signal vectors at each time point $t$.widthsa matrix containing the individual window widths of each variable at each time point $t$.overall.widtha vector containing the overall window widths at each time point $t$.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.

encoding

latin1

Details

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 $t$ the test procedure of the adaptive online Repeated Median filter (Schettlinger, Fried, Gather, 2008) is used to determine an appropriate window width $n(t) \in [\code{min.width}, \code{max.width}]$. Then the signal vector at time t is estimated within the time window $(t-n(t)+1,\ldots,t)$ by a slight modification of the multivariate Trimmed Repeated Median-Least Squares regression (Lanius, Gather, 2004). A more detailed description of the madore.filter can be found in Borowski, Schettlinger, Gather (2009).

References

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. (2007) Robust Online Signal Extraction from Multivariate Time Series, Technical Report 38/07, SFB 475, Universit�t Dortmund, Germany. Schettlinger, K., Fried, R., Gather, U. (2009) Real Time Signal Processing by Adaptive Repeated Median Filters, International Journal of Adaptive Control and Signal Processing, Special Issue on 'Signal Processing and Diagnosis: Biomedical Applications', to appear. Siegel, A.F. (1982) Robust Regression Using Repeated Medians, Biometrika 69 (1), 242-244.

See Also

robreg.filter, adore.filter.

Examples

# load multivariate time series sample
data(multi.ts)

# extract signals from 'multi.ts' by madore.filter
# this may take some time, depending on your system
extr <- madore.filter(multi.ts, min.width=30, max.width=100, extr.delay=5)
plot(extr)