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Changes of structure in financial time series and the GARCH model

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Author Info

  • 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.

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File URL: http://128.118.178.162/eps/em/papers/0412/0412003.pdf
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Bibliographic Info

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

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

Note: Type of Document - pdf; pages: 22
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Web page: http://128.118.178.162

Related research

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;

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Cited by:
  1. 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.
  2. Chen, Ying & Härdle, Wolfgang Karl & Pigorsch, Uta, 2010. "Localized Realized Volatility Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1376-1393.
  3. Lu, Yang K. & Perron, Pierre, 2010. "Modeling and forecasting stock return volatility using a random level shift model," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 138-156, January.
  4. Pierre Perron & Zhongjun Qu, 2008. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Boston University - Department of Economics - Working Papers Series wp2008-004, Boston University - Department of Economics.
  5. Mstislav Elagin, 2008. "Locally adaptive estimation methods with application to univariate time series," Papers 0812.0449, arXiv.org.
  6. Chun Liu & John M Maheu, 2007. "Are there Structural Breaks in Realized Volatility?," Working Papers tecipa-304, University of Toronto, Department of Economics.
  7. David G. McMillan, 2010. "Level-shifts and non-linearity in US financial ratios: Implications for returns predictability and the present value model," Review of Accounting and Finance, Emerald Group Publishing, vol. 9(2), pages 189-207, May.
  8. Roueff, François & von Sachs, Rainer, 2011. "Locally stationary long memory estimation," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 813-844, April.
  9. McMillan, David G. & Ruiz, Isabel, 2009. "Volatility persistence, long memory and time-varying unconditional mean: Evidence from 10 equity indices," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(2), pages 578-595, May.
  10. Adnen Ben Nasr & Mohamed Boutahar & Abdelwahed Trabelsi, 2010. "Fractionally integrated time varying GARCH model," Statistical Methods and Applications, Springer, vol. 19(3), pages 399-430, August.

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