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Monitoring changes in the error distribution of autoregressive models based on Fourier methods

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Author Info

  • Zdeněk Hlávka

    ()

  • Marie Hušková

    ()

  • Claudia Kirch

    ()

  • Simos Meintanis

    ()

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    Abstract

    We develop a procedure for monitoring changes in the error distribution of autoregressive time series while controlling the overall size of the sequential test. The proposed procedure, unlike standard procedures which are also referred to, utilizes the empirical characteristic function of properly estimated residuals. The limit behavior of the test statistic is investigated under the null hypothesis as well as under alternatives. Since the asymptotic null distribution contains unknown parameters, a bootstrap procedure is proposed in order to actually perform the test and corresponding results on the finite–sample performance of the new method are presented. As it turns out the procedure is not only able to detect distributional changes but also changes in the regression coefficient. Copyright Sociedad de Estadística e Investigación Operativa 2012

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    File URL: http://hdl.handle.net/10.1007/s11749-011-0265-z
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    Bibliographic Info

    Article provided by Springer in its journal TEST.

    Volume (Year): 21 (2012)
    Issue (Month): 4 (December)
    Pages: 605-634

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    Handle: RePEc:spr:testjl:v:21:y:2012:i:4:p:605-634

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    Related research

    Keywords: Empirical characteristic function; Change point analysis; 62M10; 62G10; 62G20;

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    1. Epps, T. W., 1999. "Limiting behavior of the ICF test for normality under Gram-Charlier alternatives," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 175-184, April.
    2. Yao, Yi-Ching, 1990. "On the asymptotic behavior of a class of nonparametric tests for a change-point problem," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 173-177, February.
    3. Einmahl, J.H.J. & McKeague, I.W., 2003. "Empirical likelihood based hypothesis testing," Open Access publications from Tilburg University urn:nbn:nl:ui:12-117075, Tilburg University.
    4. Tenreiro, Carlos, 2009. "On the choice of the smoothing parameter for the BHEP goodness-of-fit test," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1038-1053, February.
    5. Andreou, Elena & Ghysels, Eric, 2006. "Monitoring disruptions in financial markets," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 77-124.
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