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Empirical process of the squared residuals of an ARCH sequence

Author

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  • Horvath, Lajos
  • Kokoszka, Piotr
  • Teyssière, Gilles

Abstract

We show that the empirical process of the squared residuals of an ARCH(p) sequence converges in distribution 1,0 a Gaussirm process B(F(t)) +t f(t) e, where F is the distribution function of the squared innovations, f its derivative, {B(tl, 0 1} a Brownian bridge and e a normal random variable.

Suggested Citation

  • Horvath, Lajos & Kokoszka, Piotr & Teyssière, Gilles, 1999. "Empirical process of the squared residuals of an ARCH sequence," SFB 373 Discussion Papers 1999,87, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199987
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    Cited by:

    1. Andreou, Elena & Ghysels, Eric, 2006. "Monitoring disruptions in financial markets," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 77-124.
    2. Elena Andreou, 2004. "The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 290-318.
    3. Zhu, Ke, 2015. "Hausman tests for the error distribution in conditionally heteroskedastic models," MPRA Paper 66991, University Library of Munich, Germany.
    4. Elena Andreou & Eric Ghysels, 2004. "Monitoring for Disruptions in Financial Markets," CIRANO Working Papers 2004s-26, CIRANO.

    More about this item

    Keywords

    ARCH model; empirical process; squared residuals;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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