Communications for Statistical Applications and Methods

  • 제14권1호
  • /
  • Pages.141-146
  • /
  • 2007
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

A Study on Box-Cox Transformed Threshold GARCH(1,1) Process

  • Lee, O. (Department of Statistics, Ewha Womans University)
  • 발행 : 2007.04.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we consider a Box-Cox transformed threshold GARCH(1,1) process and find a sufficient condition under which the process is geometrically ergodic and has the ${\beta}$-mixing property with an exponential decay rate.

키워드

참고문헌

  1. Barndorff-Nielsen, O. E. and Shephard, N. (2002). Estimating quadratic variation using realized variance. Journal of Applied Econometrics, 17, 457-477 https://doi.org/10.1002/jae.691
  2. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327 https://doi.org/10.1016/0304-4076(86)90063-1
  3. Chen, M. and An, H. Z. (1998). A note on the stationarity and the existence of moments of the GARCH model. Statistica Sinica, 8, 505-510
  4. Ding, Z., Granger, C. W. J. and Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1,83-106 https://doi.org/10.1016/0927-5398(93)90006-D
  5. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987-1007 https://doi.org/10.2307/1912773
  6. Hwang, S. Y. and Basawa, I. V. (2004). Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes. Statistics & Probability Letters, 68, 209-220 https://doi.org/10.1016/j.spl.2003.08.016
  7. Ling, S. and McAleer, M. (2002). Stationarity and the existence of moments of a family of GARCH processes. Journal of Econometrics, 106, 109-117 https://doi.org/10.1016/S0304-4076(01)00090-2
  8. Liu, J. C. (2006). On the tail behaviors of Box-Cox transformed threshold GARCH(1,1) process. Statistics & Probability Letters, 76, 1323-1330 https://doi.org/10.1016/j.spl.2006.01.009
  9. Meitz, M. (2005). A necessary and sufficient conditions for the strict stationarity of a family of GARCH processes. SSE/EEI Working Paper Series in Economics and Finance
  10. Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability, Springer, London
  11. Rabemanjara, R. and Zakoian, J. M. (1993). Threshold ARCH model and asymmetries in volatility. Journal of Applied Econometrics, 9, 31-49
  12. Tweedie, R. L. (1983). Criteria for rates of convergence of Markov chains with application to queueing and storage theory. Probability, Statistics and Analysis. London Mathematical Society Lecture Note Series (J. F. C. Kingman and G. E. H. Reuter, eds), 260-276, Cambridge University Press, Cambridge