IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpem/0412003.html
   My bibliography  Save this paper

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, EconWPA.
  • Handle: RePEc:wpa:wuwpem:0412003
    Note: Type of Document - pdf; pages: 22
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0412/0412003.pdf
    Download Restriction: no

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
    3. Mstislav Elagin, 2008. "Locally adaptive estimation methods with application to univariate time series," Papers 0812.0449, arXiv.org.
    4. Wang, Yudong & Wei, Yu & Wu, Chongfeng, 2010. "Auto-correlated behavior of WTI crude oil volatilities: A multiscale perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5759-5768.
    5. Xu, Jiawen & Perron, Pierre, 2014. "Forecasting return volatility: Level shifts with varying jump probability and mean reversion," International Journal of Forecasting, Elsevier, vol. 30(3), pages 449-463.
    6. Shi, Yanlin & Ho, Kin-Yip, 2015. "Modeling high-frequency volatility with three-state FIGARCH models," Economic Modelling, Elsevier, vol. 51(C), pages 473-483.
    7. repec:bpj:jossai:v:3:y:2015:i:4:p:321-333:n:3 is not listed on IDEAS
    8. Adnen Ben Nasr & Ahdi Noomen Ajmi & Rangan Gupta, 2014. "Modelling the volatility of the Dow Jones Islamic Market World Index using a fractionally integrated time-varying GARCH (FITVGARCH) model," Applied Financial Economics, Taylor & Francis Journals, vol. 24(14), pages 993-1004, July.
    9. repec:eee:ecofin:v:42:y:2017:i:c:p:393-420 is not listed on IDEAS
    10. Chun Liu & John M. Maheu, 2008. "Are There Structural Breaks in Realized Volatility?," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(3), pages 326-360, Summer.
    11. 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.
    12. Roueff, François & von Sachs, Rainer, 2011. "Locally stationary long memory estimation," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 813-844, April.
    13. 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.
    14. Andrés Herrera Aramburú & Gabriel Rodríguez, 2016. "Volatility of stock market and exchange rate returns in Peru: Long memory or short memory with level shifts?," International Journal of Monetary Economics and Finance, Inderscience Enterprises Ltd, vol. 9(1), pages 45-66.
    15. 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.
    16. Shi, Yanlin & Ho, Kin-Yip, 2015. "Long memory and regime switching: A simulation study on the Markov regime-switching ARFIMA model," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 189-204.
    17. Cizek, P., 2010. "Modelling Conditional Heteroscedasticity in Nonstationary Series," Discussion Paper 2010-84, Tilburg University, Center for Economic Research.
    18. 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.
    19. Dominik Wied & Matthias Arnold & Nicolai Bissantz & Daniel Ziggel, 2012. "A new fluctuation test for constant variances with applications to finance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1111-1127, November.
    20. Adnen Ben Nasr & Mohamed Boutahar & Abdelwahed Trabelsi, 2010. "Fractionally integrated time varying GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 399-430, August.

    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;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpem:0412003. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA). General contact details of provider: http://econwpa.repec.org .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.