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Changes of structure in financial time series and the GARCH model

Author

Listed:
  • Thomas Mikosch

    (Dept. Actuarial Mathematics, University of Copenhagen)

  • Catalin Starica

    (Dept. Mathematical Statistics & Economics, Gothenburg University & CTH)

Abstract

In this paper we propose a goodness of fit test that checks the resemblance of the spectral density of a GARCH process to that of the log-returns. The asymptotic behavior of the test statistics are given by a functional central limit theorem for the integrated periodogram of the data. A simulation study investigates the small sample behavior, the size and the power of our test. We apply our results to the S&P500 returns and detect changes in the structure of the data related to shifts of the unconditional variance. We show how a long range dependence type behavior in the sample ACF of absolute returns might be induced by these shifts.

Suggested Citation

  • Thomas Mikosch & Catalin Starica, 2004. "Changes of structure in financial time series and the GARCH model," Econometrics 0412003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0412003
    Note: Type of Document - pdf; pages: 22
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0412/0412003.pdf
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    More about this item

    Keywords

    integrated periodogram; spectral distribution; functional central limit theorem; Kiefer--Muller process; Brownian bridge; sample autocorrelation; change point; GARCH process; long range dependence; IGARCH; non-stationarity;
    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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