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Robust online scale estimation in time series : regression-free approach

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  • Gelper, Sarah
  • Schettlinger, Karen
  • Croux, Christophe
  • Gather, Ursula

Abstract

This paper presents variance extraction procedures for univariate time series. The volatility of a times series is monitored allowing for non-linearities, jumps and outliers in the level. The volatility is measured using the height of triangles formed by consecutive observations of the time series. This idea was proposed by Rousseeuw and Hubert (1996, Regression-free and robust estimation of scale for bivariate data, Computational Statistics and Data Analysis, 21, 67-85) in the bivariate setting. This paper extends their procedure to apply for online scale estimation in time series analysis. The statistical properties of the new methods are derived and finite sample properties are given. A financial and a medical application illustrate the use of the procedures. - breakdown point ; influence function ; online monitoring ; outliers ; robust scale estimation

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:sfb475:200717
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    References listed on IDEAS

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    1. Ursula Gather & Karen Schettlinger & Roland Fried, 2006. "Online signal extraction by robust linear regression," Computational Statistics, Springer, vol. 21(1), pages 33-51, March.
    2. Rousseeuw, Peter J. & Hubert, Mia, 1996. "Regression-free and robust estimation of scale for bivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 21(1), pages 67-85, January.
    3. Fried, Roland & Gather, Ursula, 2004. "Methods and algorithms for robust filtering," Technical Reports 2004,44, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    1. Nunkesser, Robin & Fried, Roland & Schettlinger, Karen & Gather, Ursula, 2009. "Online analysis of time series by the Qn estimator," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2354-2362, April.

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