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Jump-preserving monitoring of dependent time series using pilot estimators

  • Steland, Ansgar
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    An important problem of the statistical analysis of time series is to detect change-points in the mean structure. Since this problem is a one-dimensional version of the higher dimensional problem of detecting edges in images, we study detection rules which benefit from results obtained in image processing. For the sigma-filter studied there to detect edges, asymptotic bounds for the normed delay have been established for independent data. These results are considerably extended in two directions. First, we allow for dependent processes satisfying a certain conditional mixing property. Second, we allow for more general pilot estimators, e.g., the median, resulting in better detection properties. A simulation study indicates that our new procedure indeed performs much more better.

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    Paper provided by Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen in its series Technical Reports with number 2004,03.

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    Date of creation: 2003
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    Handle: RePEc:zbw:sfb475:200403
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    1. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
    2. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
    3. 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.
    4. Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9204, Catholique de Louvain - Institut de statistique.
    5. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Universite de Montreal, Departement de sciences economiques.
    6. Ferger Dietmar, 1996. "On The Asymptotic Behavior Of Change-Point Estimators In Case Of No Change With Applications To Testing," Statistics & Risk Modeling, De Gruyter, vol. 14(2), pages 137-144, February.
    7. 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.
    8. Ferger, D., 1994. "Nonparametric detection of changepoints for sequentially observed data," Stochastic Processes and their Applications, Elsevier, vol. 51(2), pages 359-372, July.
    9. Donald W.K. Andrews & Inpyo Lee & Werner Ploberger, 1992. "Optimal Changepoint Tests for Normal Linear Regression," Cowles Foundation Discussion Papers 1016, Cowles Foundation for Research in Economics, Yale University.
    10. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    11. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
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