Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지

The CUSUM test for stochastic volatility models

  • Kim, Moo-Sup (Department of Statistics, Seoul National University) ;
  • Lee, Sang-Yeol (Department of Statistics, Seoul National University)
  • Received : 2010.08.17
  • Accepted : 2010.10.20
  • Published : 2010.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider a change point test for stochastic volatility models. By considering the relation between moments of the logarithms of squared returns and the parameters, we construct the cusum test to detect changes of the parameters. We also carry out a simulation study and verify that the proposed test is more powerful than the cusum test proposed by Kokoszka and Leipus (2000).

Keywords

References

  1. Andreou, E. and Ghysels, E. (2002). Detecting multiple breaks in financial market volatility dynamics. Journal of Applied Econometrics, 17, 579-600. https://doi.org/10.1002/jae.684
  2. Billingsley, P. (1995). Probability and Measure, 3rd Ed., Wiley, New York.
  3. Billingsley, P. (1999). Convergence of Probability Measures, 2nd Ed., Wiley, New York.
  4. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  5. Carrosco, M. and Chen, X. (2002) Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory, 18, 17-39. https://doi.org/10.1017/S0266466602181023
  6. Davydov, Y. A. (1973) Mixing conditions for Markov chains. Theory of Probability and its Applications, XVIII, 312-328.
  7. Gallant, A. R. (1987) Nonlinear Statistical Models, Wiley, New York.
  8. Im, C. and Cho, G. (2009) Multiparameter CUSUM charts with variable sampling intervals. Journal of the Korean Data & Information Science Society, 20, 593-599.
  9. Inclan, C. and Tiao, G. C. (1994) Use of cumulative sums of squares for restrospective detection of changes of variance. Journal of the American Statistical Association, 89, 913-923. https://doi.org/10.2307/2290916
  10. Kokoszka, P. and Leipus, R. (2000). Change-point estimation in ARCH models. Bernoulli, 6, 513-539. https://doi.org/10.2307/3318673
  11. Lee, S. Ha, J., Na, O. and Na, S. (2003). The cusum test for parameter change in time series models. Scand. J. Statist, 30, 781-796. https://doi.org/10.1111/1467-9469.00364
  12. Lee, S., Lee T. and Na, O. (2010). Cusum of squares test for discretely observed sample from diffusion processes. Journal of the Korean Data & Information Science Society, 21, 179-183.
  13. Na, O., Ko, B. and Lee, S. (2010) Cusum of squares test for discretely observed sample from multidimensional diffusion processes. Journal of the Korean Data & Information Science Society, 21, 547-554.
  14. Park, S. and Lee, S. (2007). Modelling KOSPI200 data based on GARCH(1,1) parameter change test. Journal of the Korean Data & Information Science Society, 18, 11-16.