Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CHANGE POINT TEST FOR DISPERSION PARAMETER BASED ON DISCRETELY OBSERVED SAMPLE FROM SDE MODELS

  • Received : 2010.01.05
  • Published : 2011.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider the cusum of squares test for the dispersion parameter in stochastic differential equation models. It is shown that the test has a limiting distribution of the sup of a Brownian bridge, unaffected by the drift parameter estimation. A simulation result is provided for illustration.

Keywords

References

  1. A. De Gregorio and S. M. Iacus, Least squares volatility change point estimation for partially observed diffusion processes, Comm. Statist. Theory Methods 37 (2008), no. 13-15, 2342-2357. https://doi.org/10.1080/03610920801919692
  2. S. M. Iacus and N. Yoshida, Estimation for the change point of the volatility in a stochastic differential equation, Available at http://arxiv.org/abs/0906.3108.
  3. I. Karatzas and S. E. Shreve, Brownian Motions and Stochastic Calculus, Springer, New York, 1991.
  4. M. Kessler, Estimation of an ergodic diffusion from discrete observations, Scand. J. Statist. 24 (1997), no. 2, 211-229. https://doi.org/10.1111/1467-9469.00059
  5. Y. Kutoyants, Statistical Inference for Ergodic Diffusion Processes, Springer, New York, 2004.
  6. S. Lee and M. Guo, Test for dispersion constancy in SDE models, Submitted for Publication.
  7. S. Lee, J. Ha, O. Na, and S. Na, The cusum test for parameter change in time series models, Scand. J. Statist. 30 (2003), no. 4, 781-796. https://doi.org/10.1111/1467-9469.00364
  8. S. Lee, Y. Nishiyama, and N. Yoshida, Test for parameter change in diffusion processes by cusum statistics based on one-step estimators, Ann. Inst. Statist. Math. 58 (2006), no. 2, 211-222. https://doi.org/10.1007/s10463-006-0037-9
  9. S. Lee, I. Tokutsu, and K. Maekawa, The cusum test for parameter change in regression models with ARCH errors, J. Japan Statist. Soc. 34 (2004), no. 2, 173-188. https://doi.org/10.14490/jjss.34.173
  10. A. N. Shiryayev, Essentials of Stochastic Finance, World Science, Singapore, 1999.
  11. J. Song and S. Lee, Test for parameter change in discretely observed diffusion processes, Stat. Inference Stoch. Process. 12 (2009), no. 2, 165-183. https://doi.org/10.1007/s11203-008-9033-4

Cited by

  1. Monitoring change point for diffusion parameter based on discretely observed sample from stochastic differential equation models vol.31, pp.5, 2015, https://doi.org/10.1002/asmb.2064
  2. Inference for a change-point problem under a generalised Ornstein–Uhlenbeck setting 2017, https://doi.org/10.1007/s10463-017-0610-4