In this paper, we consider a general family of asymmetric volatility models with stationary and ergodic coefficients. This family can nest several non-linear asymmetric GARCH models with stochastic parameters into its ambit. It also generalizes Markov-switching GARCH and GJR models. The geometric ergodicity of the proposed process is established. Sufficient conditions for stationarity and existence of moments have also been investigated. Geometric ergodicity of various volatility models with stochastic parameters has been discussed as special cases.
"Geometric ergodicity of asymmetric volatility models with stochastic parameters." Electron. J. Probab. 18 1 - 12, 2013. https://doi.org/10.1214/EJP.v18-1871