robfilter (version 2.5)

hybrid: function for edge preserving signal extraction from time series (smoothing)

Description

Different filtering procedures using moving centered time windows for robust delayed extraction of low frequency components ('the signal') in the presence of outliers, level shifts and local extremes. Several one-sided half-window estimates ('subfilters', specified in brackets below) are calculated in a first step and the median of these and a further estimate of the signal value in the window center is used for the final estimate. Both location based and regression based methods 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.

Usage

hybrid(y, n, methods="all", plot=FALSE, plot.methods)

Arguments

y

One dimensional data vector

n

Window width. Needs to be an impair positive integer.

methods

The method(s) used for the analyses. Possible values are "MED", "RM", "MEAN", "FMH", "PFMH", "CFMH", "RMH", "PRMH", "CRMH", "RMMH", "PRMMH" and "CRMMH". For a detailed description see the Methods section.

Example: An analysis by the ordinary RM a

plot

Plots some or all signal estimates obtained by the different methods in a time series plot if set to TRUE.

plot.methods

The estimates to be shown in the time series plot. Possible values are the same as in 'methods'.

Value

• A matrix with one column per selected signal estimation method containing the smoothed data.

Methods

• MED

{Ordinary median filter (one step only)} MEAN{Ordinary moving average (one step only)} RM{Ordinary repeated median filter (one step only)} FMH{FIR Median Hybrid (half-window averages and central observation)} PFMH{Predictive FMH (half-window LS regression and central observation)} CFMH{Combined FMH (half-window averages and LS regression and central observation)} RMH{RM Hybrid (half-window medians and central observation)} PRMH{Predictive RMH (half-window RM regression and central observation)} CRMH{Combined FMH (half-window medians and RM regression and central observation)} RMMH{RM Hybrid (half-window medians and full-window median)} PRMMH{Predictive RMH (half-window RM regression and full-window median)} CRMMH{Combined FMH (half-window medians and RM regression and full-window median)}

concept

• FMH
• CFMH
• PFMH
• RMH
• CRMH
• PRMH
• FMH
• CFMH
• running median
• mean
• moving average
• RM
• robust
• level shifts
• local extremes
• edges

Details

The method should be chosen based on an a-priori guess of the underlying signal and the data quality. Location based (MED / MEAN / FMH / RMH / RMMH) methods are recommended in case of a locally (piecewise) constant signal, regression based (MEAN / 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 median and RM based approaches are robust alternatives to the more efficient (in Gaussian samples) mean and least squares methods. The hybrid filters preserve shifts and local extremes much better than the others (MED / MEAN / RM) for the price of decreased robustness and / or Gaussian efficiency.

References

Fried, R., Bernholt, T., Gather, U. (2006), Repeated Median and Hybrid Filters, Computational Statistics & Data Analysis, 50, 2313-2338; preliminary version available as technical report from http://www.statistik.uni-dortmund.de/fixme.

See Also

double.window for more efficient and more robust delayed filtering procedures also providing some edge preservation

Examples

data(serie1t)
hybrid(serie1t$y, n=31, methods="all", plot=TRUE, plot.methods=c("RM", "PFMH", "PRMH"))