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On detecting jumps in time series: Nonparametric setting

Author

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  • Pawlak, Mirek
  • Rafajlowicz, Ewaryst
  • Steland, Ansgar

Abstract

Motivated by applications in statistical quality control and signal analysis, we propose a sequential detection procedure which is designed to detect structural changes, in particular jumps, immediately. This is achieved by modifying a median filter by appropriate kernel-based jump preserving weights (shrinking) and a clipping mechanism. We aim at both robustness and immediate detection of jumps. Whereas the median approach ensures robust smooths when there are no jumps, the modification ensure immediate reaction to jumps. For general clipping location estimators we show that the procedure can detect jumps of certain heights with no delay, even when applied to Banach space valued data. For shrinking medians we provide an asymptotic upper bound for the normed delay. The finite sample properties are studied by simulations which show that our proposal outperforms classical procedures in certain respects.

Suggested Citation

  • Pawlak, Mirek & Rafajlowicz, Ewaryst & Steland, Ansgar, 2003. "On detecting jumps in time series: Nonparametric setting," Technical Reports 2003,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200328
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    References listed on IDEAS

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    1. Steland, Ansgar, 2003. "Sequential control of time series by functionals of kernel-weighted empirical processes under local alternatives," Technical Reports 2003,19, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. Steland Ansgar, 2003. "Jump-preserving monitoring of dependent time series using pilot estimators," Statistics & Risk Modeling, De Gruyter, vol. 21(4), pages 343-366, April.
    2. Steland, Ansgar, 2004. "NP-optimal kernels for nonparametric sequential detection rules," Technical Reports 2004,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Steland, Ansgar, 2003. "Jump-preserving monitoring of dependent time series using pilot estimators," Technical Reports 2004,03, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Steland Ansgar, 2003. "NP-Optimal Kernels for Nonparametric Sequential Detection Rules," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 149-163, January.

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    1. Steland Ansgar, 2003. "Jump-preserving monitoring of dependent time series using pilot estimators," Statistics & Risk Modeling, De Gruyter, vol. 21(4), pages 343-366, April.
    2. Steland, Ansgar, 2004. "NP-optimal kernels for nonparametric sequential detection rules," Technical Reports 2004,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Steland, Ansgar, 2003. "Jump-preserving monitoring of dependent time series using pilot estimators," Technical Reports 2004,03, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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