Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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STRICT STATIONARITY AND FUNCTIONAL CENTRAL LIMIT THEOREM FOR ARCH/GRACH MODELS

  • Lee, Oe-Sook (DEPARTMENT OF STATISTICS, EWHA WOMANS UNIVERSITY) ;
  • Kim, Ji-Hyun (DEPARTMENT OF STATISTICS, EWHA WOMANS UNIVERSITY)
  • Published : 2001.08.01
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Abstract

In this paper we consider the (generalized) autoregressive model with conditional heteroscedasticity (ARCH/GARCH models). We willing give conditions under which strict stationarity, ergodicity and the functional central limit theorem hold for the corresponding models.

Keywords

References

  1. Stat. and Prob. Letters v.31 The geometric egodicity and existence of moments for a class of non-linear time series model H. An;M. Chen;F. Huang
  2. J. Time Series Anal. v.13 A test for conditional heteroscedasticity in time series models A. K. Bera;M. L. Higgins
  3. J. Appl. Prob v.35 A central limit theorem for contractive stochastic dynamical systems M. Benda
  4. Ann. Prob. v.16 no.3 Asymptotics of a class of Markov processes which are not in general irreducible R. N. Bhattacharya;O. Lee
  5. Ann. Stat. v.9 no.6 Some asymptotic theory for the bootstrap P. J. Bickel;D. A. Freedman
  6. J. Econometrics v.31 Generalized autoregressive conditional heteroskedasticity T. Bollerslev
  7. Stoch. Processes and their Appl. v.85 Extremal behavior of the autoregressive process with ARCH(1) errors M. Borkovec
  8. J. Econometrics v.52 Stationarity of GARCH processes and of some nonnegative time series P. Bougerol;N. Picard
  9. Probability N. Breiman
  10. J. Appl. Prob. v.32 An L² convergence theorem for random affine mappings R. Bruton;U. Rosler
  11. Econometrica v.50 Autoregressive conditional heteroscedasticity with estimates of the variance of the United Kingdom inflation R. F. Engle
  12. Ann Prob. v.24 no.2 A Lyapounov bound for solutions of the Poisson equation P. W. Glynn;S. P. Meyn
  13. Dokl. Akad. Nauk. SSSR v.19 The central limit theorem for stationarity ergodic Markov processes M. I. Gordin;B. A. Lifsic
  14. Statistca Sinica v.4 Probabilistic properties of the β- ARCH model D. Guegan;J. Diebolt
  15. Matrix Analysis R. A. Horn;C. R. Johnson
  16. Stat. and Prob. Letters v.32 Limit theorems for some doubly stochastic processes O. Lee
  17. Stat. and Prob. Letters v.30 A note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model Z. Lu
  18. Springer Markov chains and stochastic stability S. P. Meyn;R. L. Tweedie
  19. Econometric Theory v.6 Stationarity and persistence in the GARCH(1,1) model D. B. Nelson
  20. Adv. Appl. Prob. v.30 A central limit theorem for random coefficient autoregressive models and ARCH/GARCH models A. Rudolph
  21. J. Time Series Anal. v.5 ARMA models with ARCH errors A. A. Weiss