IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

The change-point problem and segmentation of processes with conditional heteroskedasticity

Listed author(s):
  • Peña, Daniel
  • Kaiser, Regina
  • Badagián, Ana
Registered author(s):

    In this paper we explore, analyse and apply the change-points detection and location procedures to conditional heteroskedastic processes. We focus on processes that have constant conditional mean, but present a dynamic behavior in the conditional variance and which can also be affected by structural changes. Thus, the goal is to explore, analyse and apply the change-point detection and estimation methods to the situation when the conditional variance of a univariate process is heteroskedastic and exhibits change-points. Based on the fact that a GARCH process can be expressed as an ARMA model in the squares of the variable, we propose to detect and locate change-points by using the Bayesian Information Criterion as an extension of its application in linear models. The proposed procedure is characterized by its computational simplicity, reducing difficulties of the change-point detection in the complex non-linear processes. We compare this procedure with others available in the literature, which are based on cusum methods (Inclán and Tiao (1994), Kokoszka and Leipus (1999), Lee et al. (2004)), informational approach (Fukuda, 2010), minimum description length principle (Davis and Rodriguez-Yam (2008)), and the time varying spectrum (Ombao et al (2002)). We compute the empirical size and power properties by Monte Carlo simulation experiments considering several scenarios. We obtained a good size and power properties in detecting even small magnitudes of change and for low levels of persistence. The procedures were applied to the S\&P500 log returns time series, in order to compare with the results in Andreou and Ghysels (2002) and Davis and Rodriguez-Yam (2008). Changepoints detected by the proposed procedure were similar to the breaks found by the other procedures, and their location can be related with the Southeast Asia financial crisis and with other known financial events.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: no

    Paper provided by Universidad Carlos III de Madrid. Departamento de Estadística in its series DES - Working Papers. Statistics and Econometrics. WS with number ws131718.

    in new window

    Date of creation: Jun 2013
    Handle: RePEc:cte:wsrepe:ws131718
    Contact details of provider: Web page:

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    in new window

    1. Malik, Farooq, 2003. "Sudden changes in variance and volatility persistence in foreign exchange markets," Journal of Multinational Financial Management, Elsevier, vol. 13(3), pages 217-230, July.
    2. Catalin Starica & Stefano Herzel & Tomas Nord, 2005. "Why does the GARCH(1,1) model fail to provide sensible longer- horizon volatility forecasts?," Econometrics 0508003, EconWPA.
    3. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Berg, Andreas & Meyer, Renate & Yu, Jun, 2004. "Deviance Information Criterion for Comparing Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 107-120, January.
    6. Aggarwal, Reena & Inclan, Carla & Leal, Ricardo, 1999. "Volatility in Emerging Stock Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(01), pages 33-55, March.
    7. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 781-796.
    8. Kosei Fukuda, 2010. "Parameter changes in GARCH model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(7), pages 1123-1135.
    9. Richard A. Davis & Thomas C. M. Lee & Gabriel A. Rodriguez-Yam, 2008. "Break Detection for a Class of Nonlinear Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 834-867, 09.
    10. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(03), pages 315-352, June.
    11. Leila Nouira & Ibrahim Ahamada & Jamel Jouini & Alain Nurbel, 2004. "Long-memory and shifts in the unconditional variance in the exchange rate euro/US dollar returns," Applied Economics Letters, Taylor & Francis Journals, vol. 11(9), pages 591-594.
    12. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
    13. Davis, Richard A. & Lee, Thomas C.M. & Rodriguez-Yam, Gabriel A., 2006. "Structural Break Estimation for Nonstationary Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 223-239, March.
    14. Morana, Claudio & Beltratti, Andrea, 2004. "Structural change and long-range dependence in volatility of exchange rates: either, neither or both?," Journal of Empirical Finance, Elsevier, vol. 11(5), pages 629-658, December.
    15. Sangyeol Lee & Okyoung Na & Seongryong Na, 2003. "On the cusum of squares test for variance change in nonstationary and nonparametric time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 467-485, September.
    16. Pedro Galeano & Ruey S. Tsay, 2010. "Shifts in Individual Parameters of a GARCH Model," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(1), pages 122-153, Winter.
    17. Hernando Ombao & Jonathan Raz & Rainer von Sachs & Wensheng Guo, 2002. "The SLEX Model of a Non-Stationary Random Process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 171-200, March.
    18. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:cte:wsrepe:ws131718. 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: (Ana Poveda)

    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.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.