BINARY RANDOM POWER APPROACH TO MODELING ASYMMETRIC CONDITIONAL HETEROSCEDASTICITY

  • KIM S. (Department of Statistics, Chungang University) ;
  • HWANG S.Y. (Department of Statistics, Sookmyung Women’s University)
  • Published : 2005.03.01

Abstract

A class of asymmetric ARCH processes is proposed via binary random power transformations. This class accommodates traditional nonlinear models such as threshold ARCH (Rabemanjara and Zacoian (1993)) and Box-Cox type ARCH models(Higgins and Bera (1992)). Stationarity condition of the model is addressed. Iterative least squares(ILS) and pseudo maximum like-lihood(PML) methods are discussed for estimating parameters and related algorithms are presented. Illustrative analysis for Korea Stock Prices Index (KOSPI) data is conducted.

Keywords

References

  1. ENGLE, R. F.(1982). 'Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation', Econometrica, 50, 987-1008 https://doi.org/10.2307/1912773
  2. FEIGIN, P.D. AND TWEEDIE, R.L.(1985). 'Random coefficient autoregressive processes: a Markov chain analysis of stationarity and finiteness of moments', Journal of Time series Analysis, 6, 1-14 https://doi.org/10.1111/j.1467-9892.1985.tb00394.x
  3. GOURIEROUX, C.(1997). ARCH Models and Financial Applications, Springer, N.Y
  4. HIGGINS, M.L. AND BERA, A.K.(1992). 'A class of nonlinear ARCH models', International Economics Review, 33, 137-158 https://doi.org/10.2307/2526988
  5. HWANG, S.Y. AND BASAWA, I.V.(2003). 'Estimation for nonlinear autoregressive models generated by beta-ARCH processes', Sankhya, 65, 744-762
  6. HWANG, S.Y. AND BASAWA, I.V.(2004). 'Stationarity and moment structure for Box-Cox transformed threshold GARCH(l.l) processes', Statistics & Probability Letters, 68, 209-220 https://doi.org/10.1016/j.spl.2003.08.016
  7. HWANG, S.Y. AND KIM, T.Y.(2004). 'Power transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure', Stochastic Processes and their Applications, 110, 295-314 https://doi.org/10.1016/j.spa.2003.11.001
  8. LI, C. W. AND LI, W. K.(1996). 'On a double-threshold autoregressive heteroscedastic time series model', Journal of Applied Econometrics, 11, 253-274 https://doi.org/10.1002/(SICI)1099-1255(199605)11:3<253::AID-JAE393>3.0.CO;2-8
  9. RABEMANJARA, R. AND ZAKOIAN, J.M.(1993). 'Threshold ARCH models and asymmetries in volatility', Journal of Applied Econometrics, 8, 31-49 https://doi.org/10.1002/jae.3950080104
  10. TONG, H.(1990). Non-linear Time Series. A Dynamical System Approach, Oxford Publications, Oxford University Press
  11. TWEEDIE, R.L.(1975). 'Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space', Stochastic Processes and their Applications, 3, 385-403 https://doi.org/10.1016/0304-4149(75)90033-2