Changes of structure in financial time series and the GARCH model

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Changes of structure in financial time series and the GARCH model

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Thomas Mikosch (Dept. Actuarial Mathematics, University of Copenhagen)
Catalin Starica (Dept. Mathematical Statistics & Economics, Gothenburg University & CTH)

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Catalin Starica

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.

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Paper provided by EconWPA in its series Econometrics with number 0412003.

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Length: 22 pages
Date of creation: 06 Dec 2004
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Handle: RePEc:wpa:wuwpem:0412003

Note: Type of Document - pdf; pages: 22
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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

This paper has been announced in the following NEP Reports:

NEP-ALL-2004-12-12 (All new papers)
NEP-ECM-2004-12-12 (Econometrics)
NEP-FIN-2004-12-15 (Finance)
NEP-FIN-2004-12-12 (Finance)

Cited by:
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Pavel Cizek & Wolfgang Härdle & Vladimir Spokoiny, 2008. "Adaptive pointwise estimation in time-inhomogeneous time-series models," SFB 649 Discussion Papers SFB649DP2008-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
Other versions:
- Cizek, P. & Haerdle, W. & Spokoiny, V., 2007. "Adaptive Pointwise Estimation in Time-Inhomogeneous Time-Series Models," Discussion Paper 2007-35, Tilburg University, Center for Economic Research. [Downloadable!]
Mstislav Elagin, 2008. "Locally adaptive estimation methods with application to univariate time series," Quantitative Finance Papers 0812.0449, arXiv.org. [Downloadable!]
Chun Liu & John M Maheu, 2007. "Are there Structural Breaks in Realized Volatility?," Working Papers tecipa-304, University of Toronto, Department of Economics. [Downloadable!]
Other versions:
- Chun Liu & John M. Maheu, 2008. "Are There Structural Breaks in Realized Volatility?," Journal of Financial Econometrics, Oxford University Press, vol. 6(3), pages 326-360, Summer. [Downloadable!] (restricted)
Ying Chen & Wolfgang Härdle & Uta Pigorsch, 2009. "Localized Realized Volatility Modelling," SFB 649 Discussion Papers SFB649DP2009-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]

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