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Change point test for dispersion parameter based on discretely observed sample from SDE models

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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.

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.

참고문헌 (11)

  1. A. De Gregorio, "Least squares volatility change point estimation for partially observed diffusion processes", Comm. Statist. Theory Methods, 37(13), pp.2342~2357 (2008)
  2. "Estimation for the change point of the volatility in a stochastic differential equation"[URL]
  3. I. Karatzas, "Brownian Motions and Stochastic Calculus" (1991), Springer
  4. M. Kessler, "Estimation of an ergodic diffusion from discrete observations", Scand. J. Statist, 24(2), pp.211~229 (1997)
  5. Y. Kutoyants, "Statistical Inference for Ergodic Diffusion Processes" (2004), Springer
  6. S. Lee, "Test for dispersion constancy in SDE models", Submitted for Pub- lication
  7. S. Lee, "The cusum test for parameter change in time series models", Scand. J. Statist, 30(4), pp.781~796 (2003)
  8. S. Lee, "Test for parameter change in diffusion processes by cusum statistics based on one-step estimators", Ann. Inst. Statist. Math, 58(2), pp.211~222 (2006)
  9. S. Lee, "The cusum test for parameter change in regression models with ARCH errors", J. Japan Statist. Soc, 34(2), pp.173~188 (2004)
  10. A. N. Shiryayev, "Essentials of Stochastic Finance" (1999), World Science
  11. J. Song, "Test for parameter change in discretely observed diffusion processes", Statistical Inference for Stochastic Processes, 12(2), pp.165~183 (2009), Kluwer Academic Publishers

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