Journal of the Korean Data and Information Science Society
- Volume 18 Issue 1
- /
- Pages.237-245
- /
- 2007
- /
- 1598-9402(pISSN)
Sufficient Conditions for Stationarity of Smooth Transition ARMA/GARCH Models
Abstract
Nonlinear asymmetric time series models have the growing interest in econometrics and finance. Threshold model is one of the successful asymmetric model. We consider a smooth transition ARMA model which converges a.s. to a threshold ARMA model and show that the smooth transition ARMA model admits a stationary measure, provided a suitable condition on the coefficients of the autoregressive parts of the different regimes is satisfied. Stationarity of a smooth transition GARCH model is also obtained.