The change-point problem and segmentation of processes with conditional heteroskedasticity
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.
|Date of creation:||Jun 2013|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://portal.uc3m.es/portal/page/portal/dpto_estadistica
More information through EDIRC
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.:
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- 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.
- 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.
- 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, vol. 54(1), pages 171-200, March.
- 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, vol. 55(3), pages 467-485, September.
- 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.
- 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.
- 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.
- Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
- 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.
- Kosei Fukuda, 2010. "Parameter changes in GARCH model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(7), pages 1123-1135.
- 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.
- 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 107-20, January.
- Jushan Bai, 1995.
"Estimating Multiple Breaks One at a Time,"
95-18, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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.
- Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
- 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.
- 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.
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: ()
If references are entirely missing, you can add them using this form.