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Methods and algorithms for robust filtering

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  • Fried, Roland
  • Gather, Ursula

Abstract

We discuss filtering procedures for robust extraction of a signal from noisy time series. Moving averages and running medians are standard methods for this, but they have shortcomings when large spikes (outliers) respectively trends occur. Modified trimmed means and linear median hybrid filters combine advantages of both approaches, but they do not completely overcome the difficulties. Improvements can be achieved by using robust regression methods, which work even in real time because of increased computational power and faster algorithms. Extending recent work we present filters for robust online signal extraction and discuss their merits for preserving trends, abrupt shifts and extremes and for the removal of spikes.

Suggested Citation

  • Fried, Roland & Gather, Ursula, 2004. "Methods and algorithms for robust filtering," Technical Reports 2004,44, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200444
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    References listed on IDEAS

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    1. Fried, Roland & Bernholt, Thorsten & Gather, Ursula, 2004. "Repeated median and hybrid filters," Technical Reports 2004,10, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Fried, Roland & Gather, Ursula, 2002. "Robust estimation of scale for local linear temporal trends," Technical Reports 2002,44, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Bernholt, Thorsten & Fried, Roland & Gather, Ursula & Wegner, Ingo, 2004. "Modified repeated median filters," Technical Reports 2004,46, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. Martina Čampulová, 2018. "Comparison of Methods for Smoothing Environmental Data with an Application to Particulate Matter PM10," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 66(2), pages 453-463.
    2. Gather, Ursula & Fried, Roland & Lanius, Vivian, 2005. "Robust detail-preserving signal extraction," Technical Reports 2005,54, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Schettlinger, Karen & Fried, Roland & Gather, Ursula, 2006. "Robust Filters for Intensive Care Monitoring: Beyond the Running Median," Technical Reports 2006,23, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Lanius, Vivian & Gather, Ursula, 2010. "Robust online signal extraction from multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 966-975, April.
    5. Lanius, Vivian & Gather, Ursula, 2007. "Robust online signal extraction from multivariate time series," Technical Reports 2007,38, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Gelper, Sarah & Schettlinger, Karen & Croux, Christophe & Gather, Ursula, 2007. "Robust online scale estimation in time series : regression-free approach," Technical Reports 2007,17, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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    1. Gather, Ursula & Fried, Roland & Lanius, Vivian, 2005. "Robust detail-preserving signal extraction," Technical Reports 2005,54, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Fried, Roland H., 2003. "Robust filtering of time series with trends," Technical Reports 2003,30, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    5. Schettlinger, Karen & Fried, Roland & Gather, Ursula, 2006. "Robust Filters for Intensive Care Monitoring: Beyond the Running Median," Technical Reports 2006,23, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Bernholt, Thorsten & Fried, Roland & Gather, Ursula & Wegner, Ingo, 2004. "Modified repeated median filters," Technical Reports 2004,46, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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