Journal of the Korean Data and Information Science Society

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

Cusum of squares test for discretely observed sample from multidimensional di usion processes

  • Na, Ok-Young (School of Business, Korea University) ;
  • Ko, Bang-Won (Department of Statistics and Actuarial Science, Soongsil University) ;
  • Lee, Sang-Yeol (Department of Statistics, Seoul National University)
  • Received : 2010.03.10
  • Accepted : 2010.04.25
  • Published : 2010.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we extend the work by Lee et al. (2010) to multidimensional di usion processes. A test statistic analogous to the one-dimensional case is proposed to inves-tigate the joint stability of covariance matrix parameters and, under certain regularity conditions, is shown to have a limiting distribution of the sup of a multidimensional Brownian bridge. A simulation result is provided for illustration.

Keywords

References

  1. Gregorio, A. and Iacus, S. (2008). Least squares volatility change point estimation for partially observed diffusion processes. Communications in Statistics: Theory and Methods, 37, 2342-2357. https://doi.org/10.1080/03610920801919692
  2. Henderson, H. V. and Searle, S. R. (1979). Vec and vech operators for matrices, with some uses in Jacobians and multivariate statistics. The Canadian Journal of Statistics, 7, 65-81. https://doi.org/10.2307/3315017
  3. Lee, S., Ha, J., Na, O. and Na, S. (2003). The cusum test for parameter change in time series models. Scandinavian Journal of Statistics, 30, 781-796. https://doi.org/10.1111/1467-9469.00364
  4. 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.
  5. Longin, F. and Solnik, B. (1995). Is the correlation in international equity returns constant: 1960-1990. Journal of International Money and Finance, 14, 3-26. https://doi.org/10.1016/0261-5606(94)00001-H
  6. Park, S. and Lee, S. (2006). Simulation study on the scale change test for autoregressive models with heavy-tailed innovations. Journal of the Korean Data & Information Science Society, 17, 1397-1403.
  7. 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.
  8. Rodriguez, J. C. (2007). Measuring financial contagion: A copula approach. Journal of Empirical Finance, 14, 401-423. https://doi.org/10.1016/j.jempfin.2006.07.002
  9. Song, G., Park, B. and Kang, H. (2007). A CUSUM algorithm for early detection of structural changes in Won/Dollar exchange market. Journal of the Korean Data & Information Science Society, 18, 345-356.
  10. Yoshida, N. (1992). Estimation for diffusion processes from discrete observation. Journal of Multivariate Analysis, 41, 220-242. https://doi.org/10.1016/0047-259X(92)90068-Q